So thank you so much for joining us remotely from boulders are, it's really my great pleasure to, to get to host Professor Anna Maria array for today's colloquium. I had the honor of having her as my postdoctoral mentor when I was a postdoc at jill at nist and see you in Boulder before coming here to Georgia Tech. So from the relevant information, so Professor anime array is a fellow at Genoa, which is the joint institute between nist in the CU Boulder is a nist Fellow and a professor joint at the Department of Physics at the University of Colorado, Boulder. He received a BS from Universidad de la scientists. Sorry if I'm mispronouncing. Got lumberyard and a PhD from University of Maryland. She was a postdoc at the Harvard Smithsonian Center for Astrophysics. After which he joined the faculty at Julia and their border. And I erase research interests are very broad and that was really my pleasure in working with her. Getting to do things that are really at that interface between a condensed matter in a model where you can cross fertilize ideas in both directions. And that includes across AMO, condensed matter and quantum information. Professor anime has been the recipient of many awards, including the theme or thesis prize, MacArthur Foundation Fellowship, the Presidential Early Career Award for scientists and engineers, the PKAs, the movie I could create Meyer word of the American Physical Society in the Blavatnik national awards for young scientists. And she's a fellow of the American Physical Society. There's surely many awards I mentioned netlist. So with that, it's really a pleasure to have you here. And please go ahead. Thank you. Good afternoon. Thank you so very much for the invitation to speak today and for the very, very kind introduction. And just how I'm not there in person, but hopefully we can enjoy a nice discussion today. What I want to do is to describe, but I think is a fascinating idea of how atoms and light can be used to create atomic clocks, which are the most precise, keep time keepers. Do you have ever imagined in, I want to go through the inner workings of the atomic clocks. And hopefully I can convince you that a atomic clocks are not all fascinating, but also important in C. They're helping us not only to keep time, but also to unravel the mysteries about the quantum world. And hopefully we can use that tool for building the next generation of quantum technologies. So am let me start. I mean, I think Let's see if I you can see my mouse hopefully is or I DO them. Hopefully everything goes smoothly with the presentation AI. To start my talk by acknowledging my collaborators. A, all this work has been done in collaboration with John G is actually the clockmaker and the theories. But he's the one who does the experiments and his group of graduate students and postdocs. And also I want to acknowledge my theory group a who have done many of the, of the calculations that I'm going to tell you today about. Though, I went to start very basic and I want to start mentioning what are the systems that we are using. We are using systems of ultra cold atoms. And well, of course, when you look at the ultra cold, do that, the temperature is a measure of the kinetic energy of the system. Then I went typically to introduce a thermometer and tell you a little bit about the energy scales that we are talking about. At room temperature. Atoms in the air, you move very fast at the order of three, the speed of sound. And therefore they're going to be very hard to control and manipulate 300 meters per seconds. This is very hard to do something with them. So what we want to do is to cool them down. And if you think about the coldest temperatures that naturally do finding the universe, you may be immediately think about the temperature of the outer universe, the authors space. That is about, I mean on the order of few Kelvins. So on. If I think about can you, for example, at four can be used. This is the temperature at which it condense. And, and, and the atoms are still are moving, verifies nine meters per second at this temperature. So in order to really control them and manipulated in the, in the lab, we want to bring the temperature is much lower. So we are bringing in the temperature down to tens, to hundreds of nano nanocoulombs. We are cooling down not raise of 10 to the fourth, 10 to the six atoms in very dilute comfort. Why FIFO order of magnitude, more dilute than air and velocity of centimetre per second, sorry, velocity of centimeters per seconds. Where am a we can really gain control over them. Of course this has been a big, a common effort from the MU community that has led to important recognitions. For example, the process of using lasers to cool down the atoms to temperature of microbial. These M has been done a and recognized with the Nobel Prize in 1997. Twisted choke point than luteum Bill Phillips. And what they show is that by illuminating they are the atoms with proper light. We can slow them down and remove that kinetic energy, but not at the level that we want to, not as low as a lowered them as low the temperatures that we wanted to. But it was a secretary for deborah, Eric Cornell, Wolfgang Ketterle, and Weinman. They use the evaporation to try to similar concept, but in a trap where the hot atoms escape and keep the call their atoms. And this gave rise to the formation of a Bose-Einstein condensate and was awarded the Nobel Prize in 2001 for that as achievement. Though. So this was very exciting, exciting. But one of the questions that perhaps we, we have is a, what we can do with ultra cold atoms. What we gain by bringing them, them or pull him down at such temperatures. And one of the points that I want to emphasize the stock is the idea that we can use these for a, as a tool, floor the quantity we're in. So one of the things that we think we can do. So hopefully we can use the system to emulate the behavior of real materials. But in a way that we can design and control in the lab. So we went to create these synthetic materials that M, that true paths, the capabilities that we have in nature. And for example, shed some light on the behavior of, of high-temperature superconductivity. We want also to use the systems to Bill Gates and use the full tunability to generate next generation of computers, quantum computers that will have, that have enormous promises as we all of you have, most likely hear about him, of course is challenging. In, in addition, we want to use these atoms and a source as a resource to explore fundamental physics. So we're exploring here the work of the microscopic objects. But one of the most intriguing question is, is the connection between the behavior of the connection between the microscopic and the macroscopic world. So from atoms to black holes to dark matter. And I'm going to tell you a little bit that in this talk, that is a great potential in, towards this direction. And finally, of course, we want to use these systems as ultra precise sensors with sensitivity that can surpass the capabilities of any of the systems that we have given a at hand now or with classical systems, we want to use quantum properties to enhance the sensing capabilities. So ultra cold atoms offer a window to these exciting opportunities. But in particular, I hope, I, I hope I can convince you today that in particular, atomic clocks can have direct the connections and direc opportunities to all these four different ideas. So with that said, I'm going to start this talk by discussing very briefly what is O'clock. I mean, I'm sure you're very familiar, but of course, o'clock is something that peaks at our regular and repeated manner and which we can use to measure time. So typically, when you think o'clock is made of three ingredients to elements, an oscillator, that is what kicks. And they're called counter that is quite records. The oscillations of the oscillator is so indicating we are, of course, a clocks have been be at the height of the mankind for many years. And, and, and the type of clock that I'm going to talk about is an atomic clock that chairs very similar properties. A, it indicates of the oscillator is going to be an electromagnetic wave. In, in our case of the clock is going to be actually a lecture on the counter, is going to be the atomic system. So the interesting part is that in detailed case of atomic clocks and the ones I'm going to tell you about, the oscillations are so fast that at electronic devices cannot keep track of them. So we all get there too fast for them to react. So here we are using atoms as the counter of these oscillations. And this will allow us to create a very, very robust and very useful a clock that is universe. This is because when you look at the properties of the atoms, we know that in quantum mechanics tells us that the energy levels are quantized and at the same everywhere. So an atom here, a is this has the same energy splitting that addItem like China or in their universal, so it's not man-made. They don't know the issue that we have in clocks that you are going to change the properties depending on who makes the clock. These, these atoms give us a universal handle. Him. So part a, in fact, in a sense. Him in a 667 a, we define the second as connected to the number of, of radiating cycles in, in, in, in cesium atom. So the definition of the seconds is the duration of about, I mean this number 9 million approximately videos of radiation in two of the hyperfine levels of this issue, Martin. So that's what we, how we defined in the second and since 1967. Of course, in the first atomic clock was created. It was before it was in essence, I'm firing him. And even though the definition of the standard system of units is based on the cesium atom in 1 that I want to tell you today is that when a, nevertheless the system clock is currently not the best of the war. We have other clocks that are much better and so we're just waiting for the possibility to, to update actually the definition of the second in terms of these more precise clocks. Right? So now, why we have clocks that are more precise than, than the cesium clock. And I tried to make an analogy here with two rulers, a, ruler, a, ruler B. And if I ask you which ruler is more precise, when I bet you're going to tell me ruler B, because you are going to say The clearly more thick's high resolution. And this is exactly what happens with clocks. It happens that the Cesium clocks, the energy splitting is set in terms of a microwave transition. We the energy splitting of the order of gigahertz. But nevertheless, there are other atoms where we can have a stable levels between two within an optical transition. This times the energy scales is of the order of hundreds of kilohertz. So can be four or five orders of magnitude larger energy than the, than the microwave clocks. And therefore, the frequency associated frequency of the electromagnetic wave to excite the atoms is going to be much more faster and given also higher spectral resolution. So these are the type of clocks that I'm going to tell you about today. Optical flow or optical clocks m. So, so basically the idea of, of, of the clock that we have is we have the oscillator, that is politics, that is going to be a lasering the optical, optical frequency domain to excite the transition. And what we want to do is to have a feedback cycle that allows me to lock the frequency of the lasers to the frequency of the atomic transition. And in that way, if I can aim, well, when I look, I can determine very precisely quasi is the frequency of these atomic transition. And with that, I can define or determine the second base on it. So, so, but of course, this feedback cycle, cycle is very important and of course the type of atoms that we use in our system. So for the type of atoms, what we use typically is in the atoms that are a in the second column of the periodic table or others with similar structure. A like GitHub you wish the architect a because they have a, they are in the second column. They have two outer electrodes. And these two outer electrons give unique internal structure. That is, is, is very useful for, for, for, for atomic clocks. And I'm going to explain why. But in addition, a unique atomic structure. In this talk, we are, I'm going to tell you that besides the electronic degrees of freedom and you can have a nuclei degree of freedom that opens and then level Simon level structure a, that mean by this a, the nuclear spin. So in the case of the talk that this is the atom that we use a gelatinous stones you here to see the green square. And it has a in it. We use the firm unique isotope with nuclear spin I equal to nine cats. Though that means that we have the ground and the excited state. And in addition, for each of the levels, we have this splitted by ten different internal state coming from the additional him in nuclear spin degree of freedom. Okay, So of course, if a one quiz, if you have questions, feel free to interrupt me any minute. Okay, so I was telling you that a strong Zoom is is actually one of them. A a I DID being the type of item that we use for, for interrogating o'clock and an optical transition. And the important part here is that it is transform as well as other atoms in the second column of the periodic table, has a structure when you have a ground and excited state. But this transition is, is Jake went to 0 to J equal to 0, j equal to 0 because the atoms form a seal it as j equal to 0 atom with a electronics raw electronic angular momentum. So this is total j equal to 0. Therefore, this transition is, is dipole forbidden. And we have the ground state, this is acetylated state. And we are going to have a transition to a triplet state that is the trapezoidal. And this transition is, is, is not only, not only dipole, but actually also it's been forbidden. So because of that, we have enjoyed our lifetime of this excited state that is very long. It can be longer than 100 seconds, and therefore this give us a very narrow spectral resolution. The language is just a few milliamps. So that makes these atoms ideal for clocks. And sometimes we want to make an analogy with a, with a classical pendulum and this atom. Because remember, if I, if I, if I went to, to see the stability of this atom in, you can define a quality factor that is the ratio between the frequency of the oscillations and the damping rate. And in the case of astronomy is larger than 10 to the 17. So these will corresponds to append to do that. But it seeks to streak. It will imply a swing for the entire edge of the universe. That that's the quality of data that we have. Of course, what we have is to lock our laser to the atom. And for that, we really have to build lasers that can a, a enjoyed this very long lifetime. So the, the lasers have to have very narrow spectral resolution as well. And that has been one of the very important developments that have happened in June Jen lab, that they have been able to deal WordPress table cavities that where they can do and use them to lock the laser and have quite the factors that exist 10 to the 16. And the means lasers that can enjoy more than 10 seconds of coherence time. So with these very quality of the laser and the quality of the atoms, also we of course need to avoid an important systematic. So for example, a Doppler, the motion of the atoms. It can be detrimental for measuring in the atomic transition because we know, because of the Doppler effect, depending of the velocity of the atoms we will be, we will aim at the atoms, will aim in it with the laser, will feel different in energy speaking. And therefore, if we need to trap the atoms to avoid any type of Doppler effects. But when you craft the atoms, you also add light and introduce some starships because of the interactions between the atoms with the light. And we want to minimize them. We want to avoid that the laser modify the atomic transition. All of this has been possible because we can use what is called magic wavelengths, that our wavelength at which the polarizability of the ground and excited states are the same. So they feel exactly the same trapping potential without any destruction of the energy splitting. So we can trap the atoms very tightly in and then avoid any type of Doppler shifts. But it's still enjoy no external AIM. Aim in certainties because of trapping of the trap. So that, that's, that's very good. So these are kind of the minimal ingredients that we have to build such type of atomic clocks. The next part of is that we, as I said, we have to have these feedback cycle. We want to lock our laser to the atomic transition. And typically we, this can be done by what is called Ramsey spectroscopy protocol that was invented by Gramsci who received the Nobel Prize in 1989. And the idea is very simple. So if we have a ground and excited state and we want to lock our laser to this atomic transition. Then imagine that we start the atoms in the ground state and we're went to interrogate, apply a laser to this atomic transition. And the laser is the tune from the atomic transition by this among that. So delta x omega minus omega 0. So what we're going to do is first, I apply a strong laser pulse here where the drive is very strong. So basically we have in this Bloch sphere picture of where the ground state is pointing down, the excited state is pointing up and any superposition of the atoms is eating the other is on their other port parts of the Bloch sphere, for example, you have equal superposition. You are in the equatorial plane. So what we do is that we start with the atoms in the ground state and we apply a very strong pulse start and this is thrown pots is going to drive a superposition between ground and excited state. We can control it. And this is going to be very important for the clock Excitation fraction, the number of atoms in the ground minus the number of atoms in the excited state by these pools area omega t. So if theta role, you are in the ground state is Theta is Pi, you are in the excited state. Is that actually what byte have during the equator. So try the transition and then do let it, creating the superposition of ground and excited state. And then you let the atoms involved in the dark, in the dark. But in this case in a, we are in the rotating frame of the lasers. So in during the time evolution, the atom's going to precess and the face because of the excited and ground state has different energies. And the rate of accumulation is going to be delta a. The truly TO then M, You can see that you have this precession anaphase accumulation, but a mixture of measuring the coherence is very hard. So what we do typically is we apply our second pulse that transforms the coherence into population measurements. And by measuring the number of atoms in the ground or in the excited state, we can get information of this phase are related. And we use these to actually determine and lock our laser to the atomic system. Though this aim function of the tuning, you can see this is the Ramsey fringes, a zombie. This is the excitation fraction or the number of atoms in the excited state. And this gives us an information of the faith. And of course we want to have a very coherent fringe so we can look at the oscillations and truck oscillations for a very long time in order to lock our laser with, with atomic transition. So that, that's, that's great And, and that's in principle. But we have, the advantage of atoms in a neutral atoms is that we can interrogate many atoms at the same time. So here you can see that I have an n. Here. N is the number of atoms that i'm, I'm assuming that the atoms are uncorrelated. So all of atoms are doing exactly the same. But that's not necessarily the case. If so, if we have more atoms, we're going to have larger signal to noise proportional to n, the number of atoms. But nevertheless, there is an issue is that when we have large number of atoms, atoms actually finish shorter because they're starting to exhibit a coalitions therapist start to collide. And unfortunately, coalitions introduce systematic a in the clock because they modify the frequency of the transition depending of the number of atoms that we have in our system. And this is of course very bad for clocks. You don't want to have a clock that the frequency that we measure depends on the number of factors that we have. In June when he was building his clock a, when I pass the Arabian Peninsula. He of course was aware of this very important issue. And he had the clever idea of using fermionic atoms and to use quantum statistics tend to suppress these type of questions. And I'm going to explain this a little bit better. So of course we are working with ultra cold atoms and then coalitions are also trying to characterize in terms of an angular momentum there, in terms of partial width of the collisions. And add at very cold temperatures in when the atoms is scatter in, the coalition is mainly characterized by a phase shift that datum secondly, after the collision. So and, and this phase shift in actually depends on the partial wave that you are colliding. So in it, the lowest partial wave is the L equal to 0. This wave coalitions and these are characterized by what is called an scattering length. So this phase shift scales in some way that is universal and it is wave conditions is characterized by a single parameter that is the scattering length. And for when you have this next accessible coalitions daily one-to-one collisions. It that is called P wave conditions that are characterized by scattering book. So is kind of him as a function of the inter-particle distance you have. The, this is the effective game is called a potential that the atoms feel during, during the collisions. This in the relative distance between the atoms. In the bottom part is that the S wave coalitions don't have any, any barrier. They're not simply forgot there is not a centrifugal barrier and they can cop and they're the ones that are not suppress or truck or temperature. On the other hand, when you are colliding that for l equal to 1 in channel, then you always have a centrifugal barrier that prevents a coalitions at, at low energy. And therefore, typically wave conditions are suppressed by Yaffe spot is called the centrifugal barrier. For example, in the strontium descent, typical carrier can be as large as 30 microkelvin. Where does the energy of the collisions is always below one micro cap. You are always called upon by microkelvin. So the point is that a is not only the fact that a P wave conditions are suppress a and is where R not. But the fact that quantum statistics at these cold temperatures start to matter in the sense that for fermionic atoms, we have org is the poly exclusion principle that forbids to identify that two identical thermos to have the same quantum state, I need in terms of coalitions, means that if you have identical fermions, you cannot collide in the L equal to 0 channel. That is the one that is not to press at very cold temperatures. But the only coalitions that you are allow a, I have four identical fermions, or the l equal to 1 coalitions. But this l equal to 1 coalitions cause energy. And therefore, they hope that you've had is that because we are ultra cold and because these coalitions cause energy by operating with a Fermions, we can suppressed Him in general, these positions, if happen, they are characterized by scattering volume by a single parameter m. That is different if you are colliding in the ground. Calculating the excited state or your coalition between the ground and excited states. There are three different scattering volumes that determine these conditions though. Okay, So that's quite June. Make the experiments with Phemius, he chooses strontium-87 and they started to run the clock. But unfortunately it back in 2008. Even cloud but still so sensitive that even in these very weak coalitions where detrimental for the crop. And they give rise to the second larger, largest. Insert a plea to the 10 to the minus 16 error budget that they have at that time. So coalitions where even the week, they were really, really, really detrimental for his experiment. Though. They, then, it's immediately clear that we really needed to understand these coalitions in we really want to use these items for building a good cook. So this is where the theory, the story enters in the DOD interest into the story. And so, but we have, is that we have atoms that are trapped in, In a, in elaborate on that range of pancakes. So we have the laser introduce a generates an optical lattice. And in this optical lattice, we generate an array of pancakes, a funky. If we have a few atoms in, like between 100 to 500 atom in each panky, in the emotionally 4-bit along the lattice direction. But I need the English pancake. The atoms can move in and soak. So you can understand a, well, let's look at a single pancake and a single package. You can imagine the confinement as an harmonic oscillator. This is introduced by the lasers. Do so you have a bunch of ad for Munich atoms, troponin molecules later. And typically they're at microwave temperatures, the clock. This is not necessary in the quantum degenerate regime in, at least in the first part of the story that I'm going to tell you. So you have a thermal distribution of these quantized energy levels in honor of atoms in an harmonic oscillator, a thermal distribution of these states in, So in generally the damping frequency was a strong, it is of the order of 500 hertz. The important part is that I told you that there is very, very strong big wave barrier that, that reduces the, the coalitions. And in fact, there are very weak they, the interaction energy can be of the order of just one hairs per particle. That means that in a single particle, a energy levels are the dominant energy and the particles due to collisions, atoms cannot collide and scattering two different harmonic oscillator level because it cost too much energy. But that's ideal for the theoretical treatment because what we can assume is that they are not changing coalitions and therefore atoms are pin in. These are molecules later levels, atoms. They're prepare. Even with coalitions, they, they, they cannot move our molecules later levels. They started like that. And the only thing that they can do is that they can flip the spin. This doesn't cost too much energy. That means if you provide too great, I'm Hamiltonian that describes the behavior of atoms in this harmonic potential. But you can gripe is just any spin model. Because atoms are frozen is this energy lattice where the lattice sites are going to be harmonic oscillator levels. So what spin models are most simpler to deal, that's going to have to deal with motion. So that's what we did. So we have a lattice in our molecules leave the state space. Atoms are pin in these different lattice sites. In the pancake. This is an XX and XY. And now, Okay, even though the interactions equal atoms are our contact interactions atoms have to bump and be the same lattice site to collide. Because our energy lattice is in harmonic oscillator, a space in energy space, nodding position in space. That means that in the wavefunctions are they localized, for example, in momentum, the waveforms that are totally delocalized. So when ingredient in these energy basis, they contact interactions that are look like long branch is like when you have atoms in the, in the momentum. If the atoms are very localized position in momentum mistakes, they're very delocalized. So in that case a, because atoms are, are, are interacting with other atoms. But the wave function of the atoms have the localized. So the interactions are very old pool or a very collective. We can, instead of worrying about the spin of a given atom, we can write a collective spin operator that is the sum over the spins of each of the atoms in the, in the debris. So in that picture we are going to think about our blushes spin. And we can define a collective operator if we put component is in C, for example, is the exit, that is the number of atoms in the excited minus the number of atoms in the ground state. And this, and this number is set by the first pulse. So I remember that in the Ramsey protocol I start with atoms in the ground state. I apply oppose that, promote some of the atom from ground to the excited state. And the step that is set by the pool Apple, sorry, I honestly. Finally the dynamics though, when I look at the dynamics of the atoms, of these atoms spinning, that is interacting via these very long grains, collective interactions written in terms of this collectivist be operators, the Hamiltonian that proves the dynamics. Not only the detuning that e, that we had a single particle levels, but the interaction in the P-wave interactions at as, as, as a non-linear term of the form of chi square, as well as some effective magnetic field. A way without a component that all of these CN or a high K depends on the, either the P-wave interaction parameters of the atom, of the number of atoms in my system. So the important part that we have simplifies enormously the collision of the atoms in this clock by soil or collectivist model that we can really solve almost analytically. And if you tried to look at a movie picture, that is what we look at, at parties. The collective is one, if the other atoms as, as, as an effective magnetic field. If to the OEM. I mean these SES squared term can be factorize, factorize as NSC times the average is C. So that means that the other atoms us as an effective magnetic field in a, on a single eye on the, on the, on the collective spin. So this Hamiltonian greetings as minus delta plus two chi as see just from this term, plus C and a C. And so the idea is that the effect of interactions is to add an additional term that competes with the detuning. This is what we call the density shift. That that's the idea that that's why coalitions modifies the ticking rate of the atoms because the, the interaction between the atoms actually had an additional effects that compete with the detuning. And as I said, this term can be very reduced to aim to them. An effective magnetic field that depends on the number of atoms and also strongly the 10 on the excitation fraction, this cos theta. That is that their mean by the first balls that were applied. So, so because of that, this is the simple theoretical model. So what we call June is that he has to operate at the point where this term is equal to 0. And in fact, that's what they did. So this is the density achieve that they see as a function of the excitation fraction. This is controlled by the first pulse area of the laser. And you can see that this obeys a linear behavior. Next edition fraction, that's the cost data with a slightly offset that despite this parameter. But the point is that at this time, the clock we're able to operate at this point where the density shift cancels. And therefore we were able to improve the precision of the clock. Insignificant. One hand. We put on the other hand, by fitting this line, we put determine the scene, the slope and the, and the, and the 0 crossing. And these allow us to determine the P-wave interaction parameters in the system that are not no. The only problem that we had done. And even though we have this cancellation in steel, there are collisions between atoms in the excited state. And these collisions between atoms in the excited state. Unfortunately, they are inelastic. That means these atoms in the excited state has a lot of energy when they collide, that they can escape on the truck. So if there was some cancellation, but it's still the time at which they talk. The talk, we can operate the crop was limited by these coalitions as steel. But with, by doing that, a at back in 2014 in the Cloud was able to operate, become a all around a onetime, one talks in time better that the cooling system is styled nice standard that was a big deal in and therefore reaching a fractional uncertainty or two times 10 to the minus 80. And just to give you an idea of, of, of this number, it corresponds o'clock that either gain or lose 1 second in some 50 million years. That is roughly the age of the universe. So that was a very, very big accomplishment that with them between the marriage between many-body physics and precipitous high precision spectroscopy. So the next study that I'm going to tell you is that now in the last year or early this year, we have gain a factor or an improvement of three order of magnitude was again a by controlling further the coalition. And this is done in, in a, in a, by adding some additional ingredients to the clock that I'm going to stay. So, and so before we were able to improve, improve the sensitivity by three order of magnitude, Have improve it even three order of magnitude more. By understanding, by adding 14 ingredients to control the interactions. And telling us that there is a very nice exciting opportunities between clock, a spectroscopy and many-body physics. Because basically what we are doing is that the clock is becoming so precise that is allowing us to understand the energy, many-body energy levels of our, of our system and vice-versa. By understanding the many-body energy levels of the system, we are able to improve the clock even more. So this is these very continuous feedback between precision spectroscopy. And many-body physics, that is very exciting. But I mean, in order to him, I mean, let me tell you a little bit, what are the ingredients that we have at hand that we are starting to, to, to, to enhance this marriage. Marriage. The idea is that if you think about the strongly correlated materials, if they're so complicated and so exciting and half so a complex behavior because they have an intrinsic interplay between the charge degree of freedom, the orbital degrees of freedom, and the spin degree of freedom of the electrons in the material. Though the interesting part is that index transient clock. We have an orbital degree of freedom, the ground and excited state in. We have any spin degrees of freedom that is opened by the nuclear spin. And we also have actually a chart degrees of freedom that even though the particles are, are neutral, if we can make the atoms behave as, as charged electrons and, and feel an effective magnetic field. And this ingredient is, is, is, is going to be a key for actual him in understanding coalitions in the clock and manipulating them. So, but also it's not only in the discharge emulating a, making the neutral atoms behave as charged electrons. It is a true lasers. Introducing what is called a string or decoupling is very exciting because the spin orbit coupling, this is a process that is fundamental in nature in, and for example, is or originated except relativistic effect a and E, for example, that couples the electronic motion. And it has been and is at the heart of the intronic anthropological insulators and invisible when there is a single big coupling in terms in pre-presence, in the proximity of the superconductor, there are predictions that you can generate micro nano particles that can be useful for, for quantum information. So there are a lot of exciting possibilities. That is spin orbit coupling opens in materials. It could be very easy, very exciting to have the capability to, to emulate these in Iraq well Athens. So it happens that in our clock spin orbit coupling scum emerges naturally. And the only thing that we have to do is decrease the lattice potential. And before the pancakes that we have the atoms, we're trapping pancakes in isolated pancakes by decreasing the lattice potential. We are going to allow the atoms tunneling from one lattice site to the next. And why is that spin orbit coupling happens? By doing that. The important point to observe is that we have a ground and excited state and we are illuminating in a garden manipulating the atoms. I mean, it's an optical transition and therefore we need an, a laser in the optical domain to write the atom. So that means that the wavelength of the laser to interrogate the transition is, is large. So K, the wave vector of the, of the laser times a, the lattice spacing that we used to trap the atoms is of the order of pi or larger than pi. That means that the phase of the laser that atom experience from one lattice site to the order is different. There is a differential phase between one and the other atom in interrogated by a pancake here or a pancake here. I'm sorry. In, therefore, in this phase, in a, a can be experienced by the atoms when they tunnel around and generating an effective magnetic flux in, during the motion. So here, for example, if you have the, you have I'm representing the 1D lattice as these direction along this, along, along this direction with my mouse. And this is the ground and the excited state. So because the listed on the face of the laser is different between here and one lattice sites on the other. Then there is a next flocks that the atoms can accumulate when anatomy do a motion across these, these, these synthetic brackets. So let me stain a little bit more. Have anatomy one lattice site, and that'll add four, absorb a photon from the laser from bone to the ground to the excited state, and there is some phase phi. Now the atom can Toulon from the, from the one lattice site to the other in one equal to 0, then the atom can emit a photon, but a front to the laser. But these are stimulated emission has a different face it because he's at a different lattice site. So and then it can tunnel back. So in the process of moving from one, let Arduino a closed-loop. There is a phase accumulated phi that resembles our magnetic flux influx in the system. So this another way to interpret this face, and this is by trying to look at the dispersion relation of the atoms in the lattice. So you have atoms that are moving in this 1D lattice when tunneling is allow to have a dispersion relation for the ground and for the excited state that is the same because the atoms feel the same lattice potential except from a global detuning. But imagine that we have an atom with momentum in the ground state with momentum q 0. It absorbs a photon from the laser that has a momentum. It is going to translate and implement them in. If it's going to transfer our abdomen to 500, that is the momentum of the laser content. So the atom absorbs a photon from the ground, it goes to the excited state, but in doing that it feels I kick, it changes the momentum because absorbing a photon from the laser. And in order to add, this can be captured by also instead of doing a change in momentum. But we can do is that we can do a gauge transformation where we displace the dispersion relation of the atoms in the excited state. So the atoms are, the laser again is coupled atoms with momentum q one anatomy momentum q 0 plus phi. And the only thing that you have done is just changed to modify to just displace they effectively the dispersion relation of the lattice of the exe, of doing a gauge transformation of the, of the excited state dispersion. So do you map k to k plus phi? By doing that, you can see that in an atom now in this case, anatomy is promoted from the ground to the excited state. But the tuning know the energy difference between the excited and ground state actually depends on the momentum of the atom. So here's from the tuning, there is some detuning. So basically, if we have a bunch of atoms, we can imagine them as a bunch of two level systems depend that, depending of the momentum is going to have an effective magnetic field. Where the magnetic field consists of the drug, the laser drive for you excited and added tuning, that the global tuning, but also that the tuning that is the energy difference from the ground and excited state it because of the spin orbit coupling. So this delta Q is going to be the difference in the momentum imparted by the laser. So you can see that in this case, the ground state of the atoms are going to point at different look at directions depending of the momentum, because the magnetic field orientation, the effective magnetic field orientation depends on the momentum of that. So there is a coupling between the spin of the atoms and the momentum that there is an intrinsic chronic, a coupling between them. So basically we have been able to explore these spin orbit coupling in, in, in our, in our system, in our clock came first in the non-interacting regime. And the basic idea that we did is very simple. So we have this dispersion relation of the, of the atoms that we can control by controlling the crossing of the two ones can be controlled by, sorry, by, by, by changing the global, the tool. So basically what we did is we start with all the atoms in the ground state. And given the tuning, there are only certain window of momentum. There is a closed, the crossing atoms can be transferred to the ground, to the excited state. Pulling from the other eight regions of all the items in order momentum is very strong, so they all did atoms that are close to resonance can be transferred. We apply a beriberi in a narrow pulse and then blow up all the atoms and prepared the atoms only with a certain window of momentum in the excited state. So we have selected atoms in the excited state. We then a specific window of momentum. So we can change came in the dispersion. We can change the global tuning. And by changing the crossing point, we can transfer atom from the ground to the excited state vise and selected and narrow window of momentum. And then after we transfer the atoms to the excited state, we can turn on the drive. And I might buy stronger drive and look at the dynamics of the system. So basically, we prepared the atoms in a given excited state. But depending of the momentum transfer to the, the, the eigenstates of the Hamiltonian are going to experience different Rabi oscillations at a different rate because they, they orientation of the effective magnetic field that depends on the momentum. And that's exactly what we see in the experiment. Where we see that depending on the, on the momentum window that we prepared atoms, they're going to experience different Rabi oscillations. A confirming that there is a spin orbit coupling networks. Exactly Very simple physics of the coupling between the spin and momentum that we expect. Though this was exciting, that we were able to see SB orbit coupling. But of course, it, the idea is what happens if we start to explore these in a sample in mind here is a single particle physics. One of the question is what happens if we allow the atoms that have a spring or decoupling it to, to, to interact. I mean merge their sample. And the problem is that as you can see, because in this decoupling, the face of the atoms are different. Pancakes is different. So we have a laser that is imprinting or different praise from one side to the other. And therefore, because of this differential phase, atoms that were indistinguishable all of down. When we went after the basic pulse, they are become distinguishable. And when they become distinguishable, they can start in the two to live. When they Toulon. Do. They start to feel the distinguishability of the atom. So we can have anatomy has been up to an atom with spin down in generating very strong as wave interactions. And these are the strongest interactions are very bad for the clock. So that, so this pure decoupling the, actually didn't help us too much. But now we added the last ingredient. A wish is make digging the clock vertically. We add the gravity to the rescue. And this is the way that we have been able to control the interactions and actually use them to even engineer them in the way that we want. So basically is that before we were oriented, operating the clock in at horizontal lattice. Now what we are doing is adding gravity, so we have a kill the potential. So here gravities are at this direction. So we have the ground state, the excited state, they can tell me that. But there is an energy penalty from grown from one lattice site to the next because of the gravitational potential, this is mgh. So what happens? So even in this hill, that potential to link is not that easy, even at moderate lattice sites. Actually, the eigenstates of the atoms in a tilted lattice. It's got this called Wernicke started states that are, that are local. I mean, our localize, if I am at this one-year study, states are localized at a given lattice site and without that, of course depends on the lattice, a potential depth. So, so basically the width of the degree of delocalization is set by the ratio between the two lending and MGA, this is our basal functions. So all but I'm trying to say is that if we have an atom that is in beam at modern late lattice, a 12th recoils, it's almost fully localize, whereas without the gravity in, it will be completely delocalized. So bye, bye. Thanks to gravity, we can add partial delocalization of the atoms in a very controllable way from, from very weak lattice, they are totally delocalized. But as we increase, as we increase the lattice, we localize them in a much more controlled way. So that was very exciting because we can operate a more shallow lattice but is still suppressing. Therapy would be undecidable motional decoherence in. But moreover, because we are at most shallower depths, then we, the local density is much weaker and therefore we can suppress the detrimental P wave inelastic losses that where we were suffering when we were operating at very deep lattice depth. So it allow us to control interactions better. But moreover, if winter day by also taking in we using the interplay between the spin orbit coupling that we have that pulls on is wave interactions. We have been able to operate at a magic lattice depth where we can suppress density shifts and allowing us to reach a regime where really a density shifts are totally suppressed and we have new opportunities to store new physics that was not possible before because of the presence of density shifts. So let me explain a little bit. You have just a couple of minutes warning for thought. Yes. Perfect. Yes. I'm going to be finishing in 55 minutes. Yes. So basically we have a atoms in, in our lattice that are localized, but now they're eigenstates instead of being our molecules later leg or a States we have there are molecules later and the one-year states that the atoms are localized at a given lattice site. Basically it now we can rewrite the same Hamiltonian that we had before in the, in the pancakes. But in additional to the on-site terms, we are going to have now, because there is some degree of delocalization, we have interaction between two nearest neighbor lattice sites. So we have the on-site interaction and we have the near neighbor lattice sites. And these coupling constants are set by the P-wave interaction parameters. And there is an S wave interaction studies allow by just being orbit copying 500. The atoms are in distinguish these indistinguishable, so we don't have it, we cannot have is wave interactions. So is the interplay between these two terms that allow us to add. Besides the on-site terms, we can have an additional nearest neighbor interaction term. And it's the combination of these two that allow us to operate at the lattice step where all these terms completely cancel. And we are able to operate at a reduced the density shifts. So actually, by controlling the last step we were able to operate. These are experimental points of the density shift that they measure. And we can operate at the point where the density is completely cancel out. At this point there is no more effect of density Shift M. And what we hear is showing that we can cancel the density achieved. But this is very exciting because actually we know from Newton, from Einstein that in contract in contrast, Newtonian mechanics in Einstein tells us that in the presence of, of gravity, actually clocks at a different rate can pick a different. So the talk, talk at a higher hierarchy, at a higher altitude can tick faster. So there is an energy difference in the ticking of the clocks that depends on the height when they are from the, from the Earth, for example. And for the case of the parameters of air density, the redshift is actually set by by a 110 to the minus 19 and one millimeter distance separation between the two objects. And in fact, prior experiments done at nice with ions were able to measure these density shields it by separating two clocks at 30, or are these 30 centimeters a difference? But actually the experiment, by considering the density shift, they were able to actually compare the ticking of two parts of the cloud that are separating at a millimeter distance. And they were able to actually see that they take out a different rate. So this is over a course of 10 days. We completed almost 14 measurements. These are here. For each measurement, we measure the differential, achieve the two samples of the clouds separating at a millimeter distance. This is a plot for each measurement. In the weighted mean is the black line. And a statistical uncertainty is the dash, a black line. And actually they, they, actually they mean is, is proportional to the expected a 10 to the minus 19, a gravitational density shifts. So we were able to for the first time to see the rest chip in and a microscopy nine millimeter sample. And this was in a pool, is these early this year in nature. So with that, we can see that there is a very nice interplay between optical clocks on many-body physics. So I'm running out of time, so I, I cannot tell you a little bit about the interplay between a orbital and it's being physics. But hopefully with what I have told you, I convince you that there is a great Mr. Hit. I mean, we can we have been able to use a clocks to explore many-body physics and also in-store many-body physics it with the clocks in, uh, hopefully at the moment, the clocks are operating the classical regime. So we hope that in the future we can entangle the atoms in the clock and create even a better clock. I've been using a spin orbit coupling some clocks in a three-dimensional lattice potential, not enough 1D. We hope that we can start to have the capability to be some gates. I unfortunately didn't have to tell you a little bit about that, but we have the possibility to engineers, some spin Hamiltonians and engineers, some gates that hopefully could open a door for future exploration of quantum computing in clocks. And because we were able to measure the gravitational redshift, incorporate that we can start to explore the deep secrets of the universe and trying to start exploring connections with quantum gravity. And with that, I have been in class, so I would led you here and thank you for your attention. Thank you so much. Who was a bit late, but we can make some time for a few questions. So let me open the floor for any questions. Unmute yourself and go in. And I've got two nice talk. Hear me. Yes, I can hear you. Yeah. Thank you. So I just have a very simple question. So the reason to choose formulas as a caucus to trying to suppress the P-wave collision. But I think if you are using a hammer one there are a number of keeping increasingly just means you're occupying more and higher momentum states, right? Though, that effect, that clock performance also compared to just using both on which if you carry a managerial cathode is scattering? Scattering? Yes. That's a good question. I mean, we are suppressing the S wave interactions that are detrimental. P wave are much quicker. So that's one of the big advantage with fermions, not, not bosons, yes, because Watson's can collide with S wave, can be significantly larger. So at the moment we are when we notice being orbit coupling and extra things, I mean, we, we have only P wave interactions. And it's true that the atoms, because fermion, they occupy different harmonic oscillator levels. But that's exactly what we use to create our energy lattice. So if you look at what that's exactly what we are using, the fact that we have fermions and there is one firm your harmonic oscillator a state. And these are our lattice, effective lattice sites in our it's been Model. So they are of course interactions the pen off in a, as you can see that aim, sorry, maybe I'm going to just go to the slide that I want to show in here. Here. Here. So we have fermions and therefore we are having one atom per lattice side. We can not have more atoms per lattice site. And that's what allow us to have a very simple, It's been mole. Because in this bin model, I mean, atoms are on the product side and these atoms can be in, initially it's all in the spin down. And then when we apply the poles, we can convert that up to down. But what I mean Yes, I mean is, is we Fermi exclusion principle is helping us to have only one atom per pair harmonic oscillator mode. That is good. Of course, the interactions is a scale with the particle numbers. So you can see that the number of particles is always present. And is, is, is, is, is not good. But we are trying to use the cancellation of the intrinsic parameters of the system it to cancel that out and been able to scale the, the, the clock with as many atoms per, per panky as we can. That is good for signal-to-noise. The answer that I answer your question. Yes. Thank you. Thank you very much. My question. Would it be possible to go to 3D lattice confinement completely suppress interactions? Yes. Yes. I mean, I didn't have time to do that. We are there is another, there are two generation of clocks, the 1D lattice clock, and then that is the 3D lattice clock. And this clock app, you are correctly fine. Do you have one atom per site? But the issue that we have with this, I mean the reason why the 1D lattice is outperforming after we operate that this crossing point is that a light scattering start to significantly limit the lifetime or the block atoms in the 3D lattice. Though, if the new generation of experiments have been able to go to a 3D lattice. In principle, we have one atom per site, t over tf is 0.1. So ideally, turbine to say, you are going to pack as many atoms as you want, one atom per site. Poverty exclusion principle doesn't allow me to have more than one, even prevents the, if the if the interrogation is, is, is collective MD. But the problem is that in the, the, the lattice beams introduce is lagged Roman law, rightly the scattering. And at a very intense lattice depth, lifetime of the atoms is reduced to 10 seconds instead of 100 seconds that we have. In the 1D lattice. The lifestyle can be as long as 30 seconds or Muslim or longer. So we are trying to see how we can engineer a little bit of, of the best of the worst dancer. It's a little bit tricky and I didn't, I think there's a lot of basic nutritionally Flexbox. Imagine you are going to go through a very, very shallow lattice, very shallow. And it still happens. The lowest band lot, lot, lot the lowest lattice time. Because they're fermions. In principle you cannot tuning. But the problem is that the clock introduces this face that changes from one lattice eyes to the order. And therefore, after clocking tradition you continent. So by June is working. Now. It's trying to make it into an engineer, an accordion lattice, where the lattice spacing is commensurate with the wavelength of the lattice spacing because may be k take wavelength of the laser. So case time aim for this phase is equal to two pi. And therefore in that case, we can operate at very shallow lattice and, and use the best of the yeah. So this is in progress. Thank you. There's any either like very quick questions We have time for maybe one very quick question isn't even mean. I can ask another quick one. Would you use showed diagrams of all of the nuclear spin states. So how come the atoms don't interact if they're in different nuclear spin states. They do. But add there, we are always worked for me and then I sample. So you'll get an clocks. And I guess that's the other part of the club, but you can close them out in different states and then you are openly were to SU, any traction because they, this, they have a very special symmetry. So it's another ratio of word that connects North many-body physics and quantum simulation. When we are allowing nuclear spin degree of freedom. A TBI. I have a quick question. Hello? Yes. Yes. Okay. I was a little bit late to the talk. So it seems like a great talk. Is then a relationship with three electrons refactor. Can you obtain more significant digits on that using this technique? I think in general, do need to be sensitive to magnetic fields in order to measure this d factor. So I don't think we can do it. I mean, I mean, maybe let me tell you something. So if you have the ground and the excited state, and the fact that the excited state has a different effect. This is actually, this is a picture of the energy levels of the atoms in the presence of magnetic field GCC repurpose that. You see that the g factor between the ground and de facto between the excited state is different. Him in principle, you can't control. That means that if you are in this state, the transition to these estate is going to be different to the transition two different nuclear spin state has a different energy, energy, energy. So the clock can be so precise that it can be tuned to only coupled to you can you can determine, I mean, you can, for example, guideline have to have some energy to go to length half. But if you have seven, have, you have different energy to go to 27 have to in principle, you can tune the laser to, to, to measure very precisely is this energy difference. But I don't think we were going to be as precise as other experiments, a binary. Thanks. Okay, thank you so much for all these interesting questions and thank you anyway for this great talk. So let's say I thank the speaker again. Thank you. And thank you all for going a bit late with it. Thank you for this as a great talk.