 Ich hoffe, dass jeder einen Kaffee hat und für Artus Talk bereit ist. Es ist mein ganz tolles Zeichen, dass Artus Edena, Professor von Kaiserslautern Universität, vielleicht mit dem neuen Namen der Universität jetzt, Rheinland-Pfälzische Technische Universität Kaiserslautern Landau, choose simple names. Ja, Artus hat seinen Untergrad in Wirkbroker Universität gearbeitet. Er hat seine Masterstudien bereits mit Marc Reisen in Texas verabschiedet. Er hat dann seine Diplomararbeit mit Ted Hensch gearbeitet. Er hat dann von dort weitergegangen, vielleicht im Immanuel Bloch zu Meinz, als er mit dem Immanuel gearbeitet hat. Er hat dann von vielen Artus zu wenigen Artus gearbeitet, als er nach Bonn gearbeitet hat. Und seit 2010 hat er den Kaiserslautern Universität gearbeitet. Er hat wirklich ein paar Arbeit gemacht, das für uns in diversen verschiedenen Richtungen interessant ist. Zuerst mit dem Respekt der Impurität, das wir sehr interessiert haben, mit dem Respekt der Quantum-Maschinen, in denen wir nicht so lange verabschiedet haben, aber vielleicht finden wir einen Ort für das. Vielmehr, ich habe es nur herausgefunden, als du das letzte Mal visitiert hast, weil wir uns interessiert haben, warum wir es nicht finden konnten, als du das letzte Mal visitiert hast. Es turns out, ich habe mit Paul Pilsen gesprochen, der erste PhD-Studie hier, in der Lapis-Lap, der ein Gespräch bei der Alumni-Fair steckt, wie ein Employee des Investors, und er sagte, ah, Artur, ja, sicher, er war Alexander. Genau, ich erinnere mich. Das letzte Mal, dass du hier warst, war es 2014, für die PhD-Defense der Fotos. Neun Jahre, wow. Wir sind sehr glücklich, dass du heute bist. Vielen Dank. Vielen Dank für die Invitation. Es war ein extrem erster Tag. Sehr interessante Gespräche, und ich erwarte, mehr zu kommen. Ich möchte dir heute ein bisschen über die Arbeit, die wir auf einem Experiment gemacht haben, wo wir, wie ich sagte, Single Atomic Impurities zu einem Ultracode Gas, bevor wir so zwei Szenarien über Kaiser-Slautern, für die, die keine Ahnung haben, wo es ist, wenn du nach der Rhine-River, also Nord-South, du kommst zu Mannheim-Heidelberg, du bist in dieser Region, und dann gehst du nach Weste, bevor du in Belgien oder der französischen Bordern hitst. Hälfte ist Kaiser-Slautern. Es ist eine Stadt, 100.000 Inhabitanz. Zu den Deutschen habe ich gesagt, es ist nicht Karlsruhe. Ich weiss nicht, warum, es ist einfach oft mixiert. Und wir hatten renownen Speakers, enden in der falschen Stadt. Kaiser-Slautern. Was ich dir heute sagen möchte, ist, ein bisschen über, ja, generell, warum Ultracode. Viele von euch might know this, but I figured, since the work I present today is not in a Boseinsenkonenzate, still why do we want to become Ultracode? What is the benefit of doing so? I'll tell you a little bit about the experimental tools. And then I have three topics I would like to discuss. The first is, how can we use single atoms as quantum probes to probe properties of the gas? The second is, how can we maybe, if we think about miniaturisation, use a single atom as a quantum engine and really, well, do work with this? How can this be understood at all? And then in both cases you will find one peculiar observation, that is if we look at the spin distribution in the non-equilibrium dynamics, that we reach a point of entropy in the system that is maximal. And that was striking until I met a colleague and with him we now do a project or we did a project on a phase transition in time in an open system. And I'll explain you, if time permits, I'll explain you what this is. And if there are any questions, please feel free, interrupt me, ask. I'm happy about this. So this is the team and let me first point out the PhD student. So that is Jens. He is for the machine and the probes, the one. Sabrina and Sylvia, the next generation students and Julian, he started a year later. The others are master students and let me point out collaborations with Eric Lutz in Stuttgart and André Eckartling-Navoux and Alexander Schnell in Berlin now. And we get funding from the German Science Foundation and State Research Centre of Dimas. All right. So, why ultra-cooled atoms? So, you all know because it's cool, it's ultra-cool, but you can do a Bosein-Serkoholensate, but as I said, that's not what we want to do. We want to go to ranges where the de Broglieway, so here is a temperature scale and you see we want to go to a temperature region here around nano-Calvin where the de Brogliewave length becomes large, that we see it easily. We use laser cooling for this and actually this I skip, laser cooling is done, you know. The dream I started with like it's now 15 years ago is the following. Why don't we take a Bosein-Serkoholensate or an ultra-cooled rubidium gas and put in a well-controlled number of impurities, in this case cesium atoms? And the way I envision to do is to just shuttle them in using some kind of conveyor belt. And I'll tell you later that that is exactly what we have realized. And the question is now what can we expect? What is the picture you should have in mind? What are the relevant energy or scales that we have? And let me contrast this a little bit against our everyday experience in air. So if you look at the temperature in our ambient air it's of course room temperature 300 Kelvin whereas in the ultra-cooled gas as I said here far below micro-Calvin maybe 100 nano-Calvin. The direct consequence is that from hundreds of meter per second if we could pick out a molecule here we would have few hundred meter per second down to centimeter or even millimeter per second. And that means that technologically it is absolutely possible to track the motion of single particles in the trap. So in principle that is possible. At these low temperatures of course you would expect that the ground state of any system is a crystal. And the same happens for us when we are dealing with a chunk of rubidium or whatever we need to dilute the system and go from particle densities in air of 10 to the 19 to maybe 10 to the 12, 10 to the 13 per cubic centimeter. And that makes the collisions that form a crystal extremely rare and thereby we can work with a gas on a relevant time scale. If you look at phase-based density that means the product of density and de Broglie wavelength cubed then in air we have a very small number but most of you will know that in cold gases this can become significantly larger than one than you form a bosonic condensate not so relevant here but what is relevant is the collision rate that you have in these gases so how many collisions do particles do per second and in air we have a mind-blowing number of 10 to the 9 to 10 to the 10 per second whereas in our experiment on the order of one collision per second maybe one collision per millisecond and again that is a time scale or a rate that is experimentally absolute easy to follow we can see in principle the consequence of each individual collision in the gas and what we can do with this well, lots of things classically it can be a model system for friction or diffusion but especially for quantum systems like a study of open quantum systems study of decoherence and the dream is that we do condo-physics and really simulate see effects that have been predicted for solid state physics good, how do we do this and the sketch again that you should have in your mind cloud, atom, we shuttle it in how do we do it the heart of all this is a vacuum system that is shown here these blocks are iron pumps everything takes place in this glass cell here and I usually say the whole lab that you'll see on the next slides is there to look and to shine lasers from all directions into a volume of 100x100x100 micrometers so that's where it all takes place and the whole lab is just there to serve this purpose if you work with single atoms and gases it is clever to find a way to produce the gas, the cold gas or the Bose-Einstein condensate very rapidly because the statistics is limited by the single atom if you have one result the Bose-Einstein condensate is gone and then you have to redo it again and if you work with single results from an experiment then you have to accumulate statistics and doing here an experiment a Bose-Einstein condensate in 40 seconds or 4 seconds is the difference between 4 year PhD or 10 year PhD so it's a real significant change and therefore we took great care to optimize this so we have laser cooling in 2 Dimensions here forming a brilliant beam of rubidium into this glass cell here we trap it all in all optical trap we evaporate and produce a Bose-Einstein condensate in a few seconds and this was optimized among others by for example a genetic algorithm keeping track of keeping track of all the subtle correlations that is my pointer okay so it's a cool thing because people can see it also on zoom but sometimes it crashes so this genetic algorithm or evolutionary algorithm keeps track of all these technical correlations that you don't know and you don't want to know it just optimizes it and the PhD students don't like to hear it but whenever they optimize it the algorithm could get a factor of 2 or something so it really pays off in the lab it looks like a standard quantum gas lab there is one table here for all the lasers we well prepare all the properties like frequency, intensity, polarization whatever you like then couple it into glass fibers feed it over the ceiling and the vacuum system is here buried in three layers of optics quantum optics labs good now, you are familiar with quantum gases let's turn to the single atoms what we do to get single or a few atoms is we take a laser cooling region a magneto optical trap but we reduce the loading rate a lot that we do by cranking up the gradient of the magnetic field and this is the very very first picture of our single atom mod so here you see the aperture of the objective and something fluoresces and if you now look at this over time then and plot for example here the fluorescence rate as a function of time then you see individual steps and you see dynamics going on if you do statistics on this then you can assign these levels to the background light and the presence of one atom two atom, three atoms and so forth in the trap so we know exactly from the fluorescence how many atoms we have and that's fine the problem is we don't want to have our atoms fluorescing all the time we want to trap them also in a trap that is where they are dark where we can do quantum physics with them that means we need a dipole trap that is ideally seen only by the cesium atoms and what I plot here is the dipole potential that is exerted by laser beam of a wavelength that is shown here onto the two atomic species rubidium in blue what do you see is for any of these alkali you have two resonance lines and these resonance lines are the positions where the dipole force or the dipole potential diverges you see that on the left and to the right of this resonance the dipole potential has a sign change and that is what you know from physics 101 a driven harmonic oscillator if you drive it above or below the frequency if you go across the resonance frequency you get a exactly the sign change we see here or the phase jump of pi and you see because of that directly between the two resonance lines there is a zero crossing of this dipole potential that means there is one wavelength where one species does not see any dipole potential of the laser for rubidium it is here at 790 nanometers and at this wavelength cesium is far detuned and you see a potential for cesium rubidium does not we tune our laser to this wavelength and we shine two counter propagating lasers to form a standing wave and trap the single atoms as shown here in the minima of the potential and now we can detune the laser beams a little bit by using acousto-optical modulators and that sets it in motion and we can shuttle the cesium atoms in our trap as we wish and here is a picture what you see here are three atoms so we have these marble properties completely under control and now to show you how we take our data and what's behind then later on all these data points that we have let's imagine if we could see the traps in our glass cell there is a cross dipole trap shown indicated here in red and just 180 micrometers away from the crossing region is the laser cooling region so we have a single cesium mod now we can do a very simple experiment we can release the cesium atom into this dipole trap it will do some motion and after a certain time we want to know where it is we flash on our lattice we freeze its position then we take a fluorescence image and that is what we get so in every single run we get one of these images here in the first one we have five atoms then we get classical probability distribution and if we are interested only on the axial position we bend this vertically and get the axial probability distribution as shown here and then we can do this of course time resolved and see for example here in a very simple way one quarter of an oscillation period of the atom in the trap you see the center of mass does just simple oscillation the shape changes due to residual temperature und because there is anharmonicity due to the crossing region so this shaded area indicates where the crossing region is nothing special but now we can put the rubidium cloud in the crossing region and what we observe then is that the cesium atoms get stuck and that is also not so surprising its diffusion just by elastic collisions the cesium atom lose energy they become diffusive but now fun starts and now we can do physics looking at the interaction between single cesium atoms and the rubidium gas and now we have to talk for a few minutes about interaction processes and atomic physics so the picture you should have in mind for the rest of the next 20 minutes maybe is this one its really the gas is a classical gas point like particles there is one impurity and you interact you collide with the cesium atoms from the gas and of course now you all know there is one interaction process that is usually there and that is elastic interactions what does elastic mean elastic means that the kinetic energy is redistributed among the colliding partners but the internal states are preserved and with internal states I mean here the hyperfine states of the atoms, rubidium has a ground state, hyperfine ground state ethical one with sub states that are indicated here as these little rings and this is preserved and cesium has an effigual three hyperfine ground state and seven Zeeman sub states and again these are also preserved in the collision so these elastic collision they lead to thermalization, they lead to later on we will talk about coherence properties and decoherence defacing so that is associated with some kind of scattering length A associated here with this elastic collisions for a large part of the talk we will be interested in a second process and that is spin exchange and as the name says the two colliding partners exchange one quantum of angular momentum so rubidium in this case enhances its angular momentum and cesium gives away one quantum of angular momentum and this is as you can imagine a flip of the spin here a little more complicated because the spin state is larger but that's in principle not a big deal now we have to talk a little bit about the details of these spin exchange processes because that will be important so these processes have a certain scattering rate or scattering cross section and that can be calculated by coupling channel calculations I do not talk about this much more we don't do them I mean in the meantime we do it ourselves in the beginning we took them from Ibar Timan he is an atomic physicist from Hannover and did for decades calculations of molecular potentials where all these numbers came out with extremely high precision and here is an example of what he can calculate for us so what is shown here is the scattering cross section for the spin exchange collisions that depend now on the internal state of the rubidium atom that is fixed to one Ziemensubstate and all the different lines correspond to different Ziemensubstates of cesium I didn't even bother to write it on there because it doesn't matter for you it's just important it's all different and there are very different regions where this scattering can have different character there are regions where all the scattering cross sections are essentially the same there are resonances and these are low-lying Feschbach resonances that occur also in the spin exchange and you see there is a region where a new process comes into play and I'll talk about this in a minute first let's focus on this case and I want to show you that also experimentally we see all this so let's go to one of these magnetic fields here and let's see what happens we prepare the cesium atom in a spin state we let it evolve and what we expect is that by individual spin exchange processes the spin changes so goes to the other extreme value and what is shown here are the seven Ziemensubstates with the initial population prepared here in the uppermost and as a function of time you see color coded that the population indeed is brought to the other extreme so it just goes completely down and here of course we do it with full counting statistics we see for every single atom how many collisions it has made but we need to take the statistics in a quantum mechanical sense now let's go to one of the zeros here of the Feschbach Resonance and what you find there is indeed that we can block one of these channels essentially and if we compare this with a model with a scattering cross-section by Ibar Tiemann it fits here to a percent level so we know very very well what the spin dynamics of our atoms are okay now we need to talk about this region where this additional process comes into play and for this we need to go one step further into detail of the rubidium cesium system what I have shown here is the Zeeman splitting in a given magnetic field of rubidium and of cesium and you see that the values of the Zeeman splitting changes or is different by a factor of 2 this factor of 2 comes because the Lande factor this Gf factor differs by a factor of 2 in die Zombriatomic physics lectures this Lande factor summarizes just all this complicated angular momentum coupling of the nucleus with the electronic shelf so this is all hidden in this Gf and it just turns out that there is a factor of 2 difference now this has a consequence let's imagine rubidium goes down from this M equals 0 state to an energetically lower lying state and cesium takes this up so in other words angular momentum conservation is fulfilled and energy conservation says cesium has half of the energy left that is kinetic energy and it's dissipated by elastic collisions in the gas and in our case we have 10 elastic collisions on average between 2 spin exchange collisions so it re-thermalizes no problem we call this collision an exothermal collision it can always occur now let's imagine rubidium is down here and wants to go up so cesium if it goes down can provide half of the energy but the rest is missing where is it coming from and the only way it can come from is from the kinetic energy of the collision and these endoergic processes therefore cannot occur every time for every collision but it depends on how much energy comes from the thermal distribution that means if rubidium wants to go up half of the energy half of the cesium spin change and the rest must come from the thermal energy distribution and if you plot here the distribution of collision energies you see this grey shaded area all the collisions here cannot contribute to an endothermal collision only the purple shaded area has enough energy to really promote the endothermal collision so that will be the most important tool that we use because what it does it couples the thermal distribution of the gas to the internal quantum states and this will use from now on in every possible way this fraction can be calculated it's not a big deal there is a formula you can integrate it and then you find here the probability for these endothermal collisions is just a function of the temperature of the thermal energy and the magnetic field of the Zeeman energy with the Zeeman splitting with the width of the thermal energy distribution that's all alright and with this we can now make the first experiment and what we'll do now in the following is what you see here is a typical result here the 7 Zeeman substates of the cesium impurity that is the population of the individual impurity and this is the time evolution that we have in a polarized state then something happens you have dynamics going on and then eventually it will come to some steady state and in the following I will first explain how from this we can make a probe like a thermometer for the gas in several ways and in the next I will explain how we can engineer to use this as a little machine to really, well in our case we don't extract work of an Otto cycle that we do in the system alright Thomas okay so in our case first the gas is so dilute that three body collisions are I mean they will limit us but they are very rare so in the cesium we have like five maybe ten cesium atoms they are during this experiment usually separate from each other by the optical lattice so there is one in each exactly and even if it was not then the probability would be a factor of 100 larger than a three body recombination so we exclude this good so let's talk about thermometers and this brings us to the question und the paradigm of the thermometer is you take a system a sensing system you stick it into your target system you let it equilibrate and then you measure some measure of mean kinetic energy right, that's what usually most thermometers do and this you can transfer to the cold gases and many people have done it so you can just take impurities and measure the maxl-woltzmann distribution and assign a temperature to this and that has been done many many times before so for example people have done this and looked at different Zeeman states in a rubidium cloud that stands by current group there are groups that stick little bozeinsen condensate in large fermi clouds in woody grims group and we also measured the kinetic energy distribution of our impurity and by this looked at a thermometer that's all possible but that's all a classical thermometer right, you look at the kinetic energy distribution we want now to map thermal information onto the quantum states to really make this a quantum information and the difference is that the equilibration to the thermal energy distribution is done by the elastic collisions and the key to map this onto the quantum states is the spin exchange collisions and as I said it is exactly this comparison of Zeeman splitting by the thermal energy distribution so what we do is exactly now this sketch, we shuttle the cesium atoms into the gas let it evolve and then measure the spin population distribution as a function of time and let's see what we learned from this that's exactly the same data you just saw now let me give you one intuitive explanation of what happens you start here with a polarized with one spin polarization you let it run you see there is a lot of dynamics going on but the dynamics goes on because the endoergic processes tries to push the population to the right the exoergic tried to push the population to the left until you reach in the end the steady state now let's go to the extreme limit if we had hypothetically t equals zero there were no endoergic collisions and that means the steady state would be just all population in the extreme state down here now every little bit of temperature gives you a little bit of endoergic collisions and that means the temperature information must be in these small fluctuations here that bring you away from the smallest energy state so we just looked now at the energy fluctuations of this steady state distribution that is just the variance of this and here I plot this energy variance in divided by kb as a function of the gas temperature and what you see it's really a very nice line so that's what you hope for a thermometer that the quantity you measure these fluctuations are somehow proportional to the real temperature the only problem could be and now you can imagine what could change this because it's the steady state it cannot be the initial state it cannot be the atom number or density in the gas it cannot be the number of physics change collisions because in the steady state you don't care about all this the steady state is just a question in the end of the rates that you have the only thing that could now modify the slope of this is the magnetic field you are at and this is shown here that the slope is essentially in the range we look at so if resonances come then resonances are not covered by this so in principle that works and we thought we are happy until we noticed if we look here at the time 400 milliseconds and tomas question yes why do you do the portrayals not just the average spin that should also be taken yes I mean there are several ideas you could have one would be to fit a Boltzmann distribution but then you could argue that a Boltzmann distribution already sticks in some knowledge that it should be a temperature or something and to just look at the fluctuations was the most model independent quantity we could think about and you say you want to look at the spin distributions directly you get more information out of that than this expecting this linearity between the fluctuation and the temperature doesn't I mean this is not an expectation this is really now here inferred this was not clear from the beginning it could be different and I agree if you calibrated once then it's also fine but yes in the end maybe it's yes you can expect it if you see what I said it's just a comparison of thermal energy with Zeeman splitting there is not more to this I mean here the final state you just wait long enough and you measure the population so the question is you saw the pictures of the individual atoms so what we do is we selectively decide one MF state that we want to probe we remove all others from the trap and see if the atom remains so we do it in a very inefficient way because at that time we had no other means now there are some other camera technology is much better that we can do this much faster in a different way at that time we had to do it very inefficiently what I wanted to say if you look at the times here and what Thomas asked before about three body recombination this is a timescale indeed where the cesium atom can get lost and we were aware that this is not the best way to do on the other hand you can ask there is a lot of information going on in this non-equilibrium distribution and the question is can you learn something from this and in particular one question was what's the entropy of the system doing so we just for fun or we checked what is the Shannon entropy of this distribution as a function of time and what you see is that it peaks extremely fast after just three spin exchange collisions that is the case when you have here the most extended spin distribution before it relaxes to the steady state and the question was this point in principle tells you that there should be a lot of information in this system how can we extract it and clearly if we are in the non-equilibrium not in the steady state then we cannot expect that the information here is independent of everything but we have to put knowledge in to get the information out so we had to make a model of the spin dynamics it's a very simple rate model where we have here all the difference even spin states between the states and the modes population between them for the exo or the endoergic and each rate is a product here of the mean gas density the colliding velocity and that's where the thermal distribution comes into play and the scattering cross section and this value we get from Ibarthiemann it's in general magnetic field and temperature dependent so with this we model the dynamics and then we just model it and make a least squares fit and see at which temperature we get the best agreement for the given interaction time that is an example here the histogram is the model and the data points is our data so there we get also after much earlier after just three spin exchange collisions temperature information of the system and now the question is how good is it and what I show here is a graph that is showing on the vertical axis the temperature we get from our cesium spin that means the cesium atom and we measure the spin population and on the horizontal axis we take the temperature of the rubidium gas by time of light velocimetry so different method, different system just in thermal contact and this is not a fit but that's just the equality line so same temperature everywhere what do you see, there are deviations where we have to admit what we find however is that indeed the error that we have here in the spin population measurement is significantly smaller than for the time of light velocimetry and the reason is that at these low densities where we are density measurements are difficult and therefore the systematic errors increase so in principle that works and now the question that you could have if you talk about a sensor is how sensitive is it and what do you get and the sensitivity can be defined derived as follows so our spin population can be written as a density matrix that is diagonal you have here the population for a certain spin state and the ends of the spin state that you have and then you have to ask the question if you have a different population at a slightly different temperature what is the difference between the two states mathematically you can cast the difference between the two populations into a length kind of length that is called the Bures distance and depending on where you look there is also something called the Hellinger length that is a classical measure in our case because we don't have any off diagonal elements it is purely classical diagonal system then you can ask the question if we now take this Bures distance for very small changes of the temperature we can make a Taylor expansion and the proportionality constant in front of this Taylor expansion is something like the square of the Fischer information that we take as the sensitivity so how strongly is the change if you make a little deviation from your original temperature and this can be calculated now for all the for all the data points we have and what you see here is for the same data points as we had before as a well here is the sensitivity as a function of time the dash line is the ideal steady state sensitivity where it decays to and you see that in non-equilibrium you beat the steady state sensitivity by an odd of magnitude that means in this non-equilibrium dynamics you can measure temperature much more sensitively than in the steady state and the intuitive reason is I told you it is the endo-urgic collisions that give you the information so what the system has to do is to distinguish how many endo-urgic do you have compared to the exo-urgic in the steady state it's a difference of the rates that you have that make this little fluctuations in the non-equilibrium with the state we start with it is all the population that is to the right to the higher MF states compared to the others that give you this information with the lowest ratio of the two rates that you have in the end all right now you cannot only do this you can turn this around and do a magnetic field sensor because in the end it's just a comparison again of the thermal distribution with the Zeeman splitting that means for a fixed temperature you can also infer the magnetic field that you have and here is the magnetic field versus the rubidium gas magnetic field that we infer by the standard radiofrequency spectroscopy and here the same works also nice and also the sensitivity peaks here after a couple of spin exchange collisions yes please I think they are swapped right I think the two graphs are swapped ah I'm sorry that exactly it is maybe we go to this graph the question is how steep if you're at a certain point you want to know how well can you measure for example temperature if you make a very small change along magnetic field and so you're interested in so you wiggle along this line on one temperature then you change the temperature a little bit in one direction or in the other and that means you look at the curvature of your change along for example the horizontal magnetic field axis so it's really the question if you look at the sensitivity along the magnetic field axis or along the other axis I think the two graphs were swapped on your slides if you just go ahead stop there so that one should be in milli kelvin now it's in milli gauss according to your explanation and then the next one is the one in vice versa or not let me see if I have this is the sensitivity of the moment it is no let me see I hope I have it here so you see I prepared 100 yeah it's ah da da da so maybe I don't have it here but we looked into this in more detail so it's really the question in which direction in parameter space in which direction in parameter space you go so you have a sensitivity with respect to temperature changes or with respect to magnetic field changes and it might be I did not swap, it's really here the change of temperature so you have a given temperature and you want to know all your magnetic field change and the other I can show you also but I think it is not swapped it is really what we have here but anyway I promise I'll show you but it's in another talk good so very short I wanted to show you that we can also do this using coherence because I know you're interested in this so what we did is we did this so so so so so so so so so so so so so so so so so so so so so so so so so so so Das ist eine Funktion des Magnetik-Fields. Das ist der Quadratik-Siemann-Schiff. Das ist alles sehr gut unterstattet und wir nehmen das in Anruf. Wenn wir das jetzt in den Robidium-Gas bringen, dann sehen wir zwei Dinge. Hier sind zwei Remse-Fringer, wo wir hier die Zahl der Caesium-Adams in einem Spin-State als Funktion der Fähigkeit der letzten Pi über zwei Pulse. Und ihr seht, dass es die blaue ohne Robidium-Klaut ist und die grüne mit Robidium-Klaut ist. Und ihr seht, dass es zuerst eine Fähigkeit der Fringe ist, d.h. es gibt eine zusätzliche Präzession der Bloch-Vektor und es gibt eine Reduktion in der Amplitude, also eine zusätzliche Diffasung oder Dekoherenz. Und beide geben uns ein Stück von Informationen und die Frage ist, wie wir es verstehen können. Um es zu verstehen, müssen wir wiedersehen bei der Molekulopotenzia, bei der Interaktionsstrengung und bei dem Magnetik-Field, wo wir sind, gibt es wieder eine Fäschbach-Resonanz, zwischen der Robidium-Klaut und einer der Caesium-States. Und usually, if we talk about Fäschbach-Resonanzes, you know Fäschbach-Resonanz only as a function of magnetic field, you have the typical resonance line. However, in our case, the Zeeman-Shift and the thermal energy are approximately the same and that means we can tune the Fäschbach-Resonance not only by the magnetic field, but also by the collision energy. And these are lines calculated by Ibar Tiemann for particles having a well-defined collision energy and you see that the resonance position shifts with collision energy in a very well-defined manner. So what we do in the following is, we go to one magnetic field, we fix it and ask the question, how is the scattering length distributed over collision energies. And that's the answer. So this is the scattering length as a function of collision energy and what you see is that for very low collision energies you have extremely high scattering lengths and for higher collision energies you leave the Fäschbach-Resonance for this one magnetic field and there is no, you have left the resonance. Yes, please. Of collision energy. It's the cross-section explained, in the end the scattering length is the absolute approximation if you have no energy dependence anymore and you neglect this 1 over k dependence. So it is the square root of the cross-section. Exactly, yes. All right. So now you can ask the question, how is for several temperatures the scattering lengths or these cross-sections here distributed? And the answer is here. For a very small temperature you have a strong contribution of the low collision energies and that means you have a large weight here of the strong decaying cross-section part. For higher energies you include more collision energies but all these collision energies contribute the same scattering length or cross-section that is shown here and essentially does not change the mean value very much. From this distribution we get now two pieces of information. The first is what is the mean scattering length or cross-section and the second is what is the distribution of scattering length or cross-sections. The mean one, that is the one that is responsible for the precession of the block vector. What is shown here is the mean scattering length or cross-section as a function of temperature and it tells you for lower temperatures the block vector will precess faster and for higher temperatures it will precess lower. If we look now at the dispersion at the variance of this distribution we find that and that is counterintuitive for small temperatures we have a larger variance of this distribution and that means more defacing and that is just due to the proximity to the Feshbach resonance and at high temperature we have a much lower defacing. Ah, that's strong, complicated. For the moment you can just keep in mind as a function of temperature the angular velocity without the block vector precesses changes and at the same time the speed without the block vector the phases or disperses also changes. So now what we can do, we can do an experiment and what you see here is Ramsey fringes for every cut here you see the phase of the last pi over two pulse and in color coded the number of atoms so you see here a typical sinusoidal Ramsey fringe as a function of interaction time and what you see here the slope that is the changing phase that is due to the interaction with the mean field of the gas that just changes the phase. At the same time what is not shown here very well is the decay of the amplitude and that is here shown again in the visibility in this Gaussian decay of the amplitude of the visibility. Another question is can we from these two numbers the phase shift and the decay can we infer temperature or density information? And the first thing is if we look here what we expect is that for low temperatures the defacing will dominate and we will not be able to follow the phase shift for high temperatures defacing is very low so we will be able to also follow this phase shift change. So the first experiment is we look at a density variation and behind so what is shown here is at one density we take a full time evolution of the phase and each point here is a difference between the Ramsey fringes with and without atomic cloud. So the density induced change of the phase is the slope and this slope is shown here for the correct density. And if we increase the density we expect that the slope or the detuning the defacing should follow this we see a strong deviation here but it's not surprising because if you look at the T2 time the defacing time it decays it goes extremely fast down it's just a few milliseconds here and if you look at the defacing still there is not enough time left defacing time to resolve this phase shift so that means that it's consistent with our observation and the most important information comes here from the defacing as a function of the density. We can however also do this as a function of temperature and there again it does not really is not useful to look at the phase shift because the phase shift essentially is gone we don't see it, we cannot resolve it it defaces too quickly what we instead do is we look at the visibility change and from this deduce the T2 time again behind every point here for a certain temperature there is a full visibility curve and behind every point here of the visibility curve there is the difference of amplitude of two Ramsey fringes with and without rubidium cloud so this is the rubidium cloud induced defacing that changes here indeed as we expect in a certain manner with temperature for small temperatures we have a strong defacing for higher temperatures we have a smaller defacing and this counterintuitive behavior again is just the consequence of the proximity to the Feshbach resonance and people didn't believe that we were doing our math right with people I mean some referees of papers so they made us do some Monte Carlo simulations which we did and it agrees very well also with our expectation here so this model is a very simple one just looking at every collision taking some effective phase shift into account but it works and is somewhere hidden in some supplemental material ok so much on the probe and now I see that the time is almost up I have something on the engine I would like to hear about but I don't want to I speak a bit faster ok let me start with what is an engine and what you all know is a typical auto engine you have a fluid in your motor and what you do is you heat it up by igniting it it changes temperature by keeping the volume constant and then it expands that does the work and then you get rid of the fume of the exhaust which reduce the temperature you bring the vessel or the cylinder to the piston to its original position and you close the cycle and the figures of merit are the efficiencies so how much work can you output per energy that you put in and what's the power so the energy per cycle time is intentionally very suggestive to use the harmonic oscillators because people early on ask the question how can we go into the quantum regime and if you have the harmonic oscillators well you just quantize them so then it's very simple that you also have here thermal distribution of populations and you do exactly the same and people have done here theory on this and this is pretty well developed and people have done first experiments there was a very famous experiment in science by Fenerentz Mitkala in Kilian-Singer there was still a classical engine so there is no quantum levels involved but there were others here on spins and NMR systems or also Pekola here on solid state systems is working a lot of it so that is all a lot of interest in these kind of engines and one important thing maybe is how do you define heat and work in the system and I follow the standard way to do it that heat is in this picture of the harmonic oscillator you keep the energy splittings constant but you change the populations that is shown here the energy splitting or the harmonic oscillator frequency is the same you just change the populations among them that is heat and work is you keep the populations but you change the energy splitting by changing the frequency in this defined I follow this and now you look at this and you think ah equidistant levels that you can tune that looks like a spin system that you could do and we were thinking maybe we can do this in our system so here is a spin system equidistributed the same cycle why don't we do it and then we did theory and if we have the temperatures we can afford like 200 nano kelvin and 1000 nano kelvin I hardly see any difference in the first row you might see there is a teeny weeny 1% population change here and that would be the one that does the job I thought I talked to Eric and I said let's forget it I'm not going into this business and it's even worse it's even worse if you think about thermal states you all know from quantum optics that the fluctuations of thermal states are larger than the mean that's fine in an engine we have 10 to the 23 atoms and you form a decent average but if you have a single particle and you run an engine with large fluctuations then in one cycle you have high power in the next cycle because of these fluctuations it's very small and you have one that is stubborn on the highway that's not a good engine and there was a lot of theoretical debate can quantum machines be efficient at all if they're efficient can they output large power if they combine high efficiency and large output power can there be small fluctuations and there were two papers that solved this a little bit as saying there is a trade-off between power efficiency and constancy or you have to somehow use the cycling to tame these fluctuations and that's all for thermal states now the cool thing is we don't have to stick to thermal states what we can do is in the spin system we have a bound system and we can do population inversion so what we did instead is the following we use instead of heating we use spin exchange and instead of thermal energy we use spin polarization we bring the engine which is the single atom into a bath that is fully spin polarized and the spin polarization is here the energy that is stored the fuel the spin exchange now is directed and that is in these bath states the energy to the engine until you are completely polarized now you are in a state that can do a lot of work and the work is done here we change the magnetic field it could be a magnetic field gradient where you do work in and then to cool the system we bring it into a gas of opposite spin polarization and now every spin exchange takes out energy from the engine and that is like removing we change the magnetic field to close the cycle and that is the same cycle now in a slightly different way instead of heat in a thermal bath we have spin polarization and the Zeeman energy transferred to the system so the nice thing here is again the spin polarization is the fuel the heat transfer between engine and bath is directed and the work is performed by adiabatic changes of the magnetic field and this is an auto type cycle that you can run you have full counting statistics and in addition to the mean energy that you put to the engine or take from it you also have information about all the fluctuations that we can now study so now the question is like what's the figures of merit what's the efficiency, what's the power and this we can calculate and for the efficiency there is a fair and an unfair comparison the unfair comparison would be you say what's the energy that goes into the engine in this output then we are perfect then we are at a formula that replaces the Carnot efficiency instead of the thermal of the temperatures of the thermal bath we just have the two magnetic fields we are in and there we have an extremely high efficiency but that's not fair because I told you that the laundry factors between rubidium and cesium are not matched so in this you have here the ratio of the laundry factors entering and the efficiency drops to still surprising almost 50% and that tells you in the end what we conclude from this is that this engine is something which is called endo-reversible the engine internally runs completely reversible it's a unitary operation of course how could it not be it's a single atom, nothing surprising and the only losses occur is that there is no contact to the bath and there is a heat leak that wastes part of the energy about the power the power can be also extracted by standard means looking at all taking from data the energy we put in take out in the cycle time and here as a function of time you see it peaks and up here this is the number of collisions that we have in both ways so intuitively the highest power 6 collision downwards that is the 12 unfortunately the last collision has a lousy scattering cross-section and therefore the 1 over T decay of the power is already decreasing this and therefore the maximum is a little bit before the 12 collision and that means it tells us the highest power is if we go completely to saturation to population inversion and then if we have this all what comes is a 1 over T law so that the constant interest cycle time is increased and the last is the fluctuations where we just look at the fluctuation of the population distribution normalized to the population distribution and what we find is we go to a regime in the end at population inversion where we have supersonic fluctuations and if we plot it all together we see we come indeed to a position where we have maximum power output high efficiency and low fluctuations because we're in this regime of population inversion alright let me skip this very cool project at some point you'll read about this goes into a universality of the dynamics that you see afterwards and let me point out the people that I'll show you in a second are because I have more projects there is an ultra-cold Fermigas BCBCS crossover which is a combination with disorder potentials and also recently built a many body engine we have a quantum computer demonstrator together with my colleague Kavik Ott Thomas Niederprüm, Klaus Engstock from Hamburg and Henning Moritz and Peter Schmelcher that's a fun project and I have a solid state project of envy centers and nano diamonds where we bring them all to the tip of an optical fiber here you see to silver wires and the glowing green point here is an optical fiber for the excitation of this nano diamond because of these many projects I have many people with lots of work and much dedication and I thank you for your patience and your attention, thanks