 The talk by Sebastian Deffener unfortunately had to be canceled, but we now have De Vera Sagal, and she will give a 30 minute talk on quantum flicker noise in atomic and molecular junctions. And Vera, I'll give you a heads up after after 20 minutes. Okay, thank you. I will share my screen. Just a moment to organize it. Can you hear me properly. We hear you and and I see your screen as your cursor. Okay, thank you very much for this very nice organization and today is about quantum stochastic thermodynamics so I hope I fit in here. I'm going to tell you indeed about a platform and a specific experiment that very well fit into studying a some of the questions some of the topics that were raised in this conference. We will talk about whether it's different bounds trade off so other questions regarding stochastic thermodynamics specific title a quantum flicker noise in atomic and molecular junction. This work was done actually by an experimental group and our role was just to support them to model from the theoretical side to suggest the theoretical picture but I will describe the experiment and I will also try more broadly to describe this platform that again could be used when we have used it actually to study other questions. So the reference to the, the work is written here below I will get back to that and you can already see in this illustration, what the system is about I don't think it was mentioned so much at this conference. These red pencil like objects are actually gold electrodes. So just plain gold. And as you can see the system is I hope you can see my hands. It's banned. And the idea here indeed is to control very carefully the separation between these gold electrodes such that eventually you can create a very small constriction a very fine. You can see here in the, yeah, the edge here are only few at home at this contact region such that you can realize quantum conductors, and the extreme limit of actually pulling it and again stretching it in a very careful way you can even break this junction. And in between you can trap molecules and also study how molecules single molecules conduct electrons. So that's experimental setup ignore the circuit here it's the circuit is for something else but overall you apply voltage and you measure charge current in the system. Just a moment here. So how do we think about the conduction of electrons in the system a very rough model and I will get back to that later on. We think about this see supposed to represent this very narrow constriction in between. So small just few atoms in this gap or even one atom. The pictures that we have in mind is that electrons transfer this region coherently. So the mean free path is just longer than this constriction length, such that there are no scattering processes within the same sea region. Outside that yeah these are the other regions I will get back to them later of course there could be defects there are other scouterers and life are more hectic. So we measure in this experiment as I've said they apply voltage the measure measure charge current there are also other possibilities you can also apply temperature difference. And this is really just my matlab depiction of here is a charge current as a function of time and again if you can watch me yeah you get this a fluctuating current. So you can just calculate the average current and from there you can already gain a lot about the system, whether they are interesting interactions between electrons or between electrons and phonons electron and the environment. So oftentimes people just ignore the fluctuations but this is where we are here this week, trying to find out what we can learn from fluctuations. So overall in my group, we have been indeed looking at the current noise for charge or as you have just heard before, for energy transport, motivated by different questions, and very briefly just to lay down yeah what could be the, what are the several aspects of noise. As we just have heard, looking at noise can help us understand whether methodology is actually thermodynamically consistent read feed for example suffers from issues, fundamental issues. Question number two, and that concerns the talk, my talk, what information can we gather can we gain from current noise that is obscured in the mean current itself. And number three which I will touch very briefly but it was a motivation for me and many talks that we've heard. So this also means something about the performance of your system in terms of the thermodynamically in terms of trade off relations in terms of bounds and I will also say something about that. Oh yeah so I have here I just did some illustrations okay for the second law the microscopic level question about devices what we can learn for about charge transport and questions about trade off or bounds concerning fluctuations not just the mean power or efficiency. So this is an outline of a different talk that I've never given, I guess my dream talk about noise, which I'm only going to talk about the flicker noise highlighted in yellow, but in my dream talk I divided to three parts I will, I would have talked about these interesting relationships that many people have worked on in my group we focused on what they mean in the quantum domain, the thermodynamic uncertain uncertainty relation. This bound at the center of the page on the tighter bound on efficiency or yeah we'll say actually few words about it in the next slide. And then I will tell you about different measurements so we have been working with an experimental group my group is only doing theory. And collaborating with an experimental group and trying to understand from the theory side, different aspects of noise and finally method development, which is also close to our heart. But again today just for the flicker noise and yeah maybe in the future. So here is Matthew once more I wanted to advertise another project of him from last year which is relevant to the to my talk here. So here's the aspect of this type of system and electronic conducting system you can see here in a illustration below. So one can test the thermodynamic uncertainty relation and this is a y axis here. And our point in the study was to point out that in the quantum domain you can actually fully violated so that's a black line here. You can design the conducting junction. In the picture here in the inside you can see the transmission function such that you get something which is really not interesting because there is no bound it's really the uncertainty relation is such that they are from the last from the right side from the lower bound you just get zero. However, our point in the study was that once you get beyond this idealized limit of a very perfect box car type transmission function, you actually recover the cost precision trade of relation and that's a dashed blue line. So I will not dwell on the study but I'll call you to look at it, and another work related to fluctuations which again involve Matthew and I realize. And again, can be realized with the platform that I'm going to discuss in more details concern this interesting game. So what do we have here. This we proved it in in our response and we also tested it beyond in our response it's generally valid for people have demonstrated violations say in some special cases. So what we have here if we focus on the heat engine that's a thermoelectric power generator that is illustrated here for quantum dot system. Why not the center supposed to represent a quantum dot and at the left and right we have two metal electrodes, a different chemical potentials and a different temperatures, and the idea is to use heat and generate work in the form of electron transfer and form of power output, electrical power output. So the efficiency we all know what it means it's really just about the output power over the input heat. So that would be just a efficiency when I think about the means what we have here at the center which we refer to us it was the same type of ratio of power output power over input heat but now for the variance. So this is what we refer to us it too it looks like efficiency but for the fluctuations and at the right hand side is a karma efficiency. So this is an interesting tighter bound for efficiency or you can also think about it as a bound on relative fluctuations for input heat and output power. And again we tested it and try to understand implications and it can be also tested with atomic scale and molecular junctions. Okay, so finally today type of to present this platform. I've been working in the last five years with the group of oriental from the Weizmann Institute and back then he's graduate student of fear. And again you can see here the type of experimental system that they have been working on. Now, if again it's just a scheme but trying to show the atoms and doing the game. So this is all gold and again it's banded with that's the way they control the separation between the two metal electrodes. And they can control it such that there are few atoms in the region in the contact region or ultimately only one. And what they would measure the very basic quantity quantity would be just the electrical conductance. Yeah, so it's really just a voltage current over voltage in units of the quantum of conductance genot. So let's focus on the top one in blue. This is conductance histogram so we refer to it. So you just see counts and what does it mean they repeat the experiment many many times generating such junctions with few atoms in the contact region measuring the conductance and again reforming the junction. So these are the histograms and as you can see for example you get many points around conductance, which here in the units of genome is about one. And that refers to according to theory, having about single single atom in the contact region. But you also have as you can see conductance at multiple values of quantum of conductance. And again the theory here describes or corresponds to having multiple atoms in the contact region for the so the top blue one was just a pure gold and contact region. One below concerns the situation where the system is peppered with hydrogen molecules. And the main distinction here if you look here at the tail is that you start to notice that you do get some junctions some of these setups, where the conductance is below one. And in this situation where the conductance is so long. These are situations when you actually break the junction there is no longer in this single gold atom at the contact region, but actually only a single hydrogen molecule sitting there in whatever conformation it lives. So that's why there is some yes you can see some variance in the what could be the value of the conductance, but these corresponds to having single molecule in the junction. So this is a basic measurement of just electrical conductance. But obviously, as I mentioned before they are also doing noise measurements or not just a charge current but also focusing on not just the mean current but also its fluctuations. So the basic observable here would be the power spectrum of the current, and that's this S of omega so yeah you take the current. And you have the fluctuations around the mean, and they take the full transform absolute value square and that's what we refer to as a power spectrum of the current. Experimentally, they would get something quite messy. So that's this figure at the right hand side. That's a power spectrum as a function of frequency. And the different lines as you can see there are many each one is saying it's all for one single junction but changing the voltage. And the chaos at the center corresponds to what happens with the detector so ignore this mess at the. Overall, you can see that the power spectra has different regions. There is a what we refer to as a white noise region where the power spectrum does not depend on frequency. And you can extract a lot of interesting information about the system from there. And then there is a region. Here it is, which we refer to as one over F noise, because if you analyze it more carefully. It always pays us one over F or one over frequency. And it has different names, pink noise flicker noise RTS sometimes yeah, but that's what I refer to as a flicker noise. So, generally when a orange group and other groups in this community have measured the power spectrum, they focused on the white noise component, and again try to understand what oftentimes in this community is referred to as short noise. And it has been, it has been used in the last is it already 30 years or so to study many interesting effects in correlated electron system for example or electron phonon effects, just based just by watching the noise and analyzing it. And but today I will focus on the one over F noise and indeed a question that Owen came up with couple of years ago was, is it really just garbage, because that's how people treated this one over F noise in this community for a long time it was really just a new sense. We're exploring this component of the noise. But the question is whether it actually tells us something useful about quantum transport. And that's what we were about here and yeah I guess it's about 10 more minutes to get to that. But before that I wanted to mention that one over F noise is very ubiquitous in many systems in physics not just in electronic devices. It has been a hot topics for many years. Still there is a broad community that is very much after it. In electronic devices, the agreement is that it's not very exciting. I mean this way it is a component of the noise that you see over there at low frequency. It's a, it's a new sense for measurements for detectors, because as you can see when you go to low frequencies it diverges, but the physical origin which people were after and quite curious about this for electronic devices. And that's because of different defects in the system so because of imperfections in the design in these materials, where you have defects that oftentimes are referred to as two level system fluctuators that can change their mobile or they can change their confirmation, such that they change the, they lead to changes to fluctuations in the current. So the argument in the community and indeed in physics or in engineering in the last decade or even more these studies of one over F noise were very much in the engineering community. Just trying to get rid of it rather than think more deeply whether there is something interesting quantum mechanically that you can learn about your system. Yeah so here's a collection of reviews you know when a field already has many reviews it means that it's maybe not so exciting. So here's in the already a century, moving from solid state systems to graphene devices and even more so in the last 10 years or so thinking about one over F noise, indeed more creatively. What can we learn about it, thinking about single molecule devices or single graphene sheet. This last slide also wanted to mention that one over F noisy revival also because of quantum technologies. It is a hindrance in superconducting qubits and this is a conference from last year very interesting and touching the one over F noise, this low frequency noise and from different directions. Okay, so back to this slide or back to this picture of you know it's just an illustration of the power spectral noise as a function of frequency. We're going to tie enough frequencies we see it getting to the white noise region, but low frequency. Yeah we have this one over F noise. And again people asked, where does it come from is it because some fluctuations in the contact region. Is it because a molecule changes conformation. Maybe there are slow processes where the molecule moves between different states. Is it because we arrangement processes again of gold atoms maybe in the contact. So these are the types of questions that were interrogated. Now, what theory are we going to use to actually try to model this effect. So far what we did, which is, we think appropriate for the systems that were studied but of course once going to more rich system one would need to include electron electron effects. What we have used so far is a theory of non interacting electrons a very basic one. It's called Landau scattering formalism as you can see quite from some time ago, quantum coherent transport the idea is that the mean free path of electron is longer than the constant length of the size of this construction. So this picture is taken from a different context but I just liked it because of again you can see this atoms around and the size of the construction. And again the idea is that atomic contact is atomic scale atomic scale. So what do we think about it theoretically with this quantum coherent transport, the main name quantity that we consider is so called transmission probability or transmission function which is energy dependent in general. So the conductance the electrical conductance one can show is given by the sum or overall it's given by the total transmission for ability and the transmission probability can be decomposed into come to contributions of different so called channels. It really depends on the system. If you are into something that is at the level of mesoscopic or even microscopic something like waveguides, this could be transverse modes that are the different modes of your system, and each of them could contribute different contribution to the overall conductance. At the atomic scale or molecular scale the different channels really correspond to different orbitals that line up together to contribute to the conduction. So there is a lot of, there is a big deep connection between the transmission function and the actual atomistic or molecular level picture of what actually drive allows electrons to transfer the system. But again from the theoretical part, the creature that we are going to look at is a transmission probability and considering that there are multiple possible multiple channels multiple orbitals that allow transport of electrons in the system. So if you just measure the conductance I showed you before the histogram, you just know that it's a total transmission that it gives you, but you don't know how many channels are possibly contributing, and what is relative or what is the contribution of each one of them. So you are really missing some insight into what's going inside your system by just measuring the total conductance. Noise measurements come to play. This is an example at least where they can be useful. From noise measurement you can start to dig in more deeply into your system and find more information about these different transmission channels and their contribution. And obviously if there are interactions you get into another application of noise measurements. But today I'm just going to focus on this decomposition of total transmission into the separate channels. You've got about 10 minutes left. Thank you. So yeah so this is where I'm finally getting into the experiment. Again, contribution experimental work was done by Oren and his student from my group, Abhay and Junji, a former postdoctoral fellows contribute to the modeling. So this is again from the experiment they measured in so you can see here the noise as a function of frequency. The different lines are just for repeating experiments, forming again these junctions. And first they verify this one over F dependence. And the basic question was, yeah, can we learn something useful about from this one over F component about the system. So this is a summary of the results and last time allows I will get into more details. I already told you that the total electrical conductance of the system is just given by the total conductance so you by measuring the left side the conductance. You don't know about the decomposition into different channels, what people have been doing in the last 20 years or so they also measure the short noise, which is a white noise regime here. So really what one can show is that it's given by this interesting connection again between transmission contributions. So as you can see the second equation is distinct in terms of the functional form of transmission from the first one, meaning that if you have, let's say two channels you can play with these two equations if you measure both the conductance and the short noise. And now you can start to analyze and find out what are the channels and what is their contribution. But these are just two equations. And what we showed in this work and that's indeed the main contribution here. The third equation and we show that the flicker noise here there is obviously one over F dependence which is not, I omitted it here from here, but the pre factor of this one over F, again depends on the transmission probability in this form. This is distinct from the short noise it distinct from the form of the electrical conductance. And as such, it's another no to learn about the transmission channels in the system. So again from the fundamental side I will point is that the one over F noise emerges indeed from mobile defects in the junction so this is a picture that I'm trying to show here. Yeah, you can see the red and blue lines. There are some for electrons crossing the system. There are some scatterers that lead to this reflection probability. So this is the origin of the one over F noise just having this mobile defects. That's just the usual story. What is interesting is here is that the total transmission is given by this superposition of processes of electron going directly left to right or electron doing this. The process where it's scattered by the same mobile defects, such that the pre factor of the one over F noise does tell us something useful. It does tell us about the channel decomposition. So that's the main story here the one over F dependence itself is again sorry boring, but the pre factor does convey a useful information about the quantum transport of electrons in the system. So the sketch of the derivation here I will not get into the detail the sketch is that the total transmission probability for an electron is given by an interference process where some electrons. So not so much one pathway is going directly so that's a black one, and that's the one here. There are some processes to the lowest order in the in the collecting these processes where either there is a scattering by defect at the left side, or there is a scattering by defect at the right side, and overall the transmission amplitude is given by the difference of these effects. And when I calculate from here, the current, and then the power spectrum, I will find the, the one over F contribution showing up due to these defects, but furthermore I will see this town when I take the absolute value square it will become our square and from the reflection amplitude I will get the additional one minus now. So here I will just summarize a what we can learn from this. So this is a power spectrum again the details you can see in the supplementary material how we derive this expression, but this is from the theory part our prediction of how the power spectrum should look like. There is a voltage dependence. It was verified experimentally v square. There is a one over F dependence. Okay, well that's one can verify but the interesting part again is that the pre factor tells you about this interference of electrons and it does depend on the transmission probability in this unique one. So in the last few minutes I'll just mention what experimentally they did. We came up with this expression and from the experimental side they repeatedly generated constructed these junctions. So each dot here each circle corresponds to an experiment. So in the theory side we in the gray region, we predicted where they should find them junctions well. Yeah what are the possible values for the flicker noise as a function of conductance so that's a, yeah that's a region where you, you can measure flicker noise. The magnitude that you can measure for the system. And indeed, I hope it's convincing. Most of the points say or we could at least rationalize what's happening. Let's say in the region in terms of the lower bound also in the upper bound in terms of how many channels and what's their relative contribution. And furthermore I will skip that another useful. This is actually an application of the study I mentioned to you that there are now three equations that we can use to decompose the transmission total transmission into the separate channels. So if you focus for example on point number one that's a measurement of the final factor the white noise short noise measurement, as well as the electrical conductance. So if you just use these two equations the first and the second, you get a blue regions, which means that you have quite some uncertainty in terms of what are the channels and what's the, yeah, what's the contribution. You just know that there are maybe four channels and the second one contribute about point between point zero five to point two so there is quite some uncertainty. So once you put together the information for the flicker noise, you get this red. Now, predictions for what are the different values for the channels. And as you can see you can get a very significantly narrow and prediction or result for what's possible for the transmission values. So I will quickly summarize what's next for the flicker noise. And ongoing work. Thinking about thermometry. This was this flicker noise that I've described was activated by voltage or was a probe by voltage. One can also use a flicker nose for thermometry. One of the components one can probe more than material properties. And today I describe situation where we assume, again, based on other studies that electron electron repulsion effects are not significant, but one can design systems purposely with interesting electron, or many body effects in general, and use a flicker noise again to try to prove them. One of the messages that noise is actually diagnostic tool I think that was a general message from this conference. And I just wanted to that's the last point. Now to touch again is something that maybe goes back to general uncertainty relation or bounds and games that the auditions like but we can prove experimentally with the same platform. We studied from two years ago where we use the same platform before and here again from the experimental side and offer. And we looked at this thermodynamic uncertainty relation that was studied a lot in the classical stochastic thermodynamics, and we looked at it in the again in the quantum regime using this atomic scale junctions. And we wanted to see, as I've told you before one can actually fully violated. We wanted to see in the systems what happens. And it is that's the answer. Where is it. Oops, sorry. That's uncertainty relation. Thermodynamic uncertainty relation. It's plotted here. Okay without too many details in this system it satisfied, but we gave a prediction that when gamma which is an interaction effects in the system are strong enough, there is a possibility to actually break down and violate this result. So with that I would like to just acknowledge my group and my collaborators and again thank you very much for inviting me. Thank you for that for that very, very nice talk, I certainly agree with you that noise is not always a nuisance, we should all love noise. And with that, let me open up the floor for questions. There's a very clear talk. Actually, since some of the since we don't have the final speaker here. And I know that some of the earlier talks went went quickly if there are any follow up questions or comments or discussions that anyone would like to have related to any of the talks during this session. The floor is open. I may, if I can I would like to comment about the question actually regarding the previous, the talk of Matthew. So related to the point about the V model. Matthew responded to reply to that but I wanted to emphasize we were not claiming that this effect of coherence in the V model is a new effect we. It has been analyzed beautifully with previous work so that was a new element in our study. As Matthew mentioned, what we wanted indeed to it. We use this system as a case study to start to find out what different master equations predict for it. So we've, there's a beautiful literature indeed on the system about coherences at equilibrium out of equilibrium, and so on. Okay, thanks for clarifying that and I see we do have a question in the chat. Jose Daniel would you like to ask unmute yourself and ask that question. Okay, thank you very much. Yes, I would like to, to ask a professor finally in your in your results, which is the, the origin of the one over F square noise. No, of these three regimes in the noise. Yeah. Okay, so you're asking about one over F square. I know the one over F because in our system. The functional form was actually one over F not the one over F square. What I can tell you that they found was, I didn't highlight it enough. They test they consider two systems one with when it was just plain gold. Actually, there was no one over F component or it was extremely weak and the second system which I mentioned briefly, they peppered it with hydrogen molecules. And once they have these hydrogen molecules around. That's when they saw this one of the components so they. We didn't do more like atomic scale simulations that's actually something really interesting for me, but the pictures that we have in mind is that these hydrogen molecules are small enough to penetrate the gold. So they're sitting inside and they're mobile they can diffuse on the surface or inside. And that's where they can lead to indeed changes in the temporal changes in the scattering cross section for electrons. So that's for the system at least. Thank you. It is that we put there intentionally. Thanks for the question as well. Any other questions, questions or comments related to this talk or any of the other talks. Okay, if not, I suggest we let's thank collectively all of the speakers for very, very nice talks and thank everybody I thank everybody for attending this final session of the of the workshop and indeed for attending for attending all the other sessions as well. So I'm going to stop recording now.