 So good morning. Is it working the microphone or? Yes, no? Copy? No. OK, so good morning. So we start. OK, I hear some echo. Have to mute your computer. Otherwise, we will have echoes here. Yes, I will start with the first presentation from Tanya Milstoy, who talks about non-equilibrium dynamics and nanofriction in iron-gulon crystals. OK, thank you. So yeah, good morning. Welcome to the new day. And I have the honor to be the first speaker. And that's also actually my first day on the conference. I apologize. I'm late. There were some unfortunate other coalitions coming in that were so important that I had to come later. I apologize very much. But thank you very much for inviting me. It's really a pleasure to be here. It's the first time. And it's a wonderful place. I'm absolutely amazed. Yeah, so my name is Tanya Milstoy. I'm from PTB. I hope the power is struggling with this laser. So I'm from PTB. That's the National Meteorology Institute of Germany. So National Meteorology Institute means that we're actually building atomic clocks. So I'm from the time and frequency community. So I understand I'm maybe a little bit the alien on this conference. And our group is called Quantum Clocks and Complex Systems. Why? Because we are building novel atomic clocks based on complex cooler crystals. Mixed species crystals, 1D, 2D crystals. We're heading towards entangled clocks, cascaded clocks. So I can teach you everything about atomic clocks. But here, in terms of nanofriction, I'm here to learn from you. And we have five working groups, multi-ion clock, precision spectroscopy, where we're testing Einstein's general relativity, doing fundamental tests. We're also doing a lot of technology projects, building integrated ion traps with nano photonics, also a lot of industry projects, outreach and quantum technologies. But a very important part is to really understand the dynamics of ion cooler crystals. So while I was building the atomic clocks, I got interested in what are these creatures, these ion cooler crystals, how do they behave, what is their dynamics, and I wanted to understand it. And this is what this talk will be about. So what all of our projects share is to work with trapped ions. So I just would like to introduce a little bit to ions for those who are not familiar yet with trapped ions. So here you see a picture of a single trapped aturbium ion in our experiment. So this is the dressing on the monitor screen here. Ions are typically trapped in these kind of ion traps. They also look rather complex and evolved. So they have to be ultra-high vacuum proof. You have to put like 1,000 volts of voltage here. You drive them, and you drive them here with the spondromotive potential. You see. So an RF ion trap, a Powell trap, which was invented by Wolfgang Paul, is basically shaking the electric potential faster than the inert mass of the ion allows it to leave the trap. While the ion is trying to leave, it's always seeing this changing saddle potential. And on a time average, it's staying, and it sees actually a perfect harmonic oscillator. And why is this harmonic oscillator so perfect? Because it's very deep. It's like 10,000 of Kelvin deep. Like this, we have trapping times of an ion and such a harmonic oscillator will stay for several weeks up to month. And that means the anamonicities are very small. So we have this very perfect, parabola trap with the quantized states of motion. So we can do really very applied quantum mechanics with our atomic system. We can couple with a laser to the pseudo-spin of the ion and excited, fluorescent. But we can also excite and engineer the bosonic degrees of freedom, the motion. And we can couple the fermion with the bosonic degree of freedom. This is how you do quantum gates, how you build quantum computers based on trapped ions. So it's a very powerful system and we do laser cooling. We can bring everything to the millikelvin regime. So we freeze out pretty much all the motion. At the very end, this is rather tedious, but at the very end, we can also cool the ion to the quantum mechanical ground state. So, and then we know really the position of the ion within a few nanometers. And this quantum mechanical wave function. And for this reason, because everything is under such a high control, atomic clocks based on trapped ions actually have the world record currently for atomic clocks. So they're reaching just barely now at the 10 to minus 19 level. So 19 digits after the comma. But I promised to speak about cooler crystals now in this talk. So not about optical clocks. So let's start with the dynamics of cooler crystals. This is not a crystal yet. This is a liquid. So it's a self-organized system of when you put many ions in such a ion trap, it's very nonlinear with the cooler interaction, very chaotic dynamics. And this is happening when the kinetic energy is larger than the potential energy. Then we have kind of a liquid phase. It was very nice detailed by Dubin and O'Neill in the 90s. Here you can find all the different regimes. We are working in a strongly correlated regime. That means temperature needs to be below three Kelvin when we have something like one ion per cubic tens of a few micrometer. So that depends on the density of the crystal. If we increase this gamma coefficient giving us the correlation. So above one, it's basically in the liquid phase. This is already the strongly correlated regime where you will see strong correlations here from ion to ion. But if you cool even further and increase this gamma parameter, then the cooler crystals freeze out. And then you see these beautiful pictures of ion crystals. Here's the potential energy, then larger than the kinetic energy. And the ions can't hop anymore from lattice side to lattice side. That happens typically if the temperature is below 20 millikelvin. And there you have the different phases, 1D, 2D, 3D phases. Here in the 1D phase, we even reach temperatures of something like 1 millikelvin. We can cool the crystal even better. And I also want to point out everything what I'm presenting here in this talk is based on uterbium ions. So everything what you see here fluorescing in blue are the uterbium ions. Well, we're not only interested in the phases and in the static dynamics, but we were interested what happens when the crystal is changing the phase, the non-equilibrium dynamics. To recap here, you have these three different phases, 1, 2, 3D. And we can control them with our ion trap by setting the aspect ratio of the trapping potential right. So the control parameter alpha is basically the ratio between the radial confinement and the axial confinement. And depending how we squeeze or relax our ion trap, we can set 1D, 2D, and 3D phases as the ground state of lowest potential energy. And we're asking ourselves, what happens if we change now from one phase to the other phase in a fast way? This is, of course, very well known to you, especially in solid state physics. This is a thing that you are investigating, second order phase transitions. It's very universal dynamics, so you find it in so many subjects, like in ferromagnets and metals superconductors. And even in the early universe, phase transition happens, symmetry breaking happens. So you know all the Higgs fields. And actually, this is exactly the type of potential landscape. You also have an ion traps. Because on one side, you have here the two-dimensional potential. When a coulomb crystal is going from linear to zigzag, then you have basically such a type of symmetry breaking with a double-well potential forming. But if you take the third degree of freedom, the rotational degree, the ion crystal can rotate. And you basically get even such a goldstone mode. So it's quite funny. It's the same symmetry. And that's why it was proposed in 2008 by Fishman and Morici. They were looking at this phase transition from linear to zigzag. So where you break the rotational symmetry of such a potential landscape, and you go to a mirror symmetry with a double-well, they calculated that in a thermodynamic limit, solved the Ginsburg-Landau coefficient, and found that this is in fact a second order phase transition for really large coulomb crystals. So the idea came up. What happens if you undergo this phase transition in a very fast non-adiabatic way? Is it possible to form defects? That was proposed by Adolfo del Campo in 2010 to use the system as a test for kibble-zurek dynamics. We did this, and within a given time frame in this talk, I will not go into the kibble-zurek thing anymore, because I want to speak about nanofriction here. But this is how we started out. We wanted to test kibble-zurek dynamics. It was in 2012, 2013. Here, I just would like to recap how we produce topological defects. Because it's a very strange system. It's not a large system. It's not a thermodynamic limit. And it's an inhomogeneous system. You have a finite system and a parabolic trap. So when you undergo such a phase transition and you do a fast quench from linear to zig-zag, the phase transition actually starts out in the center of the coulomb crystal, where you have the highest coulomb density. And then the phase front spreads out over the crystal. And when you do this quench faster than the speed of the phase front, then the ions can't communicate with each other, can't talk to each other, so you're faster than the speed of sound in the coulomb crystal. And then you possibly can create defects. At that time in 2010, nobody had seen that and was heavily debated if it's possible at all, given that you have micromotion and very complicated dynamic in coulomb crystals. So we did this in our experiment in 2013. We published that. So we did this very fast quenches, fast means a few microseconds, undergoing this criticality. I will not go in experimental details, don't worry. But what we obtained in the end were indeed topological defects, so kink solitons. In a very finite system, fair enough, we see different types of defects, localized defects, extended defects, again, depending on our trapping parameter. And what do we mean with defects? So if you look, for instance, in Brown-Kiffcher, the Frankel-Kontorov model, it's basically a linear chain and you just map it so that you take every other ion, like if a ion has an odd place, you map this order parameter. So A is basically the distance from the linear nodal line. How far the ions buckle out from this linear line. This is the parameter A. And you see it can be positive, negative, positive, negative. This is when the zigzag forms. So you take every other ion and you multiply it with minus i to the power of k, k is the number of the ions. So you make positive, even one becomes positive, every odd one becomes negative. So this is how you define this discrete field phi. And then you see even such a zigzag chain becomes nothing else but the linear field phi, where you can define the order parameter here, which is like plus one on this side. And when you undergo this defect, you see the cooler crystal is changing from zigzag to zigzag, and here in the center, it doesn't match anymore. Here you have a collision, a domain wall forming, and then the field becomes negative. So these are the two different orientations, basically in this potential, that you can roll either to the left or to the right side. I know I'm preaching to the choir, you know all that, but this is how it looks in ion cooler crystals. And yeah, why we call this topological solitons or why theorists call it topological solitons, obeying this Lagrangian of the phi to the four model. Well, it's really, despite being a very finite system and the kink for sure can leave in the boundary effects, but nevertheless, just by looking at the boundary effects, you know if a kink is present or not, if the cooler crystal has flipped or not, and you can't destroy it locally, you can't deform the field locally and get rid of the kink, I mean two kinks can annihilate, but one is stable and stays. So you can only leave it at the finite boundary effect. And actually this is something that I saw in the experiment when we did many topological defects, I saw such a picture from the ions in a chain when you have maybe some background collision, some hydrogen particle flying by giving a bit of extra kinetic energy. And then I saw that the cooler crystal was still stable and localized on one side, but the topological defect that was present here was actually leaving the crystal to the left side. And you really can see how the ions are sliding on top of each other. So that was very beautiful and that gave me the idea, I mean a part of studying phase transitions and past Navarro barriers of different kink realizations, can we also possibly do nano friction in such a system? It's a self organized system so we don't have any constraint from outside. So of course here, this I will not tell you because it's teaching to the choir. I mean we are looking of course here in our many body system to the Franco-Contorova model. So our ion chain is very strongly coupled by long range interactions. And of course we're interested in the regime where something interesting happens. So in commensurate regime where basically the distance between the ions on one row is different than the distance, the periodicity of this corrugation potential. So can we see something like superlubricity what Obrien Perra predicted in 1983? And yes, there have been many interesting proposals also coming from these groups here that inspired us. So mainly in 2011, the papers by Benassia and Putivarasin inspired us that proposed to use actually ion cooler crystals, linear strings of cooler crystals to study nano-friction. They proposed to put a cavity around this cooler crystals to have a corrugation potential. So a standing optical lattice and then do a Franco-Contorova physics with it. Well, we are clock metrologists. We don't want to put a cavity next to our ion traps because that would disturb very much our atomic clock. So I will show you how we try to do it differently. But first of all, what have you predicted basically? What should be the observables of the types of nano-friction? The first thing that was predicted in this papers was the symmetry breaking in a finite chain that at such a pinning to sliding kind of a Obrie type transition in a finite system you should see a symmetry breaking and you should see the vanishing of a vibrational soft mode when you undergo the criticality. In an infinite system, it would stay in a sliding regime in a finite system. Actually, it would come up again and take on a finite value. So this is what we would expect to have. And as you know, in MIT and Vlad and Willetich's group for these types of experiments have been implemented very successfully and beautiful papers came out and Vlad was doing that in parallel to our endeavors at PDB in the beginning, we didn't know of each other but Vlad was really basically taking your suggestion putting this cavity around this linear chains that gives them a lot of degrees of freedom and seeing the onset of the Obrie transition in the system. We do it differently. As I said, we do not have a cavity. We're taking just a two dimensional cooler crystal with our topological defects. So we didn't want to install anything in our chamber but we were able to produce topological defects and we have seen them sliding. So we cool two dimensional cooler crystals to the level of a millikelvin. We have an imaging system with a spatial resolution of down to 14 nanometers where we can really detect the position of the ions. And our idea was can't we use somehow the back action and the self interaction between the ions basically giving us the corrugation potential because ions are charged particles. So if you have a six sack of ions, two chains on top of each other, you can think of it of the cooler interaction in the vertical direction as giving you the corrugation potential of the other chain. So the top chain would basically sense the corrugation potential of the other chain and vice versa, it's a back acting system. So the idea was if we bring these two chains closer and closer together, so basically enhancing the cooler interaction in the vertical direction, increasing this corrugation potential, we should also see some point of criticality. So we did some very simple mathematics as experimental physicists do it. So basically we were looking at the interaction strength of the ions along the chain given by the D parameter here and the actual confinement and the inter ion interaction between the chains. So our control parameter is basically then the ratio between the radial trapping frequency and the actual trapping frequency, which is again something like the trap aspect ratio. Now I come to the experimental observations, what we have seen. These are now actual pictures of our photos from our ions, so no simulation but photos. We have thought about how can we define an order parameter phi that would basically show us the symmetry breaking and we basically measure the relative distance from one ion and one layer to the other ion to the other layer. So we always took ions from layer one with respect to layer two and we measured the axial C distance. So always the next neighbor interaction and summarized over these delta Cs from neighboring ions along the whole chain here. This is the order parameter. And when we plot it, when we evaluate this data here, so the red points are our experimental measurements, then we see that the cooler crystal stays actually beautifully symmetric up to a certain point, alpha, this is this control parameter, the trap aspect ratio, given shown here also by the red line. And once we cross the red line, actually the cooler crystal takes on a certain preferred symmetry. So the order parameter takes on a finite value. And what do we see here in the experiment? That's maybe a bit confusing in the beginning because you see different types of realizations of the cooler crystal. You see here like three different types of realizations because if you do an experiment, it takes a certain time to take the photo. It takes a few milliseconds or now even longer 40 milliseconds maybe. And if you have some finite kinetic energy remaining even at one millikelvin, now it's a zoom up here. So you get different realizations, the red one and the blue one. And why? Because look at the Pao's Navarro potential. Look what happens at the symmetry breaking at this obritype transition. It's basically from sliding to pinning. This is how you call it. And well, don't be confused to Pao's Navarro potential of this complex system of the collective excitation is globally confining. It's not a flat line like what you have in an infinite system because of the boundary effects. It's basically bending upwards. And that's also the reason why this topological defect stays nicely confined in the center with the finite oscillation mode. But then when you undergo this criticality, the red line, you see that bumps, that barriers are forming in the Pao's Navarro potential. And this is the reason for the pinning effect. But in the beginning you also see that these barriers are very tiny. So in terms of millikelvin, in the beginning they're sub one millikelvin. Of course, they start from zero. And so if you have a tiny bit of thermal energy, the system can hop from one minimum to the other. This is basically the red realization and the blue realization. And when you take a photo with a long exposure time, you see both at the same time. This is what we have here. We also plotted the HAL function for our system. We evaluated it. And it's really what you expect that when you cross criticality, the HAL function is fragmentating and becoming monotonic anymore. And you have actually different gaps because it's in a homogeneous system. So the transition is at different places at different times. We're also spatially resolved over the Schuller crystal. It's quite intriguing. This was published in 2018. The analysis of the stick slip motion in the system, how basically you have different phases when you go spatially through such an homogeneous crystal and how you can explain the gaps of the HAL function. And then coming to the spectroscopic side, so far nobody had ever observed such a sliding mode experimentally. Not that I am aware of, at least. So what we wanted to do is, I mean this sliding mode, setting on the transition from sticking to sliding must be something like a shear mode. So basically one chain is going to the left, the other chain is going to the right. They're sliding on top of each other. So we must impose some differential light force with our laser. So we misaligned a focused laser so to put a little bit of light force on one chain which is stronger than on the other chain so that we can give some momentum. And we tickled this force by modulating the intensity to search for resonances. To have some resonant excitation. And indeed, when we're off resonant, this is how the Schuller crystal looks. And if you hit the resonance, it's very fragile because you have to go to very low resonances close to the criticality, then you see actually that you can excite it. It was the very first time that people have seen really the soft mode. And you know how it should look like. This is what theory predicts here. When you're coming from the pinned regime as you predicted in 2011, it should take on from a finite value and go to zero at the pinning to sliding transition. And afterwards, because it's a finite system, it should come up again and take on a finite value. This is what a theory would predict for t equals zero. We did not see that and we touched our head. What happens? Actually, we saw something like this happening in our experiment. So the blue data is the experiment. But then we realized that having one millikelvin of temperature is really quite a lot of energy at a critical point, of course, where everything becomes infinite and vanishing. So we have very strong nonlinearities at the point of criticality because of the finite temperature. And if you model this, the green line actually gives you exactly the prediction of what we observed in the experiment. And again, the reason our explanation was the finite barriers of the Paes Navarro potential make the system slide between the different first minima. There you see already that it's a very unharmonic nonlinear system. And that prevents you from seeing this perfect vanishing of the soft mode, yet at temperatures of one millikelvin. You would really have to go to temperatures of a few microkelvin to see this. Have really a more enhanced effect. But that was everything very hand-waving, yeah? I mean, this is our intuitive understanding of this. And then, of course, we wanted to get more clarity and that's why I show you now in the remaining few minutes the follow-up work. This is now the summary of the nano-friction. So actually, we had seen the first onset of symmetry breaking, non-analytical function for the first time, and also the soft mode. But we also realized we would have to go to a microkelvin to really see this soft mode vanishing or to even go quantum one day. Nevertheless, we have seen that the breaking of the commensurability biotopological defect was reducing the friction, also static friction, by more than an order of magnitude in our system and really making the system slide much easier. And we were very delighted to find that this is actually really similar to what also in biophysics was observed here in simulations of DNA unfolding. When you have a kink, basically a mismatch in the human DNA, then it also can slide and break earlier. So it's the same Franco-Contorova dynamics. We emulated it with ions, but now we wanted to understand a little bit more the thermal effect. And that's why I propose to first look at the linear to six-section transition again, because it's easier to handle also an experiment. So here, we also have the symmetry breaking where the system goes into this two potential minima and we should see also soft mode. We did this together with Haga-Landa and Giovanna Moricci. It was a very nice collaboration. We did again spectroscopy now on the linear to six-section transition at the criticality. These are the phonons that you see here. This is like the breathing mode where you have one node and the ions to the left go here, the ions to the right go there. This is the second phonon where you have two nodes and it's like an Egyptian mode. So you can basically excite the different collective phonons of the system with a laser beam. We did spectroscopy and a lot of theory together with Giovanna and Haga. And we saw that actually our experimental data and the theory can bring it to a match at the criticality if we consider the temperature effect of the surrounding phonon bath. So if you're interested what happens at the criticality where the soft mode should vanish, it's becoming everything very non-linear, of course. And this phonon can now, this mode can interact with a thermal phonon bath. So what we did is, we did a fourth order expansion of the cooler potential and then we averaged over all higher-lying phonons that are oscillating on a faster frequency and we can take a time average over them. So they give us a thermal background. It's kind of a floquet dynamics. And then the phonons, the low-frequency phonons that are driving here the phase transition, they are seeing this modified cooler potential by the other phonons. This is basically described here. We just look at the phonon one and two, these are this very two lowest energy phonons. And then we see actually a change in the frequency of these phonons in the frequency spectrum, which depends on the temperature of the system. And this mathematical approach seems to work well and describe really what we see in experiment in an intuitive point. You can also imagine that the system while you go undergo this transition because of thermal fluctuations is still bouncing back and forth between the minima. So actually the system stays more longer in the linear regime than it should before going out and deciding to take on a symmetry, zigzag or zigzag. So it's actually more a crossover regime and not a sharp phase transition, of course. And this is also something one should say because it was published in 2010 to be like a temperature driven structural phase transition. But I think in our paper we showed it's really a crossover driven by temperature. You can't say that the criticality is shifted by temperature. Okay, now I'm through with time. This is just the outlook. One day we also want to go quantum, but it's all about lowering temperature going to the micro Kelvin regime. And this is a very nice work that was also done by Lars Tim, who is here in the conference. We wanted to show that tunneling is also possible in such a system over tens of micrometer, which sounds very incredible in the beginning. But we did basically a treatment of the collective system defining the effective mass of the king defect, which can become very small. So actually the king can move a lot while the atoms are not moving at all. We solved the Hamiltonian and the wave equations for the system. So you see symmetric, anti-symmetric systems and you really can see how they couple close to the Aubrey transition and you see tunneling effects. You can see how the phonon spectrum splits up even in the quasi-classic, close to the quasi-classic regime. Here's the tunneling regime where the interact already. We have seen tunneling motion, how the quantum king can go back and forth. But this is, I could give a whole talk about that. I also should point out Vladan Vulletich collaborated with Bonetti et al. He had a different treatment, but he also could show quantum dynamics at this Aubrey phase transition. So I think that's very exciting. And in the future, we also will go towards energy transport through the topological defect. Again, nice work by last time, where our idea was to use the king as a switch when you impact kinetic energy on one side. It will not arrive on the other side, depending whether you're on the sliding phase or on the pin phase. And with our control parameter, we can switch that on and off this effect. So with this, I'm at the end of my talk and I thank you very much for your attention. Thank you for the fascinating talk. We have already over time, but I have one question. Okay. So, beautifully, this irons in different traps. So, in different external potentials, ring like 3D, how flexible can you say both? What are the limitations? Or is it... Patch potentials. Patch potentials are the limitation. Irons have many advantages, but at the same time make them disadvantages as usual in life. They're always two aspects. So irons are charged particles. That's why we can trap them in this iron traps. And maybe I show them quickly. Oops, it's very slow. The iron traps already look rather complicated, yeah? I mean, the beauty is we can control them so well. We localize them to 10 nanometers. We can move them around with all these voltages that we apply here on the many electrodes. So it's a beautiful system, but at the same time, being a charged particle makes it very sensitive to any electrons sitting on a window or on an insulator or anything. So as soon as you're thinking of rather long, spatially extended systems, you have to make sure that you control everything really to the nano volt level. And that means you need many, many control electrodes to compensate things. And I mean, Hartmut Hefner was the first one in Berkeley to make a really a ring iron trap, where you have then this very powerful geometry of having a quasi-infinite system without the boundary condition. But the problem is you really need many, many control electrons to always compensate any slightest deviation in the field. It's a very fragile system, and it's a huge technological endeavor. And it took almost 10 years, I think, for Hartmut to get this first prep, and it still can be improved. And so maybe in the future, yeah, I mean, we're working on iron trap technology at the same time, but it's really technical engineering. Okay, so thank you again.