 Good evening everyone, it's great to see a full house here. My name is Ed Hines, I'm a physicist from Imperial College and I'm here to introduce the prize winner this evening, Debbie Jin, whose work I followed from, well I'm long enough to say, I followed it more or less from the beginning. And so by way of introduction, let me just tell you a few things about Debbie that she would be too modest to tell you herself. She graduated from Princeton University and got her PhD from the University of Chicago. She is now a fellow at the National Institute of Standards and Technology, which everybody calls NIST in America, that's the American equivalent of the National Physical Laboratory. And she's a professor at the University of Colorado. She leads a group in Gila, which stands for the Joint Institute for Laboratory Astrophysics. Gila, I would say, is a leading institute, possibly the leading institute, for atomic physics. In 2003, her team made the first Bose-Einstein condensate of filmionic atoms, that is to say atoms whose spin is a half integer. Probably most of you know that particles with integer spin are called bosons and they have the property that they like to all do the same thing and when you put them in that state where they are doing exactly the same, that's called a Bose-Einstein condensate. So what she did was make a Bose-Einstein condensate without using bosons. So this is an interesting and important achievement. The trick is to make these fermions which have half integer spin pair up. Once they make a pair, then the pair has an integer spin and then after that they're able to to Bose condense. So she made the first exploration of what happens as the atoms cross over from being separate fermions to paired up bosons and in the course of that she developed and perfected the use of something called Feshbach resonances, which allows one to control the interactions between the atoms and how strongly they interact with each other. Some people have noticed that this pairing behavior is an important thing to study because it's exactly what electrons do in in superconducting materials and what helium-3 does in superfluid helium. But the difference with the atomic gases that Debbie has developed is that you have tremendous control over all of the parameters of the system, including as I told you that the strength of the interaction between the particles. So this makes her lab has become a kind of test bed for understanding and studying how particles interact in this kind of quantum many-body system and do the fermions pair up and form a Bose condensate. In a separate experiment she's looked at how bosons interact, how Bose condensate made of bosons works when you control the interaction between the particles. And she was the first to demonstrate and measure a thermodynamic proctical contact which was theoretically predicted to be something that you could say general about about complex systems with strong interactions. But finally I want to mention one other of her experiments which grew out of the study between of how bosons interact with fermions, spin integer and spin half integer interact with each other. And so that's developed in collaboration with Junyi who is also at Jilla into an experiment that has allowed her to make ultra cold polar molecules with a density and a temperature way beyond what was previously possible. And this has made the quantum gas of polar molecules a really important new research tool. I think she'll probably talk a little bit about these potassium through a billion molecules. With these she's able to control the chemistry so if one of these molecules approaches another one she can put them in a totally defined quantum state and control whether these molecules interact or not. So this is fundamental control of chemistry which I think is very interesting for a physicist at least we were just discussing you're not going to make kilograms of stuff this way. But nevertheless it's an important thing for understanding basic things about chemistry. The significance of all this has been recognized by a lot of the boards. I'll list just some of them. In 2003 she won the physics MacArthur fellowship which some people call the genius grant in physics. She won the Rabi Prize of the American Physical Society in 2005. Benjamin Franklin medal in 2008. Gold medal of the US Department of Commerce in 2011. The L'Oreal UNESCO Award for Women in Science in North America in 2013. And the Comstock Prize of the US National Academy of Sciences in 2014 this year. She has been elected to the US National Academy of Sciences. Anti-American Academy of Arts and Sciences. Okay that's a long list of awards and then there's one more which is what brings us here today. The Institute of Physics Isaac Newton medal which is awarded to a person of any nationality for outstanding contributions in any area of physics. This is the Institute's most prestigious award. Previous winners are John Pendry. I list the names because I think you know them all. John Pendry, Martin Reese, Leo, Kadonoff, Ed Whitten, Alan Goothe and Anton Silinga. So this is a list where Debbie certainly belongs and I'm delighted that she's joined the list and it's my great pleasure now to introduce her to talk about ultra-cold gases. Okay thank you very much for the very kind introduction and it's certainly my pleasure and honor to be here today and to have a chance to tell you a little bit about some of my research. So I'm going to talk today about ultra-cold gases. It's not going to be a comprehensive talk. I'm not going to talk about everything about ultra-cold gases but just some of the things that I've worked on. This is a picture of Jella, this joint institute of laboratory astrophysics. It's a joint institute between NIST, the National Institute of Standards and Technology in the U.S. and the University of Colorado. All right so what I'm going to tell you about today is just a gentle introduction to ultra-cold gases, what they are, why they're interesting, extremely little on how we actually make them and manipulate them. Then I'll talk about some of the quantum behaviors that we see, the quantum behavior of bosons and fermions and I've highlighted the one I prefer. All of this is to get to the point to tell you about the Fermi condensate which is something that we are continuing to study in the lab today. Okay so ultra-cold gases. So I'll start with just a little bit of motivation, why you might be interested in what happens at very low temperatures. That's what I mean by ultra-cold, extremely low temperatures and basic motivation is just that you can see new phenomena if you go to some extreme regime and temperature is one regime you could look at. You could go to very high energies like a particle accelerator or you could go to very low energies or very low temperatures and ask what happens. So just to motivate this a little more let's look at say a temperature of at the surface of the sun that's about 6000 degrees celsius and I want you to imagine that you're a scientist that lives on the surface of the sun okay so this is your ambient temperature this is what you see every day you look outside what do you see you see everything is a gas or a plasma but since you're a scientist you have a laboratory there on the surface of the sun and you're able to reach much lower temperatures. So now what can you see? All of a sudden you see things that you've never encountered things like solids and liquids the things that we're used to here on the surface of the earth. Okay so this just gives you an example of if you go to some extreme temperature that doesn't exist in your ambient environment you might find some new behaviors particularly of matter. So we're going to start here as this is sort of our room temperature certainly if you live in Colorado and ask in a laboratory can we get to lower temperatures and see what how matter behaves. Okay so in talking about temperature it's useful to use the Kelvin scale so just the Celsius scale shifted so that zero is absolute zero and I have a thermometer here marked in Kelvin but it's marked in powers of 10 or logarithmic scale so every number is a factor of 10. So if we just put on here the two temperatures we just talked about we've got our room temperature at about 300 Kelvin and going up on the scale that far you get up to the temperature of the surface of the sun so very different behaviors changing by that much on this scale. Let's put some colder temperatures on there the first one I'm going to put on there is the lowest temperature you find in nature. Okay so that of course is in outer space it's a cosmic microwave background not not not accurately depicted in this cartoon I actually mean the temperature far away from any astrophysical or human body but that temperature would be about three Kelvin okay so that's about as far down toward absolute zero as this was going up to the surface of the sun but in a laboratory we can reach much lower temperatures okay then you can find in nature and so I've got a mark here at a milli Kelvin so several orders of magnitude down a milli Kelvin is a very common temperature that you can achieve in the lab you can do this just by building a fancy refrigerator so you can see a big steel can there obviously a refrigerator this is a actually a photo of a group down the hall from my lab in Jilla where they have a refrigerator that they put in liquid helium liquid nitrogen cryogenic fluids and reach temperatures of a milli Kelvin and these of course are temperatures where you see lots of interesting behavior things like superconductivity and super fluidity of helium but today when I talk about ultra cold I want to go down another four orders of magnitude down here so I'm going to talk about a gas a gas of atoms cooled down to about a hundred nano Kelvin temperatures okay so that's what I mean by ultra cold this is my cartoon picture of a gas obviously gases are invisible but we pretend we they're made up of little balls namely atoms that are flying around in that in that flask there okay so what new things happen when you reach these very low temperatures with a gas is all of a sudden you encounter that the gas is not classical so actually my cartoon here is this is a very classical picture right we imagine a gas is made up of little balls whizzing around just like billiard balls that's actually a very accurate picture for almost any gas that you would encounter but not for an ultra cold gas so the ultra cold gas behaves quantum mechanically so it is a quantum system so quantum mechanics and quantum behavior is something that we're familiar with but usually we associate it with lighter particles for example an electron okay so an electron either in an atom or maybe in a metal behaves quantum mechanically even at room temperature and this is because the electron has a very small mass an atom on the other hand is very heavy so why do we have to go to such low temperatures to make a quantum gas it's because we want the atom itself to behave quantum mechanically not the electrons inside the atom okay so the whole atom that atom might be four or five orders of magnitude heavier than an electron and why does that matter because we know that a massive particle has a wavelength associated with it a matter wavelength also called the de Broglie wavelength that's just given by Planck's constant over the momentum p okay in a massive particle p is just the mass of the particle times the velocity or speed okay so if the atom is four or five orders of magnitude heavier than the electron then its de Broglie wavelength is going to be four or five orders of magnitude smaller okay so typically in a gas the de Broglie wavelength doesn't matter because it's usually smaller actually than the physical size of the atom but if you can get the gas cold you reduce the typical speed and you can make the de Broglie wavelength large and to have the gas as a whole be quantum mechanical you really require that that de Broglie wavelength this wavelength of your massive particle becomes comparable to a spacing a typical spacing between particles so another challenge in creating a quantum gas is that a gas has a very low density that means the spacing between particles can be very large it could be a good fraction of a micron okay so you need a very large de Broglie wavelength but this is what happens when we go to 100 nano kelvin temperatures okay so again here's my classical picture of a gas of atoms these arrows just indicate the velocities of the atoms and we know that the temperature of a gas is just a measure of the kinetic energy stored in the motion of these particles whizzing around in here and we can relate the temperature to this typical speed of the particle just through three halves kbt where kb is Boltzmann's constant is equal to one half mv squared where v is the typical speed of the particles so if we look at a gas at 300 kelvin that's our room temperature like the air around us and we just do this calculation we ask how fast are the atoms or molecules in the air around us moving we find that they move at hundreds of meters per second so that's jet airplane speeds so these atoms are whizzing around about this fast okay well that's not so good for seeing a quantum mechanical behavior because this velocity we know is going to determine the de Broglie wavelength remember it's Planck's constant over the mass times velocity if you plug in the numbers you get that the de Broglie wavelength at room temperature of an atom is something like 0.3 Bohr radii okay and I'm going to use units of the Bohr radius as a length measure here because the Bohr radius is the size of an atom so in particular it's the size of the hydrogen atom but any other atom it's going to be maybe a few Bohr radii so this immediately tells you that quantum mechanical behavior is not going to be that important because the matter wavelength is smaller than the physical size of the atom okay all right so let's look at an ultra cold gas you can tell that this gas is cold one because the grad student has a thermometer with ice on it okay and also because I drew these arrows much shorter so the particles are going slowly so temperatures directly related to the typical speed at a hundred nano kelvin the atoms are going to be moving very slowly if you do the math you find out they move it a few millimeters per second so about this fast okay we have to wait he's going okay so we've got a gas of atoms where the particles are moving really really slowly again the de Broglie wavelength is h over the mass times the velocity now we plug in this speed and we find that we can get a de Broglie wavelength that could be say 16,000 times the Bohr radii so now much much larger than the physical size of the atom not only that this works out to be a good fraction of a micron that means it's as large as a spacing of particles in a low density gas so that's how we get to a quantum gas all right the first quantum mechanical gas of atoms was created in 1995 by Eric Cornell and Carl Weiman this was actually done at Gila in Boulder Colorado and this is their original data these are images of three pictures three different iterations of the experiments reaching different final temperatures you can read over on the left this is a gas at 400 nano kelvin that was their hot gas then they got cold here at 200 nano kelvin and their coldest picture here is at 50 nano kelvin and what they saw here was the appearance of something unusual the something unusual was this spike here in the center of this gas and that was the appearance of a Bose-Einstein condensate and I'll talk more about that but let me just give you some parameters for this gas okay again here it is in cartoon form a typical temperature you can read off of here something like a hundred nano kelvin it might be a little bit warmer might be a little bit colder but around there the number of particles is typically something like a million so a million atoms making up this little puff of gas and it has a density of about 10 to the 13 particles per cubic centimeter so this is a very low density if you compare to the air around us this is about a million times less dense okay so this is a low density gas that's actually important um this these pictures were taken of a gas of rubidium atoms rubidium is actually a solid at room temperature but regardless at any substance if you go toward absolute zero it wants to be a solid or maybe a liquid in the case of helium but nothing stays a gas so keeping the density of the gas very low is important to enable a metastable state this quantum gas okay it lives long enough that you can probe it you can manipulate it actual timescale it lives for say several minutes which is long for the timescale it takes to produce it and to study it okay so let's go back to the question of why it's interesting to look at ultra cold gases um and one motivation might be application so i'll mention a few applications of ultra cold gases one is for precision measurements so this is actually a photo taken with some interesting lighting of the nyst cesium fountain clock so this is an atomic clock you know the basis for gps and positioning and they use cold atoms here and the reason they use cold atoms is because as we said cold atoms means the atoms are moving very slowly it means that you can interrogate the atoms for a very long time so if you want to measure some atomic transition as the basis of your clock you have a long time to probe that transition and measure it very precisely so it's great for time and frequency standards another application is sensors so you might imagine that if you have a gas at a hundred nano kelvin it's going to be very sensitive to the environment indeed it is this is a a photograph of a gravity gradiometer device that measures gravity gradients built at stanford university you can also use cold atoms to sense magnetic fields so to make magnetometers and um you could use them perhaps for navigation okay a final application i have on this slide is for quantum computing now this is a artist's conception of an experiment that was done at the mox plonk institute um this picture is supposed to show you atoms cold atoms laid out in a nice array okay these dots are the atoms and there are laser beams coming in and interrogating individual atoms to manipulate what state they're in etc and this is one architecture you could use from a for a quantum computer where these cold atoms would each serve as your quantum bit where each one could store a quantum bit of information this is only one of a number of possibilities for quantum computing but it is an architecture for quantum computing that is being actively pursued okay so those are applications uh those are not what i work on so going back to why it's interesting my interest is really in using these quantum gases to study um many body quantum physics so it's a more fundamental physics use of the gases to ask what can we learn from studying quantum states of matter in a gas so basically quantum many body physics is just when you have a bunch of quantum particles um bunch means there are many they're quantum and you have to throw in interactions usually to get anything interesting but interacting systems of many quantum particles appear all over physics of course um it's very relevant to condensed matter physics some of the most um interesting and the most technologically relevant behaviors that we observe like superconductivity or giant magnetoresistance are related to quantum many body physics strongly interacting systems of electrons but it's this is also relevant to nuclear physics particle physics physics etc so what does our system bring this new quantum system where the atoms are the quantum particles as as ed said in his introduction what it really brings is a system that you can use as a model to try to learn about strongly interacting quantum many body physics and why is that important it's important because it turns out that even if you understand extremely well the microscopics of your system that is what what an atom does what two atoms do how they interact what three atoms do once you have many quantum particles interacting that's beyond our theoretical description we cannot describe that okay so you need models to build understanding okay because every theory has to make some kind of approximation because this is an intractable problem so this system what makes a good model system is something that's accessible in the laboratory okay um once you figure out how to make this gas cold this is an accessible system in the laboratory it's one where you understand at the microscopic level all the ingredients it's an incredibly clean system and it's one that you have a lot of control over and that control is what makes it a good model system it means that you can take this very simple system right it's just a gas particles moving really slowly right and yet you can take this system by turning on interactions into a regime where the theory is not there to describe it you can't predict what's going to happen okay and so and you can get interesting states of matter based on the quantum mechanical behaviors okay so this is the cartoon picture i used to show an ultra cold gas i just want to show you one photo of the lab because this is not completely accurate depiction of what we do in the lab this is a small portion of the experiment you're looking at an optics table full of stuff the table the part of the table you're seeing here is about a meter by a meter um and we've got uh okay first thing you notice we've got no cryogenic fluids here there's no liquid nitrogen no liquid helium um no easily identified easily identifiable big steel can that's a refrigerator right instead it looks like a optics lab and indeed most of the work we do we're using lasers to manipulate and control the atoms in the middle of of this part of the table here there's a vacuum chamber it's basically this thing inside there's ultra high vacuum which means basically nothing is inside there and it's this ultra high vacuum inside there we're going to create this ultra cold gas and it's going to be protected from the room temperature stuff around it actually the the wall of the vacuum chamber will be about a centimeter away from the cold atom gas okay so 300 kelvin centimeter away 100 nano kelvin it's hard to see in this picture the atom gas first of all because gases are invisible plus it's tiny plus it's crowded so here's this guy to show you where the cold gas is it's right in there okay um i think basically now you all know how to create the ultra cold gas so we'll move on to how do we probe it okay so you have this gas you have to hold on to it some way okay it doesn't really just fill our vacuum chamber but we'll use some kind of trap for example you could use light forces this is an optical trap depicted in this cartoon it's just a single focused laser beam and the atoms are a little cloud of atoms is this blue blob in the center here so the this is um light by the way that's far detuned or the wrong color for the atoms to absorb so the atoms aren't really scattering this light instead what it is is that the electric field the oscillating electric field in the laser is inducing a dipole moment in the atoms and that's the force you use to trap it okay so we've got atoms trapped here about a million of them 100 nano kelvin how do we measure the temperature so we obviously can't just take a thermometer and stick it in there right because there's no thermometer that's has fewer than a million atoms in it um so what we're going to do is use the fact again that we know the temperature of a gas is just a measure of the speed of the particles okay so what we're going to do is measure the velocity distribution if you want to measure the velocity distribution of a gas all you need to do is let go of it right so the gases can find now but if we let go of it it's going to fly apart and by seeing how big the gas gets this little cloud of gas um as function of time we can measure the velocities okay so we're going to let go of the gas turn off the trap and there it goes you can see the gas expand in that animation now you might notice in the animation that the gas didn't just expand it fell okay we don't usually see that behavior with a gas right usually you let go of a gas and it just expands right it doesn't fall why are atoms not affected by gravity normally oh it's that the atoms are moving at jet airplane speeds right so the expansion is usually the dominant motion you don't notice the falling but of course atoms like any other massive object falls that's my reference to newton um okay but here we're not really concerned with the falling we want the velocity distribution so we're concerned with how big this gas got this little puff of gas in the few milliseconds we let it expand so all we need to do is take a picture of this gas we actually take an optical image we send in light that's now exactly the color the atoms like to absorb so the atoms this cloud of atoms is going to cast a shadow in this laser pulse and we're going to take this shadow image of the gas now once you have your shadow image taken with a fancy digital camera you can then put it into false color it's really not colored okay and this false color just indicates how dark the shadow was so in this case white and red are the darkest part of the shadow which means the densest part of the gas and blue is lower density or lighter part of the shadow okay so that's the velocity distribution and that's exactly what these images were that i showed you before this data of the first bozeinstein condensate taken of rubidium atoms okay so these were three images of the velocity distribution um they're shown in even fancier not only are they false color they're also shown in sort of 3d so you can see the shape of the distribution so when the um when the gas is hot you see a sort of blob a gaussian shaped distribution that's what you expect for classical particles it's the Maxwell Boltzmann distribution but when they got colder and the condensate appeared they saw the spike in the center we now know this is a velocity distribution so this spike is a bunch of atoms near zero velocity it didn't go very far in the expansion okay so to tell you why that happens we have to talk about the quantum behavior of bosons and fermions okay so we're cooling the gas to where the particles the atoms are going to behave quantum mechanically when particles behave quantum mechanically they're really only two behaviors that are observed in nature and associated with those two different behaviors we identify two classifications of particles so these are bosons and fermions as far as we know all particles are either bosons or fermions and as ed said in his introduction we can easily identify them by their property of spin bosons have integer spin and fermions have half an integer spin now a nice thing about atoms is that they're composite particles right they're made up of things like protons neutrons and electrons and depending on their exact composition they can be either bosons or fermions so with these ultra cold gases we have access to either behavior quantum behavior bosons or the quantum behavior fermions so what is there quantum behavior okay bosons this is how i think of them they kind of look like this that's their quantum behavior they like to do the same thing fermions on the other hand a lot more interesting and fun fermions all do their own thing they don't like to do the same thing okay all right so more specifically on bosons it's possible for particles that are bosons to all be in the same quantum state and an example of that is a laser so the quantum particle of light is the photon the photon happens to be a boson okay and in a laser you have these quantum particles of light that are all traveling in the same direction they all have exactly the same wavelength they're the same color and that's a bunch of bosons in the same quantum state okay doing this all doing the same thing and you know that this behavior of light in a laser is very different than white light for example okay so now let's go to atoms in a gas so we know that we have to confine our our gas of atoms somehow and so for the trap i'm going to imagine a harmonic potential this bowl shaped trap because everything's harmonic to second order that's a joke okay the traps tend to be harmonic so in this cartoon depiction this harmonic potential i'm just showing in 1d and these horizontal lines are the quantized emotional states inside that potential so the quantized energy states of that trap if the if the gas is classical there's a very low probability that any one of those states is occupied and so i just show here a few atoms scattered in some of these different energy states okay so that would be like white light but now if these atoms are bosons and they can all do the same thing as we cool this gas down at some temperature some finite temperature there will be a phase transition to the boson stein condensate where a whole bunch of atoms go into the lowest emotional state the lowest quantum state of that trap okay now you have many atoms all described by a single wave function okay the wave function of the ground the ground state of that trap this is the boson stein condensate it is a quantum mechanical state of matter right it occurs because of the quantum behavior of bosons that they all like to be doing the same thing okay so back to this picture again three images three pictures of the velocity distribution this spike in the center we said was a bunch of atoms near zero velocity now we know this is the condensate this is a bunch of atoms all in the exact same quantum mechanical state in the lowest emotional state in that trap by the way in this middle picture you see both the condensate plus some atoms that are scattered in some higher energy states that's like as you go through a phase transition from water to ice right you can have a state where you have both ice and water mixed then you go colder and you have only the condensate okay let's let's switch now to talking about fermions so fermions are pretty interesting because when you look around you all the matter you see is made up of fermions okay all visible matter is made up of things like protons neutrons electrons these are all spin one-half particles they're all fermions okay so their behavior might be kind of interesting um they quantum behavior is essentially the opposite of bosons so whereas bosons can be in the same quantum state and even like to be in the same quantum state fermions obey the poly exclusion principle that says that identical fermions can never be in the same quantum state and that's why i show them here in this famous painting all doing something different all right so again if we look at atoms in this harmonic potential with these quantized energy states um for fermions i'm going to show two different atoms red and blue here schematically they correspond to say a spin one-half particle uh red would be spin up and blue would be spin down all right this is a classical picture where i've got again low probability of any state being occupied so atoms just scattered over these different energy states now for fermions um the quantum behavior fermions is not going to give us a phase transition but we can look at how they start to behave as you go toward zero temperature so i want to look at now at absolute zero how would these fermions arrange themselves they arrange themselves like this the lowest energy configuration is putting one spin down and one spin up in each quantum emotional state until filling them up one state at a time until you run out of atoms okay because they cannot be in the same quantum state this is the lowest energy configuration note that this gas would have quite a bit of energy even at zero temperature um we define the energy of the highest filled state is the fermi energy or e f here and uh you can define also a temperature just by dividing this fermi energy by boltsman's constant so this fermi energy i want you to note can be easily calculated right you just need to know how many particles you have and what what the quantum states are right because you're just filling them up until you run out of particles this arrangement is often called a fermi c um i'm showing you in this cartoon a fermi c of atoms but you may be familiar with the fermi c for electrons um i'm going to tell you why i think it's called a fermi c i think you can think of it like this these atoms or these fermions down here they really have nowhere to go right they're at the bottom of the sea there are no states for them to move to they're just sort of stuck there at the bottom of the sea but these guys up here near the fermi surface it's like the surface of the sea they there are empty states above them they can move to and at any finite temperature in fact there'll be imperfections in the fermi c some states that should be occupied that are not some states up here that are occupied and those cause ripples on the surface of the fermi c those imperfections and extend over um something that's arranged energy range is given by the temperature okay so the fermi c is the fermi energy deep and has excitations given by bolson's constant times the temperature okay okay so this is uh the data from my group from 1999 where we cooled down uh atoms that were fermions so we just chose an atom that was uh convenient for the cooling that had an isotope that's a fermion these are potassium atoms and we're looking for this fermi c behavior to emerge and we have uh atoms in two different spin states so these are the velocity distributions that we saw cooling down actually this is not the original data from 1999 but these are velocity distributions of a fermi gas cooling down where the temperatures here marked not in absolute temperature but in units of the fermi temperature and as you go below the fermi temperature so t over tf below one you expect fermi c to start emerging or this quantum behavior to start appearing well it's kind of hard to see it in these pictures unfortunately it's not like the Bose-Einstein condensate that just leaps out at you with this giant spike in the center of the cloud but we can draw artificially um ovals on here that indicate the fermi energy remember the fermi energy we can just calculate if we know the states of the trap and how many particles we have so i draw that oval here by the way the reason it's not a circle is that the trap is not spherical and it just hasn't expanded long enough if we let the gas expand longer it would be a circle okay but you can see as you cool the gas down you start to reach a situation where most of the atoms are below this fermi energy as drawn on here artificially if we look in detail the shape of the distribution so this is taking one of these images actually this one near t over tf of point one and just averaging around an angle so it's an azimuthal average around this is how dark the shadow was or optical depth as a function of the distance from the center in this average okay so the points here are the data the blue line is what happens if you fit to a gaussian so a gaussian is the distribution you expect for classical particles the maxwell-boltsman distribution and you can see it doesn't fit perfectly whereas if you instead fit to a fermi distribution what you expect for fermions in a harmonic trap you get this red line which goes through the data points okay so you can definitely detect that this gas is behaving quantum mechanically and it's following the behavior fermions but it's not exactly as satisfying as the bozeinstein condensate okay no condensate shown this way would have a giant spike right here now some of you might be thinking when i studied statistical mechanics in my physics class they told me that fermions have this distribution like this right the occupation occupation in momentum or this is wave vector k everything's occupied at low k and then there's a fermi step and nothing's occupied above that right that's the t equals zero fermi distribution it's just this function oh and by the way this is in wave vector k you can define k fermi just from the fermi energy so is this familiar right okay so why don't we see this so one reason might be we're at finite temperature right this is an absolute zero picture what if you're not at absolute zero your t over tf of about point one well it would look like this okay so there's still a step there it's a little bit rounded out how much is rounded out is given by the temperature but our data doesn't look like that either right it looks it looks way more smeared out right looks almost Gaussian okay so the reason we don't see this is this textbook example is for homogeneous gas that means a gas in a box that has a given density right fixed density instead we have a trapped gas okay our trapped gas would look like this if we could measure not the occupation in momentum but the occupation in harmonic oscillator states but that's kind of hard to measure right and so it's because it's a trapped gas that the momentum distribution looks almost Gaussian okay more specifically it's because a trapped gas has not one density but it has a high density in the center and will have low density at the edges right it's just this nice little puff of gas and you're averaging over all these different densities so you can't see the Fermi step but if you could go in and probe the atoms in the center of the trap and specifically probe their velocity distribution you should see this Fermi step in momentum and so this is something we've done fairly recently this was published only a couple years ago um where we could see the Fermi surface this more textbook-like shape um by probing the center sixteen percent of the atoms so only the center sixteen percent of the gas that was sitting right there in the middle of the trap looking at their velocity distribution we now see occupation of one stepping at the Fermi momentum down to zero the width of this is now largely a measure of the temperature okay the fact that we're t over tf of about point one okay so everything I've told you so far is just the quantum behavior of atoms in a cold gas okay I haven't talked at all about anything that requires interactions but interactions is what makes many body quantum systems interesting right interactions make things happen interactions are necessary to make things where I can't draw theory lines and just tell you what we'd expect to see so I want to talk about a phase transition to a state of matter with fermionic atoms that depends on interactions and that's the fermi condensate okay so first if you have atoms that are very cold how do they interact these are neutral atoms okay electrically neutral only way they interact is by colliding okay so most of the time in the gas they don't feel each other at all right only when they happen to encounter each other up close then they feel some van der Waals forces all right so it's a short range interaction only appears when particles collide so in this field of study of ultra cold gases we've learned how to control these interactions this was from ideas that came out first theoretically and then we're realized in experiments and basically the idea was to go to a resonance in the collisions and usually this resonance can be controlled in the lab with a magnetic field so tuning the magnetic field over a small range around some special values some resonant value you could make the collision cross-section go way up so you have very high rate of collisions and it turns out you can that means you can make the interactions extremely strong and by tuning your magnetic field say to just one side of the resonance or the other you could change the sign of the interactions whether in the many body system they are attractive or repulsive okay so we can take a system say of potassium atoms that has naturally a weak repulsive interaction and we can change the sign of the interaction to make them attractive and we can change the magnitude of the interactions basically to be infinitely strong by going right on top of this resonance and when you do that you can realize the Fermi condensate this is a phase transition to quantum state of matter where we start with fermionic atoms and yet we can produce pictures that look a lot like the pictures of the Bose Einstein condensate now Fermi condensate you should be thinking there's something wrong with it right because condensate by condensate here I mean all particles in the same quantum state right but I told you identical fermions can never be in the same quantum state if I told you I started with atoms that are fermions right how could I possibly see a condensate I'm obviously lying to you okay but you might remember Ed told you that it's possible to make fermions behave like bosons if you pair them up so remember fermions are half integer spin particles so if you put two half integer spin particles together that composite particle has an integer spin and so a pair of fermions behaves like a boson and so that's a way to start with a system that that's exhibiting the quantum behavior of fermions and introduce a little bit of the quantum behavior of bosons okay and as Ed told you this behavior is not new in these this is not the first time it's seen it's well known from systems of electrons where they can pair up spin up and spin down electrons pair with equal and opposite momentum and cooper pairs and that's responsible for superconductivity in metals okay so what was the lie these images that I showed you were not images of the individual atoms but instead they were images of atom pairs it was by looking at the velocity distribution of the atom pairs is how we could see a condensate the spike in the center a bunch of particles now pairs in the same quantum state another difference in these images compared to the pictures I showed you earlier of the Bose-Einstein condensate is that these three images are taken not at different temperatures although we could have done that but to emphasize the importance of interactions these are actually images taken at the same temperature or at least starting at the same temperature but changing the strength of the attraction between spin up and spin down atoms that would cause them to pair okay and as we increase the strength of interactions at a finite temperature we go through the phase transition to the Fermi condensate so-called Fermi condensate oh by the way I should mention this thing is a superfluid okay so much like a superconductor except it's not electrically charged okay so it's a superfluid but I want to point out that this superfluid of atoms is very different than superconductors in that superconductors always start with a nearly perfect Fermi C that is this the step function really looks like this because the transition temperature to superconductivity is typically much much less than the Fermi temperature for electrons in fact it's usually something like 10 to the minus 5 okay whereas we already talked about the atom gases where our lowest temperatures are around t over t Fermi of 0.1 which means this is this step is always going to be rounded out okay and this is basically sets the size of these ripples on this Fermi C so let's look at this in a Fermi C picture to try to convey to you why this is important difference okay so superconductivity of electrons this is well described by a 50 or 60 year old theory the Bardeen Cooper Schrieffer theory or BCS theory for short and it really applies when your transition temperature is negligible compared to the Fermi temperature so again something like 10 to the minus 5 typically so the Fermi C has ripples on top of it at finite temperature now those ripples are pretty small right because temperature over t Fermi is very small so here are the ripples nonetheless those ripples cause resistance right here electrical resistance when when you go through the transition to the superconductor these ripples go away basically these small imperfections near the Fermi C are taken away by this attractive interaction that causes pairing and causes these pairs to behave like bosons so you're only trying to get rid of some small ripples so you only need a weak attractive interaction and the pairing that's important is really only occurring right near that Fermi C okay in a tiny region near the Fermi surface all right now let's look at superfluidity or Fermi condensate in an ultra cold gas of fermionic atoms here our transition temperature over the Fermi temperature is almost a 0.2 okay that's huge this is why we could see it right because we're only reaching down to temperatures about a factor of two lower than that so this picture is clearly not right it really looks more like this okay you've got distortions of your Fermi C imperfections of your Fermi C that have a energy width that's now sizable fraction of the Fermi energy okay that immediately tells you that in some sense you really want to think about this as a high temperature superfluid obviously the absolute temperature is ridiculously low but it's high temperature in the sense that you're not very cold compared to the Fermi temperature and so you have big imperfections in the Fermi C and you need very strong interactions to get rid of these imperfections to create your superfluid okay just in a little bit more detail how we think about this when you start thinking about making superfluids with fermions you're really thinking about how to make pairs how to make these bosons the BCS way or the way that works in superconductors is really a very good Fermi C and pairing near the Fermi surface due to some weak attractive interactions but we have atoms so atoms are different than electrons if you think about pairing of atoms all of a sudden you realize you can have a real bound state of atoms right it's called a molecule doesn't exist for electrons so you can actually make a system where you just bind your fermions pairwise into molecules those molecules would be bosons and should form a boson synconancy these are two very different ways of thinking about pairing right this is a Fermi system predominantly with a tiny bit of bosons mixed in this is a Bose system right the Fermi the fact that the atoms inside the molecular fermions is completely negligible our Fermi condensate lives in between these two okay it lives in what's known as the BCS BEC crossover this is an idea that's been around again for something like 50 years and the idea that these two would be limiting behaviors of the same physics this is a very powerful idea because remember transition temperatures from here to here would vary by like five orders of magnitude interaction strength you know sort of the strength of the pairing could could vary by much more than that maybe eight nine ten orders of magnitude okay but if these are two limiting behaviors then there's something that happens in between that's exactly the region that we can access with a gas of atoms with a gas of fermionic atoms and in fact we can move just a little bit in this crossover a little bit more toward this limit a little bit more toward this limit a little bit more toward this limit by controlling that interaction strength okay finally I want to show you some visualization of the pairs some artist conception and this is important because what's interesting about this quantum behavior all comes in in the pairing the pairing of fermions and sort of to what extent these pairs really behave like bosons they are not exactly equal to a boson unless they're really tightly paired into molecules and so how do we picture this this this picture illustrates the molecule idea this is not what's happening in our fermi currency but it's the way you might think about pairing as a first pass all right so what I've got here are fermions they're the people I've got two kinds pink shirts and white shirts those are spin up and spin down the attractive interaction is between those spin up and spin down fermions and you can see they've all paired up here right okay and they're depicted as dancers because somehow it's in the motion of the particles that we're going to see this quantum behavior this is what our fermi condensate looks like in this kind of representation so again I have equal numbers of spin up and spin down fermions but now the pairs are much harder to see this is a system where you see the individuals you see sort of the fermions but they are all paired here's a pair right here here's a pair okay so you can see they're all paired the reason they're harder to see is because the pair size typical spacing of particles in a pair is comparable to the spacing of the individuals and so you get intervening individuals within a pair this is what's happening in our gas this is what happens in the crossover you have fermion statistics and both statistics somehow both playing a very important role in what's going on in the gas okay I have one last slide which just shows you what are we working on now so this is my recent work slide and I'm just going to give you an overview so we are continuing to study this BCSBC crossover with the fermi condensates we're actually focused now on the normal state so that is what's the state of the gas above the transition temperature to the superfluid and the reason that's interesting is because we want to know in the normal state of the gas before the superfluid is there pairing or not is your fundamental excitation fermionic or is your fundamental excitation bosonic and we know in the limits those are those have to be right but how do you cross over between bosonic and fermionic excitations as Ed mentioned we have a large effort now in studying ultra cold molecules the molecules we make are fermions of course why wouldn't you pick the more interesting quantum particle so you can see I've changed my gas here to be molecules and that's that's what our molecules are they're diatomic our molecules are polar meaning they have an electric dipole moment so I think one of the things that's most interesting is to look at behavior of a gas that now has long range interactions where two particles even at a typical space in the gas already feel each other and ask for example could you get pairing and superfluidity driven by these long range interactions and then finally I have a collaboration with Eric Cornell we're looking at Bose-Einstein condensates now so that they don't feel left out but we're asking what happens if you take them to strong interactions a challenge here is the condensate really doesn't like strong interactions so we're doing dynamic experiments where we ask if you suddenly turn on strong interactions how long does the thing live what happens before it goes away okay so I've been showing this is my cartoon picture of the grad students they don't really look like that they're a much more handsome bunch this is just the current group of these are grad students and undergraduate students in my group now okay and with that thank you very much for your attention I'm happy to answer some questions