 I will prologue, don't worry, reverse, to dynamics, to catch the English, I will try to do my best, I mean that's difficult, I have to think about what I'm saying about science, the delivery speech should be moderate, we will catch the professor understood everything because he is in line, but some of guys, you will find it. Please sign the list, okay, and try to not move too much inside during the lecture, but pass the list because we have to give to Frederica. Thank you. Good morning. Shall we start? Shall we wait a little bit for other students? Good morning. Welcome to the last day of the Winter College on Optics. I hope this time was for you a very nice time, good for learning, but also for having good connection for the future, for friendships. I will try today to introduce, I will show you today another phase of the resolution. We had resolution in image and today we will have the resolution in time. I will introduce today Professor Mikas Vengris from University of Vilnius, Lithuania. He will give two lectures about time resource spectroscopy and when you want to make a shorter communication on this title, you can say dynamics and that means we can see very, very interesting things at the very low scale of time. Please, Professor. Is this on? Can you hear me? All right. Well, so good morning everyone and congratulations on having made it so far. I know it was not easy and if you count all the lectures that you already listened to, I think most of you should be brain dead by now and to finish this off with a bang, we get four hours of very interesting talks about time results spectroscopy and its applications in biology and physical chemistry. Now, I will start by giving an outline of my talk and we first start with the basics. We discussed the techniques and the ideas that developed over the past 50 years more or less together with the progress in the development of lasers and so the advent of lasers and the invention of very short light pulses sort of opened the realm of very fast processes. So, that will be the first part of my talk. We will discuss fluorescence measurements with time resolution, absorption measurements with time resolution, look at some applications, talk about data analysis and then in the second part of my talk, we will go on to look into the more recent developments, more, let's say, fresher ideas from this millennium already and see how people are basically learning to let the matter, so the electrons in the molecules or in solid states dance with the clever manipulation of the laser light that is being shined on those things. All right, so let me start by showing you a number of time scales and a number of devices that people use to follow these time scales. So, a universe is about 14 billion years old and so that is somewhere in this regime. Astronomy and development of galaxies and stars and so on takes place on the time scale of centuries, of millennia, billions of years actually and for the closest thing that can follow this for people is a calendar, you know, you write something down on the clay board and leave it for the future generations to follow and then progressively as it is in physics, you have this anti-correlation or correlation between the size of a thing and the speed with which it can move. So, the smaller the thing is, the faster it moves and if you progressively go from stars to people, you already need a watch or a clock to time how they move. If you go to the cells and maybe to the discharge in the atmosphere, the lightnings, then only a fast camera can capture the event. Now, if you are entering the realm of microscales, so subcellular structures, large molecules and so on, the tools that can follow the events that take place on a time scale of micro nanoseconds are electronic devices. So, a fast oscilloscope will give you the resolution of 1 GHz or the clock in the processor of your mobile phone is probably one and a half GHz and that corresponds to about one nanosecond or half a nanosecond or something like that. Now, the interesting bits functionally in physical chemistry and biology happen on an even shorter time scale. So, when you get to the molecules and electrons in the molecules, the only thing that is fast enough to follow let's say dynamics or their behavior in time is light itself. So, basically, you need the fastest tool available that can address what's happening in a molecule, for example, as it does its biological or physical chemical function. Now, the quest for time resolution is an old one actually. So, if you look at these photographs, so there was a bet back in 19th century, people could not figure out if the feet of a horse will, when the horse is galloping, do they, is there a moment when the horse is suspended in air? Do the feet leave the ground all at once? And so, the guy named Mybridge set up a number of very fast shuttered cameras that were triggered by threads which he pulled along the track and he actually numbered the sections of the track here and took sequential pictures of a galloping horse and eventually he found that in some pictures, like here, for example, or here, the horse is actually flying in there. So, the eye cannot follow it, but the fast camera could. That is the state of the art in 19th century. You had to take the pictures, develop the film, have enough light to capture the image, and so the dynamic imaging was done by Mybridge. Now, before him actually, and this is the emblem of the state of Lithuania, so it's our night, the horses were always drawn with feet, at least one of them touching the ground. So, that was wrong and we still have it in our emblem because it's too late to change it, but nevertheless. And since I'm speaking about Lithuania, I would like to use the opportunity to invite everyone of you who has a chance. Come and visit Vilnius is a very nice city. I mean, perhaps not on the scale of Italian cities, but most of the architecture was actually designed by Italian masters and so this is the old building of the university where I work and come on. The nightlife is very nice and you can count on having good time there, so please come and visit. I promise you, no more horses. But the feet of the horse do leave the ground when the horse is galloping, so that's something we already know. The question is, if the horse is now the size of a molecule, what do we do then? Clearly, the camera will not work. And already, if you reduce the horse down to the size of a hummingbird, which is a bird the size of a big fly, basically. Well, you probably have seen it more than I have. I've only seen it once in California. If you take a picture, you cannot see the wings because they move too many times during the exposure of your camera. And only with a very fast camera that takes thousands of frames a second, you can actually take the pictures with the hummingbird suspended in flight and then use them to reconstruct precisely how the wings move when the bird is flying. And the childhood of the time-resolved spectroscopy was back in the 1950s and 60s and the Nobel Prize of 1967 was awarded for Sir George Porter for the invention of flash spectrography. So basically, this was still before the invention of the lasers. 1967 was after, but the work done was before. So what he did, he used photographic flashes to actually start chemical reactions and then a second flash synchronized with the first one to monitor the course of this reaction. So it was sort of a pump probe spectroscopy using lamps if you want to. Now, before going on, I would like to talk a bit why this is interesting. Why should we worry about the time result, the dynamic events in the molecules? And if you take a picture, so yeah, next time you fly to the moon, try to take a picture of a blue marble or if you're on a satellite, you can also use your iPhone to take nice pictures of the earth. So for you, it's not surprising. We have seen this in the textbook too many times, and these pictures are sort of innate. This is the F, we know it. But if you're interstellar traveler made of, I don't know, silicon or superconductive helium or whatever, you know, what these aliens are made of, you may wonder why here, well, it's not very visible with a projector, but especially here, why is it so green? Why is the planet green? There are no green planets. If you look at other planets on the solar system, none of them is green. And now, so you say, let's go and investigate. So you fly down a little bit. You see that the, you know, the planet is covered by some green stuff, some green mush growing over it. You go in, you see that it's a certain organisms that have green color and they are abundant. They have actually changed the atmosphere of the planet. And you look at how they, what they are made of. You look at the leaf, now this is just with the eye still. Now if you go closer and look at the more internal structure, now if you're a guy looking at the microscope and you see something like this on a leaf, that gives you a pause, but never mind that. You want to look what the green stuff really is. So the green stuff turns out to be this organella inside the cells called chloroplasts. And you have these pancake-like structures in them called thylakoids where the whole photosynthetic business is taking place. And photosynthesis is basically the process of capturing sunlight and storing the energy in the form of sugars. Now, biochemistry textbooks, you see these complicated schemes. This is actually the cartoon of one of a piece of a membrane of this pancake. So if you take a piece of this and you look at it from the side, what you will see is sort of like this. The representation is like this. And if you look deeper, you have a number of chemical reactions, all of which start by light impinging on a pair of pigments and the electron being transported across the membrane against the electric field of the membrane. So that is the condition of how you make the energy. You have to transport the charge against the action of the electric fields. Of course, you need to use some energy stored somewhere. In this case, it's the energy of a photon. And so you have photosystem 1, which is splitting water and producing oxygen. This is why the atmosphere of the earth contains so much oxygen. It wasn't always like this. And this is a photosystem 1. They work in tandem exchanging the protons between them. And eventually, what they produce from these electrons moving across the membrane is the potential difference, proton gradient, if you want, which is later used to pump the protons across the membrane and make ATP out of ADP. And that's the energy money of all living organisms. So if you are rich in ATP, you have a lot of money, you can do a lot of things. Now PS1, if you look at the x-ray structure of the protein, is a big thing like this. It is really, really a challenge to understand how it works. But you can do that by using the methods we will talk about today. Now this is, again, a little movie of how photosynthesis works. Now this time there's not plants. This is bacteria, because bacteria also have photosynthetic apparatus. And this is purple bacteria that has a photosynthetic apparatus, which is nicely symmetric. So it consists mainly of ring-like structures of proteins that are all embedded. Oh, I'm sorry. I need to click something. It's not clicking. It's just, yeah. Now so these things are called, this is light harvesting complex, the light absorbers. They are embedded in lipid membrane, which we now see from the side. So here is the membrane and there are proteins sitting there. You see alpha helices. And so these guys are just for light collection. This bigger ring in the middle is the reaction center surrounded, again, by light collection antenna. And if you put some light on it, one of the bacteria chlorophylls here gets excited. Now then it starts traveling around. It goes from the blue chlorophylls to the red ones with one picosecond lifetime. Then it jumps around here with about 100 femtosecond lifetime. Femtosecond is 10 to the minus 15th of a second. And in a random fashion, it sort of travels around these rings and it only takes about 30 picoseconds to reach the LH1 and finally hop onto this pair of pigments here in the protein called reaction center. Now when these pigments get excited or they receive the energy of light, what you see is then that the charge transfer state, so the state where the electron is separated from the rest of the molecule is created. And the electron is transferred in a sequential fashion along this chain of pigments here. This is the accessory bacteria chlorophyll. So the electron first goes here in three picoseconds. Now after that, in one picosecond, it ends up on bacteria pheophyte and it's a bit different pigment. And within some many picoseconds and even microseconds, depending on which quinones are in, it ends up here on a quinone. And after this has happened and it only took about 100 picoseconds, so much less than the excited state lives in a chlorophyll, you already have a potential difference. You have charged the bio battery and the biochemistry of the cells later exploiting the system. Now this might seem like a lot of detail, but we do have an energy issue here on earth along with the carbon dioxide issue. And if you look at the amount of energy that is produced captured and used by the plants on earth, that is actually about 750,000 terawatt hours. This is in BTUs, you probably know what the BTU, you don't know. Yeah, so nobody knows what the BTU is, but for some reason Wikipedia decides to put the the graphs in BTUs. Anyway, this is 150,000 terawatt hours and that is the consumption of energy by humanity today per year. Now in natural plants, algae and bacteria, you capture seven times that energy naturally producing oxygen and reducing carbon dioxide. So that sort of gives you an idea that that's probably a way to do it if you want to both have energy and to have less carbon dioxide. So this is important, time results, so time results spectroscopy to return back to our topic is science that basically lets us to understand how these electrons, I show you a movie, of course that's enough to make everyone believe anything nowadays, but how do we know? And we know from time results spectroscopy we will see examples coming. Other applications, we all like our nice mobile phones. If they're from Samsung, they will probably have AMOLED screens made of organic light emitting diet, the funny hetero structures where you have electricity converted into light. So it's the other way around from photosynthesis. You have energy you converted into light and each pixel contains three light emitting diets with hetero structures where one sub pixel I mean emits red lights, the other one blue and the other one green. And it also works the other way around so you can make these funny structures containing fullerines and pigments which capture light and produce potential differences. This is our let's say best effort to mimic photosynthesis to create energy out of the sun. Now closer to ourselves, our eyes are also molecular machines that are converting light into energy and in the retina of our eye sits these cells called rods and cones that contain a rhodopsin like protein. It is actually a rhodopsin. There's also bacteria rhodopsin. They are very similar. So a protein that sits in the membrane of a cell and it has a pigment which absorbs mostly or depending on which cones are in mostly green, mostly red or mostly blue light and basically the cell triggers the nerve signals in your brain. So every time you are seeing something, a number of these proteins are doing their work. The pigment there is isomerizing, falling out of the protein. The protein binds the signaling partner and eventually produces an electrical signal that travels to the brain saying, hey, I'm seeing the light. So and nowadays people have even figured out a way of cloning these proteins into the neurons. So you take a brain of a mouse for example, you genetically alter it to have these proteins in a neuron membrane and then you can trigger the neurons by light. It's called optogenetics. So basically you can make a mouse think what you want by putting proper laser pulses onto the brain. This is a bit far-fetched but the idea is like that. And again, to understand what's going on with this molecule, that's the molecule that's sitting there in this rhodopsin protein, it sits there like this. It absorbs light within a picosecond, it becomes like this. So it isomerizes around this double bond over here and it undergoes a full photo cycle with a lot of details. And again, we would not know about this. We would not be able to understand this without time result spectroscopy. Now this picture of a surprised monkey is actually a laser damage on, it's an optical damage on a laser mirror taken in polarization image. And again for engineers, for laser physicists, it's important to understand the mechanisms that lead to the laser damage. We all want bigger and better lasers and smaller ones with larger energy densities in the cavities. And the limiting factor is almost always not the amount of power you can put in but the actual robustness or the ability of the optical components to withstand this, this huge power. And again, to understand the damage mechanisms, we need this spectroscopy. Well okay, this is a funny technique where you can, you take a bit of a material similar to the filling in your teeth on which you put the light to make it hard. So to fill it with gel, we put some ultraviolet light and becomes hard. The 3D printing works like this, at least some forms of it. And now if you two-photon focus it, if you focus a very intense laser pulse into this material, the conditions for two-photon absorption, so for the material to absorb two photons at once are formed. And then this material absorbs two infrared, so low-energy photons instead of one ultraviolet photon. And basically it only gets hard inside this droplet of liquid. And by moving the material or the laser beam, you can actually draw nice three-dimensional structures like this. This is an initial paper from Kovata from 1996. And you can do microstructures in the volume so you can produce whatever things you want. And again to understand the mechanisms here, like two photons excite your molecule, produce a radical, the radical finds another monomer, it joins with it and produces a radical on the other end. And so the polymer chain starts growing and at some point it stops. How it works? Nobody actually knows. People just know the materials that work and they are producing these microstructures. Now again this is something to be addressed by spectroscopy. So I hope I have convinced you that spectroscopy is basically original spectroscopy, like hydrogen atom spectroscopy, opened the way to understand quantum mechanics. So quantum mechanics was basically science written down to figure out why hydrogen emits some frequencies and does not emit other ones. And now if you do a time result, if you follow it with time, that becomes a tool to understand what's happening with the matter, how it is functioning in time. So that is basically since steady state spectroscopy is directly related to quantum structure of material, the time result spectroscopy opens the way to understand the quantum functioning of material. So that is basically the idea why it is interesting and important science for us to study. Now it has been a tremendous progress over the years. This is actually an old paper from our university back from 1981 when I was five years old. And the people were already doing time results spectroscopy with picosecond lasers of the day. It is funny to read nowadays that the measuring data were processed by a mini computer, which in addition controlled the parameters of the experiment. And that is presented like a scientific achievement in those days. So that is nowadays when you have arduinos and all the gadgetry and wizardry of electronics, it's actually seems a bit dated. But of course the time is not standing still. And in 1996, this is a setup people were drawing in 1996 about the time when I was a student. And so basically at the time they still drew the lasers which they used, they built the lasers themselves to actually do the research on the molecules. They did a lot of nice work. But then the spectroscopy field was still first make your tool and then do the research with it. And so making the tool was very, very big part of the business. Nowadays it has changed a bit. So this is actually a picture which Nicoletta probably recognizes as a lab inclusion where they basically got a large grant of money and they bought the lasers, the spectrometers to do time result fluorescence, time result absorption and what not. And basically the whole works from a single grant and it was installed over a week. It seems to be working. So I'm getting questions from them sometimes about how to work this. This is a company light conversion who is making all these things that is from my native town from basically a spin-off from our department. And they give you the full works including the data analysis software about which we will talk a bit. Okay, so this is the way of the history and the motivation for this. And now the number of processes that can be addressed mostly involve these tiny things, the molecules and the charge carriers and semiconductors dancing around in the matter. So you can look at the charge transfer, the proton or electron moving from one part of the molecule onto the other. You can look at the solvent or environment response when you excite let's say a molecule that is sitting in a solvent. Solvent molecules will feel it. They do something to rearrange according to the changed configuration of the solute. And that you can follow with spectroscopy. You can look at vibrational relaxation. So if you dump a lot of energy on the molecule it somehow distributes it around its vibrations of nuclei. It starts vibrating in different manner. You can look at energy transfer. So the process integral in photosynthesis. You can look at the photo reaction dynamics. So like the the event that is happening in your eye. Every time you see a photon basically you have a photo reaction going on. You can also follow this big field following carrier dynamics both in bulk semiconductors. So like what happens to the electron when you put it in the conduction band by using a photon. Essentially there's a number of ways of things that can happen. We will talk about it a little bit over the coming three hours. And also in the quantum structures there's an additional twist to it when you limit the space for the electron. The quantum effects so the discrete states become more and more pronounced and that again you can follow using your spectroscopy. So basically what you're doing you're exploring how the spectra absorption fluorescence some funny spectra like four wave mixing spectra and things like that are changing in time in molecules solid state and maybe nanostructures. Now molecule. Molecule is a thing that is commonly represented in physical chemistry textbooks using Yablonsky diagram where you have you know a ground state full of vibrational sub levels excited states you have triplet states and when you excite the molecule sort of will do internal conversion here maybe do a fluorescence or maybe it will inter-system cross into the triplet manifold and then you will have phosphorescence and so basically this is a framework for understanding how a molecule works. It's not a fully explanatory scheme but it's good enough to start with. Now you excite it you can have a number of processes going on which were shown you can have radiative relaxation i.e fluorescence or phosphorescence internal conversion so radiation less relaxation you can have inter-system crossing for may formation of the triplet states salvation photo induced reactions and so on now if we look at it with fluorescence we only see the light output while the molecule is still excited while it's still high you can still emit a photon so we can follow what's happening with it and these process of course result in the change of the fluorescent spectrum all of them invariably change the fluorescent spectrum and intensity of the molecule and therefore by following it you can actually deduce what the molecule is doing but it's only useful while the excited state is preserved if you make a photo product which is different from the original ground state but it's not emitting light then it's disinformation is lost for you. Again you can do the same with bulk semiconductors so you can excite the electron from the valence band to the conduction band and follow it around as it relaxes in different valleys and equilibrates and so on you can do it an organic semiconductor as well that's a bit normally it's drawn using a bit different structures but again in order to make a photovoltaic cell organic photovoltaic cell you need to know the fate of the excited state when you when you excite the molecule or maybe a disordered semiconductor as the as the polymers normally are you need to know what the where the electron is going how it is ending up on the acceptor and what is preventing the electron from reaching the contacts to generate the photovoltaic and again in solid state you can have band to band radiative recombination with light output shock lee read hall tried trap assisted recombination so that when the electron goes first to the trap and then back to the to the valence band that can be either radiative or non-radiative you can have non-radiative recombination electrons being trapped a number of processes as long as you have light output so as long as there's still some light coming out of this material you can you can follow what's going on using time result spectroscopy and when you make the semiconductor small enough for the quantum effects to kick in full time so basically you the continuum of states becomes a set of discrete states as in as it does in a quantum dot or quantum well then you have a hybrid picture between a molecule and a bulk semiconductor so you don't they are not really discrete states sometimes but but you have pronounced bands similar to the molecule so a quantum dot is a hybrid structure which is also very interesting to study by time results but trust me now okay so essentially the signal in the very simple terms what you are measuring when looking at time result fluorescence will look like this you will excite your molecules with a short laser pulse which is drawn in gray here and the fluorescence of the of the number of molecules will grow as the integral of this of this laser pulse so basically the each bit arriving of the laser pulse will put more molecules in the excited state and they will start fluorescent now if there was no decay if they've stayed in the excited state they will simply stay there but of course the molecules will not stay excited forever the equilibrium needs to be established so they will go back to the ground state one way or the other with the lifetime tau and basically the the form of a signal that you are looking at is this integral of the pulse which is an error function plus one more or less times the decaying exponent now I have to stress that this is very simple picture and this is not very interesting in itself because if the molecule of all it does the molecule gets excited and it goes back to the ground state the only thing you can measure is the relaxation time so the whole spectrum will simply uniformly decay and spectral dimension spectral degree of freedom will not give you any information now of course life is never so simple especially with molecules not even with atoms but especially with molecules life is never so simple and you will have different decay times at different wavelengths describing you what's happening with the spectrum in time all right so let's look at the techniques that allow you to address this and the first fluorescence technique that allows you to look at it this time correlated single photon counting since this is an imaging workshop I think somebody should have mentioned it I don't know if if they did but I will briefly introduce it now if you look at the fluorescence of a sample using a fast photomultiplier and a faster oscilloscope with persistence on you will see that fluorescence is coming as a unsteady train of pulses of different amplitudes and but and arriving at random times so that is the basically the idea that when you excite the sample the sample after sometime it will emit the photon that after sometime is actually what you want to look at but the process is completely random so the molecule has a probability of decaying and it will decay at some point but when it will happen you don't know you can only do the statistics of it so so the single photon timing is actually a statistical methods that is measuring the time interval between the arrival of a photon from a sample and the laser pulse that that excited it so if you look now at the laser excitation pulse train so this is 80 megahertz megahertz laser let's say it's a titanium sapphire laser emitting pulses every 12 nanoseconds now the fluorescence after each pulse from the sample from the bulk will decay exponentially when you excite so you will see a train of fluorescence pulses now if this train is if the fluorescence is very weak so you can attenuate the excitation light as much as possible now if you if you do it look at and if you look at single events of photon emission you will have these events occurring each after a certain time period after a corresponding excitation pulse and now if you do it many many times so 80 megahertz is 80 million pulses per second so if you do it at least for half a second you have a good chance of collecting a large number of photons and if you can measure the time at which each photon has arrived you can reconstruct the probability distribution which is nothing else than the decay of your fluorescence so the good thing about about this type of measurement is that you are actually looking at the timing you are not concerned this this doesn't look like a nice signal as the amplitude of each fault produced by each photon in your detector are different but it doesn't matter as long as you only use the time information of a photon arrival not the amplitude information now so the way it is organized is like this you take a laser producing short pulses and it can be a diode laser it doesn't have to be a femtosecond titanium sapphire laser diode lasers are perfectly capable of making you know 30 50 picosecond pulses which is more than enough for this experiment part of it you used to trigger a fast photo diode and the signal of the fast photo diode will start a device called time to amplitude converter you can think of it as a capacitor being charged up using a constant current so it's a ramp generator which is started by the trigger pulse here so your voltage is increasing linearly until the photon from fluorescence is detected by the photomultiplier and the signal comes here and stops the measurement so basically what you have at the end of the sequence is the voltage proportional to the to the time difference between the excitation and the and the fluorescence fluorescence emission by the sample and if you analyze these times so you do it many many times you convert these times to numbers and you store them in a shape of a histogram that is basically your fluorescence decay curve and just to say a word you are not limited with a clever electronic tricks called constant fraction discrimination where you take this pulse delay it by a bit and subtract the two you can do it with fast electronics and you look for the zero crossing point here that does not depend on the amplitude if you trigger with a oscilloscope on the pulse it pulses with different amplitudes your triggering time will depend on how big the pulse is whereas if you do it by shifting one pulse with respect to the other and subtracting them the zero crossing point will always be constant and this timing is in fact pretty accurate so you can easily have time resolution of with current day detectors of 100 picoseconds maybe 200 picoseconds depends on the detector but it's a very nice technique and it gives you a time resolution of 50 to 150 picosecond it's relatively cheap with the electronics for it will cost about I think 10 000 euros is a good estimate for for the whole works it can produce extremely good signal to noise as long as you count long enough these photons it it basically you simply accumulating your curve and the good thing about it is that it in it's totally independent on the stability of the laser so your laser you can switch it off for half an hour or you know take it away for repairs then you bring it back put your light back onto the sample and the thing keeps counting and your and your curve is still what it was before so that is actually very nice it's inherently single color because there's one detector one start and one stop signal but that makes it suitable for the imaging in fluorescence lifetime imaging type of microscopy so basically you can measure the fluorescence with time resolution under a microscope now for a little bit more advanced technique you have a device called a street camera which is an optoelectronic device so basically what it does it converts lights into electrons it uses a very fast rising electric field to sweep these electrons in space so basically like an old fashioned oscilloscope or old fashioned tv or old fashioned tv use the the coils but this use a deflection plates so the electrons that are knocked out of the photocatod they are accelerated and then they pass the deflection space between the two capacitor plates with a fast rising voltage there and basically the arrival time of electron will then since the late electron will see higher voltage than the earlier electron the arrival time of the electron will be converted into the into the position in space so what you can do with this street camera you basically change encode temporal information the time of arrival of a photon into the spatial information so the position of a photon on the on the the micro channel plates that's a type of photo photomultiplier which amplifies the electrons and basically it's consisting of a number of little channels where you have photo photomultiplier action the electron knocks out another one then another one a number of them and basically you have a large torrent of electrons at the end of it and so these electrons later will hit the phosphor screen like again like in an old fashioned tv and this image of electrons will be converted to light again and be detected by a ccd camera so that's basically the way it looks it's a box like this the only supplier in the world of these things is Hamamatsu in Japan and these things are unfortunately quite expensive but the nice the very nice thing about them is they're very sensitive and very nice in the sense that you can use one dimension in space to measure your time information and the other you can spread the spectrum in so if you take a grating or a prism you make a spectrum at the entrance of the street camera so you come in with a spectrum you have a spectrum spread in time so simultaneously record the entire spectrum with a time resolution of one to two picoseconds and it's a lot more sensitive than other methods with femtosecond time resolution that i will briefly talk about and so if you can afford it this is what you can what you should have now this problem with street camera is still that the time resolution is above one picosecond the realistic one is probably two to three picoseconds from my experience and so you need to use clever methods to get down to the femtoseconds the very very fast events you cannot measure with street camera and so you you turn to non-linear optic tricks this is the bread and butter of laser physics when you shine two intense light fields onto a crystal you can have conditions where the two photons are glued into one that's called some frequency generation so omega one and omega two come into the crystal and they become omega one plus omega two so it's a second harmonic generation is a separate case of that when when the frequencies are equal but the nice thing about it is that the intensity of this outgoing field of the up converted field up conversion means the frequency goes up up is proportional both to to both intensity so if you mix your fluorescence with a laser pulse that can be arbitrarily short the signal that you are measuring will be proportional to the intensity of your laser pulse and your fluorescence so if your laser pulse is constant what you what you will have at the end is the proportional signal proportional to the intensity of fluorescence of course the wavelength of the sum frequency will be shifted upwards well downwards will be shorter than the the one of the fluorescence and now so if you can afford having a very short gating pulse you can make it arrive earlier or later with femtosecond resolution so femtosecond resolution is obtained by letting the lights travel more or less in space so in one nanosecond the live the light will travel 30 centimeters now if you want femtoseconds it will be some microns but that you can arrange with precision mechanical stages and by varying the arrival time of the gate pulse you are measuring the signal that is proportional to the intensity of the fluorescence at the arrival time of the gate and if the intensity of the gate is always the same then essentially your signal will simply be proportional to the intensity of fluorescence at that instance in time so the way you do it in the realistic setup you take your femtosecond laser light from a titanium sapphire laser you split the beam into two part of the beam is your gate pulse that is the the delay which you can vary so by by varying this delay you change the arrival time of your gate pulse and you put this gate onto a crystal together with the fluorescence which you excite here so if you focus your beam into the crystal to make ultraviolet light and then focus it onto the sample the sample will emit fluorescence which you from which you will filter out your excitation light and eventually you get what you get is is a fluorescence light falling onto the crystal together with a gate light and that light becomes upconverted inside the crystal what you then do is you send it through the spectrograph and record it with a conventional sensitive ccd camera now the problem with this technique the nice bit about this technique is the fact that you have femtosecond time resolution it's only limited by the gate pulse and the dispersion of the optical components but it's easy to have it down to 150 200 femtoseconds with a titanium sapphire laser now one problem is that of course this non-linear process which you use to map out the fluorescence is sensitive to the to the non-linearity of the crystal so the crystal parameter is different at each wavelength the detectivity of your spectrograph is different at each wavelength and so basically the relative intensities of these traces need to be calibrated to match your steady state fluorescence spectrum otherwise you can only look at the time behavior but the intensity the absolute intensity has no meaning here now of course you need a lot of excitation light and that's that can be bad for biological samples and experiments of course take time because the phase matching conditions so basically the momentum conservation law for that these two beams you need to rotate the crystal to actually be able to upconvert different frequencies of fluorescence so since you are rotating the crystal and recording the spectrum that takes a bit of time to record and your wavelength resolution will be limited by the by the spectral width of the gate pulse now another non-linear optical trick that does allow you to get femtosecond time resolution and fluorescence is optical care shutter optical care effect is the effect where you put a very very intense light on the sample and basically the refractive index of the light becomes dependent on the intensity of the field that you are putting so to the first approximation is just a refractive index of the material and to the second order it is proportional to the intensity so what will happen to the beam inside such material it will start to make a beam profile like gradient in the refractive index and the beam will start to self focus but we are not talking about that right now but what I want to talk is the optical care effect where you basically produce the refractive index using a linearly polarized light and if you do that your sample in the electric field a glass a piece of quartz a piece of sapphire water whatever every material will become birefringent because this n2 part will depend on the polarization of the field which is which has intensity i now if you have birefringence you can have rotation of polarization and if you now arrange your polarizer and analyzer in such a way that fluorescence cannot pass it and then you do that your birefringence using the optical care effect again with a short gate pulse for a very very tiny moment of time so for the duration of the gate pulse this material will become birefringent and rotate the polarization of your fluorescence so basically some of the fluorescence will pass the second polarizer and you you will be able to detect it again by varying the delay of the gate pulse you can map out what's happening with the fluorescence in time now the nice bit about it is that you don't change the wavelength so you don't mix the wavelengths and you don't lose the spectral resolution the way you did in the upconversion experiment the problem with it there are many problems with it as there always are with non-linear optics is that you need extremely high laser intensities and your material your cure medium so the your shutter starts is prone to start generating all kinds of unpleasant light by itself when you put so much light on it and some of the materials like water or cs2 that are traditionally used for this they have a non-momentary response so basically they remember a bit that there was a pulse which oriented the molecules there so water and cs2 are only good up to a picosecond time resolution so experiments are troublesome and but this is one of the ways to get down to femtosecond time domain now a funny technique that I should say a few words about is called frequency domain fluorescence lifetime measurements or phase flow symmetry and that's based on a fact that if there's a delay between the time when you excite the sample and the time that the fluorescence is emitted and the delay is fluorescence lifetime obviously the will if you modulate your excitation light there will be a phase shift between between the emission and excitation and if you mix the two in the in a you modulate your excitation life with very high frequency so in the megahertz and gigahertz even regime and you detect it with a radio type of detector you can detect the phase difference between the between the two lights the light beams and that would that would be a basically a fluorescence lifetime the phase shifts will correspond to the fluorescence lifetime so that tricks if you change the modulation frequency of course at high frequencies your slow sample slow emitting sample will not be able to follow the modulation and so the amplitude of the modulation will fall with respect to the lower frequencies and from that you can actually even get more than one lifetime and again this is the way you do it you basically treat your molecule as an electronic filter the response integrating filter the response of which you are measuring and you can even do it for several lifetimes so multi exponential decays can be addressed from that but it it's not without its problems it seems good on paper but of course the the problem with it is that it relies on the Fourier transform or for the filter response to be mapped onto lifetimes and this can be tricky you get non-intuitive artifacts and your data recovery is essentially based on the model for fluorescence decay which assumes exponential decays and maybe they are not exponential so since you are not measuring it directly you don't know but it's a very good choice if you have a number a large number of samples a batch of a cell cultures or something like that that you want to measure and so it's it's normally made implemented in a simple fluorometer so you just swap one after the other and you get fluorescence lifetime measurements or multiple samples now so this is for the techniques now let's look at the applications and my first application of single phototyping is called flim for threat and if you want to look cool you should always use a lot of abbreviation and okay flim is fluorescence lifetime imaging and the threat is first resonance energy transfer now fluorescence lifetime imaging is a is a simple alteration to a confocal scanning microscope with which I'm sure you're all familiar basically what you do is you simply change the detector by a photon counter here and connect connected to the photon single photon timing electronics that's all you do so it's a couple of boards in your pc and and the photo multiplier that can count single photons and you can turn your microscope from the intensity measurement in at each single point that you are scanning you can now measure the fluorescence decay so essentially one number fluorescence intensity is converted into a curve that is representing the fluorescence decay at each pixel of your image first energy transfer is a is basically a mechanism of transferring the excitation between two molecules so if you have donor molecule excited it and it's interacting weekly with the acceptor it can go down from its excited to the ground state and it can produce the excited state of the acceptor so in the end you have transferred the energy from one molecule to the other and it's important in photosynthesis and as well as in other fields and basically the transfer rate between donor and acceptor will be proportional to the overlap integral between donor fluorescence and acceptor absorbance and basically the experiment that you do you excite your donor and you look for the fluorescence of the acceptor now this is in our one over distance into the six power so this is a very sensitive ruler this thing I should probably say about something about the assumptions of the model but that can be done later it's a very sensitive ruler where you label the two pieces of cell or a single protein even and you want to follow how it's folding basically when the donor gets close to the acceptor you get the fluorescence transfer rate increasing as a r to the power six is a distance to the six power and so it's very sensitive to the distances and it's basically an optical ruler for the distances of about 10 nanometers and you can follow protein folding and interaction of some substrates and enzymes inside the cells and things like that and it's a it's a widely used tool in biology now the assumptions for the first time model are actually quite stringent it's very strange that that the model works to some extent so the assumptions are that when the transfer is over the acceptor will forget everything about where it got the energy from there is no orbital overlap so the molecules cannot be touching each other more or less the coupling is dipole dipole type that's okay that's probably always the case or almost always the case with the molecules and the donor has to be in the so the bottom of its excited state before emitting now it's a miracle that the model works but it does and it even does for photosynthesis which is interesting and you can do it under a simple fluorescence microscope simply looking for your acceptor fluorescence intensity by exciting the donor and that will tell you something about whether the energy transfer is happening or not and hence whether the donor and acceptor are close one to the other or not but a much better way is to look at the donor lifetime so if the if the donor has acceptor siphoning away the energy from him the fluorescence lifetime will decrease so it will lose the excitations more quickly and if you look at the intensity you don't know the concentrations you may have overlapping absorption spectra between the donor and acceptor so you don't know whether you're exciting acceptor directly or you're exciting the donor and the calibration on control is tricky whereas if you look at the lifetimes it's very simple what you get compared to the donor without transfer would be the decay like this and when the transfer kicks in your donor fluorescence develops a fast component which corresponds to energy transfer time to the donor and so the example here for example again from an old paper in 1999 you have three cells you micro inject one with the activator and you basically look at the fluorescence images and you see no change so basically the middle cell between these two is not really signaling the difference between the three cells is not obvious how whether the activation process has taken place or not whereas if you look at the lifetime image so you just plot the lifetime and false color here after the injection you see this middle cell lighting up like a Christmas tree which basically tells you that okay this one has been activated these ones are still the same as they used to be okay another application of fluorescence that I would like to discuss is the isomerization of retinal bacterial rhodopsin and that's a you know a protein that I told you about it's in fact bacterial rhodopsin is a workhorse for molecular biology and is a polygon of application of new spectroscopies and back in 2012 I did literature research and so you have on bacterial rhodopsin you have 34 papers in nature 43 in science and 173 in PNAS which is basically to say that it's a very attractive system to study it's not if not for for understanding the system itself then for applying new methods that you want to investigate on a well-known system and it's a protein that is a part of purple membranes in bacteria and the function of it is a proton pump so it absorbs the photon and it uses the energy to pump the proton across the membrane the protein itself looks like this and it's very similar to rhodopsin part of your eye this is a pigment that sits in it it's called retinal and basically when you put some light on the pigment it absorbs in the green in the yellow 580 nanometers when you put some light on it it isomerizes and further the proton transfer takes place but the isomerization step was a challenge to laser spectroscopies for a very long time you read the papers from the 60s throughout the 70s 80s and the early 90s and it's always the conclusion is that the isomerization is of the order of the instrument response function of your laser center so basically the very short pulse was still not available at the time and the nature was faster and the first time when this was addressed was in 1993 when Graham Fleming and Maydew did fluorescence up conversion experiments on on bacteria rhodopsin and what they saw actually is that after the absorption of light the fluorescence develops very quickly but with within one picosecond so 10 to the minus 12 of a second the most of the fluorescence is already lost and so basically the isomerization takes place very fast on the excited state potential surface and basically the after one picosecond bacterial rhodopsin has already come to this point where it takes the decision whether it wants to go to the isomerized state or go back to the ground state and so but this was the first time when when it was demonstrated that nature does actually use the photon energy within a picosecond and this is very fast and without fluorescence up conversion we would know not know about it and now another favorite tool of molecular biologists is green fluorescent protein that was awarded a Nobel Prize of back in 2008 this is a protein that comes from a jellyfish and it's interesting because it when it is synthesized it falls into this beta sheet structure and out of three amino acids inside it will form a chromophore something that absorbs in the visible and the myths more importantly the myths light in the green hence it's a green fluorescent protein it's not a dye it's not toxic it's a protein so you can genetically code it for any organism you like and well there were these experiments where they made transgenic mice with green fluorescent skills so they basically fuse the green fluorescent protein into the epithelium of the skin of the mouse and if you put the mouse under UV light it starts emitting green light like it's radioactive or something so poor mice but but it's I mean this is not a very meaningful experiment but this molecule is actually as is a tremendous value to molecular biology because as a label to actually label different proteins and follow their interactions in the cells using fluorescence now the chromophore that is formed out of the amino acids looks like this is a view from the top it's protected by this beta sheet structure and if you look at the absorption spectrum it absorbs it's basically a UV so their main absorption band is at 400 nanometers and it emits light in the green and the reason for this huge stoke shift why the fluorescence is so far away from the absorption wavelength was not really known before the experiments the time result experiments were done and so basically the usual suspect is this hydrogen sitting over here so back in 1996 Steve Boxer and company did the experiments where they measured the fluorescence at two wavelengths one in the in the green again with a with a picosecond time resolution that is with fluorescence up conversion and what they saw is that the blue fluorescence appears instantaneously when you excite the green fluorescence protein fluorescent protein but then it decays with about 20 picosecond lifetime and with the same lifetime you see the green fluorescent right fluorescence right so it sort of tells you that there is something going on with a timescale of 20 picosecond that makes your fluorescence go from blue to green and that's something could be addressed by replacing this hydrogen that's sitting there in the pigment so this guy here which in the protein structure will be here if you replace it by the deuterium you get these the same dynamics only a lot slower so you make the your hydrogen two times two times heavier and instead of 20 picoseconds you now get maybe 100 picoseconds and the rise of the green fluorescence mimics that so their conclusion was was that it's actually sorry it's actually the the proton transfer that results for the huge stock shifts for the green fluorescence protein so it depends on the weight of the proton and you can see one state initial state disappear and the green emissive state appear in in in this system now my favorite molecule light harvesting complex from photosynthesis you saw these rings in bacteria in the movie that i i showed you earlier this is a ring containing two rings of bacteria chlorophyll so that tightly packed one called b850 which is responsible for this absorption band here and the loosely packed ones the blue ones that are here and they are responsible for the absorption at 800 nanometer and there are also carotenoids which absorb the green light so these are red open glucoside molecules orange ones that are here and again the energy transfer this the the whole function of this protein is actually capturing the solar light absorbing photons at whichever wavelength and transferring them over to the reaction center so this is the antenna that collects the light from the sun and the again it was not known how fast and precisely how the energy is traveling in the system and and in 1996 Ralph Jimenez and again Graham Fleming did these experiments where they excited this complex with 800 nanometer light so they excited these blue bacteria chlorophylls and looked at the fluorescence of the complex in the 870 nanometer region and what they saw was actually that the fluorescence did not appear instantaneously but it took about 800 femtoseconds for it to grow in and that means that what happens is you have your energy from these this blue ring being transferred to the green ring and that takes 800 femtoseconds now that's all nice and well except for the fact that when and this is downhill energy transfer so you put the energy here and it hops on to here 800 femtosecond that's okay that that you can follow by exciting selectively this band and then following the fluorescence somewhere here but how fast are the excitations transferred within the green ring here that was a question that that was a bit more difficult to address but using their ingenuity they also answered that question and what they did is they measured fluorescence and isotropy so basically when you excite a molecule it has a dipole moment which will sort of be happy to be excited when when your polarization of the electric field is along the direction of the dipole and not so happy when it's perpendicular and so when you have your sample you're excited with polarized light you will pre-select all the dipoles that are lying along the polarization of your laser light and then when the energy gets transferred distributed around the molecule of course the dipoles of these of these acceptor molecules are oriented differently from the dipole that you are looking at now then what happens is that with time as the energy is being baseballed around this this green ring your fluorescence will decay anisotropy will decay so from remembering the direction of excitation your fluorescence will start forgetting it and the speed with which it forgets will correspond to the energy transfer time within this single band of bacterioclorefils and that is that was what Jimenez and Fleming did they measured fluorescence anisotropy and so the measurement is more or less the same you put the polarized light on the sample and you use a polarizer through which you look at the emission and you look at the parallel so if you excite like this your parallel will be like this perpendicular will be like this and the parallel component initially well it's always a bit greater than than perpendicular but if you calculate the anisotropy which for a single molecule which is standing still should be 0.4 you can actually see that there is a very very fast decay of anisotropy here so it starts off maybe at 0.4 you don't really see it it's faster than your time resolution but then it decays within more or less a hundred femtoseconds already to the terminal value which represents the degree of anisotropy corresponding to the excitations equilibrated over the entire ring so of course if you excite chlorophyll here at some point with energy transfer it will be distributed equally but it still will visit this chlorophyll here sometimes so there will be some terminal anisotropy left and basically the answer from this experiment is that within this tightly packed ring of bacterial chlorophyll the energy is being footballed around at the rate of 100 femtoseconds between each pair of bacterial chlorophyll and that's very fast and that was a fascinating realization that in nature you have energy transfer on the 100 femtosecond time scale and this is why perhaps the collection of light in photosynthesis is so efficient so quantum efficiency of photosynthesis is close to unity is about 95 percent that means that each photon that is absorbed is actually used for separating charges it doesn't mean the energy efficiency is that high it's probably less it's probably 30 percent but nevertheless it is formidable that the photons are used so well now and so these this is for the applications of time result fluorescence it's a very nice technique and it's good but the problem with fluorescence is that it only is giving you information while your sample is emitting light and not all samples emit lights most of you don't emit light in your active state so to speak so and even if you excite the molecule with the light a lot of times the energy of the light is used to produce some different sort of molecule that does its job in the ground state and the light emission is lost so since we also want to look at these processes we switch to time resolved absorption spectroscopy also known as pump and probe well the reason I have a car and the rainbow here is just you know it's a spectroscopy and the observation of spectrum is after the rain when the sun comes out so we talk about pump probe spectroscopy and come on so basically again to think about what we are measuring we want to measure the change of the absorption in the sample when we have excited the sample beats molecules nanostructures semiconductors and so let's use a concept of the molecule to illustrate what's happening so if you don't touch the molecules they happily sit in their ground state you excite them using your laser light what happens is that part of the molecules have left the ground state so if you now compare the absorption spectrum of the molecules of the sample before and after the excitation you will see that some of the absorption is lost so there will be a negative contribution to a signal called ground state bleaching so basically molecules left the ground state they are not absorbing there any longer therefore negative contribution to the difference absorption now as the molecules that left the ground state they have appeared in the excited state what they can do then if you look at the absorption spectrum of the sample they can either absorb the light with which you are looking and that causes the so-called excited state absorption so that's this contribution absorption that was not there before you excited it but after you excited it it appeared and now another process that can happen is a stimulated emission so basically it's like a lazing action the molecules in the excited state they can amplify the light with which you are looking at the absorption spectrum so the at some wavelengths corresponding roughly to the fluorescent spectrum of the sample you get more light after the excitation than without the excitation so basically you get a signal a negative absorption so the amplification we will have another negative band appearing in your difference absorption spectrum and that's called stimulated emission now if the molecule is doing something interesting is going along happily along his its reaction coordinate of course these energies of the excited states and the ground states will change and if you look at the excited state spectrum and a stimulated emission spectrum the wavelengths may be different so these bands will shift around with time and as the molecules return to the ground state they will gradually disappear and if they return completely to the ground state they will basically recover the original spectrum and the difference signal will go back to zero so pump probe spectroscopy is a type of time resolved spectroscopy that monitors the time evolution of a difference absorption spectrum that is absorption difference between sample is excited versus sample is not excited okay so to reiterate quickly the spectrum consists of ground state bleaching the shape is identical to the absorption spectrum and a signal is negative stimulated emission the shape of which is trivially is almost in molecular well this almost always the same as the fluorescent spectrum it is an omega to the power four multiplier in the way in the Einstein coefficient equation but in at large frequencies it doesn't really matter and so you have stimulated emission which is also negative you have excited state absorption which is positive and if the molecule forms a photo product and doesn't go to its original excited state you will have some ground state bleach and you will have some induced absorption that corresponds to the absorption of the product state and so this is what you want to look at basically the experimental scheme consists of using two short pulses of light you use a pulsed excitation then you let your probe pulse which is normally as broadband as possible to look at as many wavelengths as possible you delay it with respect to the first one and then you disperse the your probe light with a spectrograph to look at the spectrum all spectrum at once you can do it monochromator doesn't really matter for the discussion purposes and you can look at the number of processes such like energy transfer reaction dynamics all the relaxation processes in the molecules proton transfer electron transfer everything very important for the for the photo chemistry that we talked about you can look at the carrier dynamics and semiconductors and nanostructures and this is really a bread and butter technique in ultrafast well the way you do it experimentally use an amplified titanium sapphire or other short short pulsed laser you split the beam you send part of the beam through the optical parametric amplifier which is a device that basically produce the spectrum that you want to which matches the absorption of your sample so the lasers are generating the light that they are generating so you cannot change that but you can use nonlinear optical devices to make tunable wavelengths and and OPA is such a device here in this beam you have a chopper which allows which keeps blocking and unblocking your pump lights to be able to measure excited sample minus non excited yeah and basically you direct and focus this light into the sample and then you block it the rest of the light you send through the delay line again so basically a variable delay with which this beam can travel that gives you the time resolution and then you focus this laser light into a nonlinear medium where because of this effect with nonlinear dependence of refractive index on the intensity out of a laser light to get white light basically it's the the light field is so strong that it generates a lot of new frequencies and it becomes a completely white broadband spectrum at a very short and retains a very short pulse and then you focus the white light probe onto the sample and then you use that as your measuring light so by having chopper open and close you measure the two spectra in transmittance you divide one by the other take a logarithm and that's your difference absorption spectrum the realistic setup is a bit more complicated than that of course there's many optical components no need to go into the detail and let's now look at the several conceptual examples so first of them will be salvation that is the process when you excite the molecule happily sitting in a solvent it will be surrounded by a solvent by the solvent molecules and since it has a charge distribution in the molecule the solvent molecules will orient their dipole moments in such a way that you know the minuses are close to the pluses and the pluses are close to the minuses now when you excite the molecule the charge distribution changes the electrons rearrange they go to the excited state that means the dipole moment of the molecule changes i drew it here very overemphasized so to speak so it's really flipped around let's let's assume that the redistribution of of the dipole moments is so bad that that the dipole moment actually flips around now what happens at time zero the solvent molecules are no longer happy they are minuses at the minuses and pluses at the pluses so they repel and what they do after some time they rearrange so they rotate around to have minus next to the plus and plus next to a minus again that that is a process called salvation not salvation salvation yes and that is the rearrangement of the environment to minimize the energy of the of the molecule inside the environment plus the environment if you look at it in energy level picture and plot a salvation coordinate coordinate here versus the energy here in the ground state everything sits at the minimum now when you excite your molecule and it absorbs some light the environment is no longer in equilibrium so the energetically is not happy it's higher than zero higher than the bottom of the well so the system starts to drift towards towards the energy minimum in the excited state and now if you think about what what does the ground state think about it so suppose you were to return back to the ground state would the the environment be happy now of course not it has really rearranged itself for the excited state so when the salvation takes place you have two effects going on first the energy of the excited state is going down and second the energy of the ground state is going up because suppose you were to return to the ground state you would no longer be at the optimal and if you look at the at the stimulated emission spectrum which is basically measuring the energy gap between ground and excited state what you will see is that the wavelength corresponding to the stimulated emission will shift to the red so it will start right next to the to the absorption spectrum in theory even exactly as the absorption spectrum it's never like that because you have dielectric component in the relaxation which is instantaneous more or less but as the salvation takes place you will see the stimulated emission shifting to the red while the ground state bleach will stay at its original position okay so this is what you can expect expect a red shift due to salvation if you have molecule in solution that the same thing happens in the proteins by the way only protein is a lot more complicated than than a simple solvent so in protein you have amino acid groups with some of which are charged and they will also move around to accommodate the excited excited pigment in the protein now another a little bit more complicated example let's think about the molecule that has one vibration so it's a hypothetical molecule again very tutorial thing represented by the same harmonic potential in the ground and the excited states we all know well at least those of us who have studied rudimentary quantum mechanics we all know what the harmonic oscillator wave functions look like and if you have the molecule that has a vibration in the ground state and in the excited state what we assume is that basically the equilibrium distance is a bit different in the excited state in the ground state so this there's this displacement of the potentials for the rest they are the same the frequency is the same and so on and now let's think what happens if you put a short light pulse on this on this molecule that can vibrate now the short light pulse due to Fourier transform short in time means broad in spectrum yeah it has a spectrum that is broad and it will excite the molecules coherent making a coherent superposition of several of these oscillation wave functions so basically the after the excitation with the broadband pulse you will have a superposition of several of these oscillator states excited together now that will of course the center will correspond to the excitation wavelength and how if you do it very in a elementary fashion you say that your excited state wave function is a superposition of ground of normal wave functions of the harmonic oscillator just multiplied by a set of coefficients that depend on time because they should depend on time yeah and these are oscillation oscillator eigen functions and these are time dependent amplitudes yeah so you you do a very yeah textbook example of of solving Schrodinger equation for this superposition and basically you have time derivatives of these coefficients and the Hamiltonian of a harmonic oscillator because that's what we assumed acting on the on the of them on the left hand side if you multiply it by eigen functions with the complex conjugates and integrate what you get is a set of equations for the coefficients a and that you can solve on the on this side you have you have the quantization condition for the harmonic oscillator Hamiltonian so these are separable equations all with time dependent probabilities and you can easily solve that getting the exponential behavior oscillation with a vibrational frequencies of these time dependent probabilities so basically what you have you have this superposition of several wave functions are prepared by your broadband pulse that are evolving in time according to these formulas so simply exponential oscillation if you calculate the basically what the probability distribution looks like what what it looks like is like this so this is a ground and excited state potentials and if we play how it behaves in time you have this wave packet so the coherent superposition is called a wave packet that is moving back and forth on the excited state pot excited state potential it's the same on the ground state but for the for the discussion sake we leave it unaddressed and now if you are probing it with another laser pulse that the frequency of which is set here for example what you will see in this case is actually at time zero when the wave packet is here you will see you will be able to see the wave packet after half a period of the wave packing moving away your signal will become weaker because the wave packet is not here and it's out of the resonance for this wavelength and so basically the thing to keep in mind that when you have when you excite a vibrational system electronic vibrational system with a short laser pulse what you get is a wave packet motion on the excited state potential and and it will produce oscillations in your in your pump probe spectrum in your transient absorption spectrum and these oscillations will have a typical time of a vibrational coherence which is from the vibrational lines in the spectrum you can estimate it at you know one two picoseconds that that would be a good estimate and let's keep it in the back of our heads for later because it will be a part of a lesson after the break now for the for the application of the pump probe spectroscopy just to show you what it can which questions it can answer I think I will go through one example and then we can have a break because we have to stop so we will talk about carotenoids carotenoids are lovely molecules that color a lot of things starting with seeds fruit fish birds flowers tomatoes they all are you know colorful pigments of nature they are in the photosynthetic systems where they actually have two functions one is collecting the light outside the absorption bands of the chlorophyll because they absorb the green light yeah well they can actually be a foot supplements as well and that is because of their second function that was also unraveled in photosynthesis is the fact that they are antioxidants antioxidants means that they can quench the excited state of singlet oxygen oxygen is a triplet in its natural ground state means it has two electrons facing like this and and when you excite it if it takes the excitation out of any molecule that absorbed light and became a triplet state which for example is a chlorophyll in photosynthetic system in fact the the triplet yield in chlorophyll is above 50 50 percent which was determined by said george port that which whom I mentioned at the beginning of the lecture and so basically chlorophylls can easily become triplet states and then they can excite oxygen making singlet oxygen which is an oxidizer that can oxidize almost anything so basically singlet oxygen is poison and this poison is produced in copious quantities in photosynthesis it's one of the byproducts of photosynthesis and well we use it to breathe but it's a poison so that's a wisely used poison can be useful it's a homeopathy yeah but but so carotenoids have their triplet state that is a little bit below the the the excited state of singlet oxygen and so they can basically take the energy from the oxygen and and make it harmless again and therefore they are known widely even in you know food supplement supplement industry as powerful anti oxidizers but for the photosynthesis it's very important if the forest on a sunny day would be dead in about 15 minutes if it didn't have any carotenoids so that's the photo protection role for for for the singlet oxygen that that's carotenoids are playing now if we look at the at the excited state well okay you can find them in carrots and these molecules are large poly in chains well my professor used to joke that you know it has to be elongated molecules because otherwise it would not fit in the carrots that's you know carrots are elongated uses of food colorant now what we know about carotenoids is that their absorption in the blue-green spectrum is because of the transition from their ground state to their second excited state and they have a dark excited state in between maybe one maybe more we don't know for sure that's a matter of the investigation and now how do we know this it turns out if you do a pump probe experiment on a typical carotenoid on beta carotene what you observe in the in the initial spectrum if you look at a stimulated emission wavelength you see it there for a very very short time so 100 maybe 200 femtoseconds you see the emission this this blip the red in the red curve the negative blip but then it disappears and in the spectrum you see a little bit of a shoulder here but it disappears very fast after 100 femtosecond and then you see the band appearing here so the growth of the signal at 550 nanometer and it's not instantaneous look you can see that the top of this curve is a bit round showing that it's not appearing instantaneously is with a 200 femtosecond delay after the excitation and and this band shows some internal dynamics which is probably vibrational relaxation and only after that the ground state bleach is recovered so basically the ground state bleach is recovered within tens of picoseconds and this is these signals are in fact how we know why we excite carotenoids up to the second excited state then they do fast 100 femtosecond relaxation to this dark state which we can actually observe by its absorption to even higher excited state and basically this is how we know that carotenoids can be well they have more than one excited state this is why they do not fluoresce and that is because their lowest excited state is optically forbidden you can have no absorption to it and you can have no fluorescence from it and i think this is a time for us to stop let's have a break and then i hope we will meet after the coffee break thank you for presentation we can take a question they are question there is a question yes you had a question no okay so you had a question thank you i'd like to know in this time regime from physical point of view which which mechanic description works i mean classical or quantum because somewhere you consider electron as a particle and somewhere as a quantum system okay that's a very good question in fact not a very easy one to address well the short answer is it's always a quantum regime to describe the bands in the semiconductor the absorption bands in the semiconductor in the molecule or in the in the protein you need quantum mechanics the problem with it is that already for a carotenoids and this this has been since 70s with the development of the computers there's no way of treating everything quantum mechanically so basically we know it's quantum mechanical but what we do is a set of approximations so first of them is a quantum dipole approximation so it's we approximate all the charges of the molecule in the interaction with the electric field as a single dipole so basically a charge a plus and a minus at some distance which can then interact with the electric field now that is actually very productive so you can do a lot of quantum mechanical calculations with it and so basically get description of your results but the problem is always the environment so the protein is big it can easily contain 10 000 atoms there's no chance you can treat it quantum mechanically so you either use mixed techniques or you use it as a parameter for your quantum mechanical calculation so the potential energy surfaces that they draw they are actually sort of since they are ground and excited state they are in a way quantum but there's a continuum of basically state positions depending on how the nuclei and the environment of the molecule is arranged so that is a mixed picture so to speak to be able to move forward it's impossible to treat everything with a Schrodinger equation I mean it's possible but you never get the right answer so if you want to annoy a quantum chemist ask him to calculate an absorption spectrum for a simple carotenoid for example will never work I can tell you they're still struggling with it and so it's you have to make compromises to move forward so you you get a semi phenomenological description okay and by this mixture point of view theory and experimental results are agree with each other or not yes you can depending on the let's say on the amount of phenomenological information that you put in your model you can we will talk about this a bit more in the next part but but you can get better or worse description for experiment so if you do it honestly ab initio more or less then you expect to capture qualitative agreement between the experiment and and and the modeling if you want quantitative then you more and more phenomenological parameters have to go in in description of the environment and the molecule itself okay thank you thank you for the interesting talk I have just a short question you presented the first excited states the second excited states with the ground state but I think it's just in the born-openheimer approximation so if you want to resolve the Schrodinger equation and to do ab initio calculation we have to take account of the reverberational and rotational degree frame of the molecular so I think to compare to the experience we have to take account of this degree of freedom okay so this is a similar question to the one that has just been asked it is I totally agree with you that normally you would do a full raw vibrational or rotations are not very important important in this context because normally you are in a condensed phase and so they are so slow that all the energies will simply shift out of the window of your experiment but vibrations yes and depending on the on the let's say sophistication of the model and the ability to treat everything let's say honestly you have to and there are the studies where you basically calculate the potential with the fully like dft approach or or even full ab initio approach so and you basically model your dynamics as the evolution on that potential the problem with it is that as I said it it is very computer time consuming and it's never exact so you do it honestly you don't get a good match but what what you normally get is a set of approximations in quantum chemistry and so you do it with this basis and you get this result you do with the other basis you get another result neither of them is in complete agreement with the experiment one works better for vibrational dynamics the other one works better for the for the environment relaxation and so I think a bit more productive way since you have very many degrees of freedom in the environment is to actually take care of them in a sort of mixed regime so to treat them as a bath a set of harmonic oscillators if you want and couple your quantum mechanical system to the bath and then trace over the bath degrees of freedom and this is sort of the way you can still be able to calculate to model and to get good agreement with the experiment but one thing that I want to emphasize is that you don't even need to do that I mean for hand waving picture for for feeling how fast the energy is hopping along the ring for example how fast bacteria rhodopsin is isomerizing that you can still do just looking at the spectrum at the lifetimes and if you can correlate let's say you know from cryotrapping experiments that pigment is isomerized after you put light on it you know that the energy of the excited state should go down when it isomerized you look at the fluorescence you see it going down and disappearing eventually you know that it's your fluorescence and you know it's in one picosecond so that's already the information you did not know before you did the experiment and so you can even in purely experimental well you can still get a lot of ideas about how this molecular machine works without having to calculate it precisely so that's another thing that I want to stress so if you have any questions you can bother and professor van Gris during the coffee break I just want to stress a little bit about being back after coffee break at 11 even it will be a shorter time and I want to ask you to be here at the end of the lecture because we will have starting with 12 30 the feedback session and closing remarks and we are waiting from you your opinion about this winter college and the proposals for the next winter college so now let's thanks again professor van Gris