 Not yet. I think it's strange because I am in display mode on my computer, but here is not. Okay, so I think I share the other screen. Okay, this is good. Okay, I can start. Okay, hello. My name is Ziwei Dou, and I'm working in the mesoscopic group in the laboratory of associate physics associated with the University of Barre-Sacré in France, and I'd like to thank the organizers to invite me to the talk, and today my topic is supercurrent noise in a phase-bossed superconducting normal ring in thermoequilibrium. So when we talk about superconductivity, the first remark that people usually have is that it supports a dissipationless current or supercurrent, and it's interesting to ask whether such dissipationless current is noisy. So indeed there are several pioneering theoretical works using the superconducting QPC as an example. So here we have two andrives spectrons, and different from the Josephson junction, the andrives level can be tuned by the phase difference between the two superconducting electrodes, and especially when we are close to the phase pi, the two levels can be very close to each other, and therefore at finite temperature the andrives states can fluctuate between these two levels, which results in fluctuating supercurrent. So indeed the noise spectrum of this supercurrent noise has a significant magnitude even down to the zero frequency limit. So in this talk I'm going to, we are looking at a similar system called the SNS junction. So the SNS junction is formed by two superconducting banks coupled by a normal metal. So here the supercurrent is supported by many more andrives states. So if we are in the long diffusive junction limit, then indeed we have a mini-gap, which is maximum at phase zero, and is close at phase pi. So different from the superconducting QPC, so if we have a long diffusive junction, the size of the mini-gap is actually proportional to one over the length square. So in this case we can have a region where the temperature is larger than the mini-gap, but still much smaller than the native gap of the superconductor. And therefore we expect to have a much larger supercurrent noise, and we have a better opportunity to observe it experimentally, which has not yet been achieved since its prediction long time ago. So at the same time from thermodynamics we have a very generic relation called the fluctuation dissipation theorem, which is valid so long as the system is in thermal equilibrium. So in our case since we have a very large supercurrent noise, then this entails a high linear dissipative conductance of the junction, and this similarly contradicts superconductivity, whose hallmark is this dissipationless current. So here for some of you the notion of dissipation might be associated with resistance instead of a conductance, but here I like to emphasize that we for the whole talk I stick to this parallel circuit model, and here indeed the conductance G equals 0 means no dissipation. So in order to solve this paradoxical dissipation rising from the supercurrent noise, we need to think a bit more carefully about how we define and measure the linear conductance in SNS junction. So this is not actually very straightforward as for example in the ohmic conductor where we can simply just put a little bias and measure the current, because in SNS junction the IV curve is highly nonlinear, and so long as we put any nonzero voltage bars we will drive the system out of the superconducting branch, and therefore we break the fluctuation dissipation theorem. Another possibility is to adopt this phase-bossed scheme. So here the SNS junction is in a ring geometry and is coupled to a resonator. So in this case the the phase is controlled by the DC magnetic flux, and on top of that we introduce a small AC flux by the RF signal, and also we have a little AC current inside the ring. So here we can define a quantity called the magnetic susceptibility chi by delta i over delta phi, and this setup has several advantages. The first one is that so long as we limit our input signal to be very small, then we can always guarantee that the system is in thermal equilibrium, and the second one that since we are measuring at finite frequency, then we can access to this junction dissipative conductance. So here for the for chi in general it has two components, the in-phase components chi prime corresponds to the Josephson inductance from the supercurrent, and we also have this outer phase component chi double prime, which corresponds to the dissipative conductance, and physically this corresponds to the finite time needed for the system to equilibrate or relax to its instantaneous ground states. And now the question is we want to ask whether this linear conductance is the same that's implied from the Flush Ration Discipline Theorem. And then to experimentally test that we realize the third advantage of this setup of this scheme. So here we actually can do both measurements using this both measurements using the same setup. So for the dissipation measurement we just measure the transmitted RF signal to the input. For the noise measurement we don't send any signal and just listen to what's coming out from the resonator. So here is the structure of my talk. So since we are going to do quantitative comparison between two set of measurements we need to first calibrate the system carefully and then I'll show the main result that I measure the supercurrent noise and this dissipative conductance using the same setup. And then for this dissipative conductance we see there's a strong temperature dependence which is very different from what you expect in classical Drude conductance for example. And to explain that we use a linear response theory and this interesting review of a high current correlation that corresponds to this temperature dependence. So now we come to the first section. So here is a picture of the device. So we have a golden nanowall as the normal metal and the superconducting alloy molybdenum rhenium is deposited for the for the rest of the device and here to close the SNS ring we have a thin line superconductor which also acts as a coupling inductance ALC. So the resonator is formed by this meander line and which provides the inductance AR and we have a large lump components CR which gives us a relatively low resonant frequency around 100 megahertz and we also have intrinsic loss for the resonator which is characterized by this conductance GR. And we also have a homemade cryogenic amplifier to be directly connected to the device. So here in order to do that without killing the quality factor of the resonator we have designed the amplifier to have almost infinite input impedance and therefore we have a gain only around unity. And this amplifier also has also has noises that we need to calibrate experimentally. So to calibrate we performed the measurement at high temperature and fixed phase and here the SNS ring is just can be considered as a phase independent small offset to the resonator parameters and therefore we can simplify our analysis but we still have this circuit quantities to be to be to be characterized and here I only show a brief sketch about how I do I do this and if you are interested in more technical details I'm happy to answer that after the talk. So here on the left is the measured transmission coefficient gamma and this can be fitted to our Thurkin model so here we see on a nice agreement from which we can extract the resonant frequency and the quality factor and on the on the right is the measured direct measured voltage noise spectrum and here in order to achieve a very nice very low data uncertainty we average by a huge amount of spectrum. So also from the second model we we can see that this measured voltage noise has two terms one is really coming from the thermal fluctuation the other is coming from from the noise of the amplifier. So on resonance this the the voltage noise is simply linear as it is simply a linear function to temperature and indeed this is what we observe and from the high temperature data we can extract the slope and therefore we can deduce many quantities of the resonator and to obtain the the noises for the amplifier then we need to fit the data to the to the complete circuit model so here we treat the amplifier noises as the fitting parameters and to do that we can indeed we get all the quantities experimentally. So here just to give a brief idea of the relative magnitude so here is our measured spectrum and the thermal contribution is relatively 20% of it. So now we're ready to show the main result so so here I show two two spectrums at a fixed temperature but one at phase zero the other at phase pi. So so again if we look at this expression what we are really interesting is this super current noise which is included in the thermal contribution but the amplifier contribution also depends on phase due to the due to the the junction impedance due to the junction emittance so therefore how can we extract this super current noise. So to simplify the analysis we take a step back so to do that we consider the whole circuit of the resonator plus the SNS ring and therefore as a equivalent circuit we what the emittance y-tort has a phenomenological quantities g-tort and L-tort and our strategy here is to first probe the super current noise for the whole circuit and then work our way our way back to extract the contribution from the SNS ring. So as a first step we want to answer whether this g-tort measured by noise is the same as the g-tort measured by transmission. So here again this is the spectrum that Dorothy measured at two different phases so the procedure we we use to treat the data is to for each spectrum we fit to this complete circuit model so it looks very complicated but here we it's enough to notice that we only have two unknown quantities which is g-tort and L-tort and for the rest of the circuit elements they they have been calibrated previously. So here is an example to the fit so indeed we see that our model is highly accurate even if we zoom in just around the the resonant frequency and especially our model is ways precise to to resolve two important cases so the first one is we indeed have an intrinsic dissipative conductance coming from the SNS ring which is what we expect from from theory. The other is that we don't actually we don't have any dissipative conductance from the ring but the observed phase modulation is due to the due to the phase dependent Josephson inductance so here is corresponds to the first case so indeed we see there's almost perfect agreement between the fit and the data and if we replace the g-tort with just a resonator dissipation contribution gr then we see that the fit can never work successfully and indeed the difference between the fit and the data is the noise voltage noise coming from the SNS ring. So if I repeat this fit for all temperatures and phases then I got this one of a L-tort and G-tort as of which I plot here so both quantities have strong phase dependence and also we have a high precision in in measuring these quantities so now we have completed half of the task and for the next half we need to send in finite RF power and measure transmission so just as a brief recap as I introduced before the SNS ring can be characterized by a linear scalability chi which is directly proportional to the junction admittance so the the in-phase component chi prime is related directly related to the Josephson inductance and the outer phase chi double prime is related to the this dissipative conductance. So again if we measure the transmission coefficient of the system this G-tort and L-tort of the total circuit can be directly measured by the resonant frequency and the quarter factor of the of the transmission coefficient. So if we transform what we directly measured into the the two quantities one over L-tort and G-tort then we indeed have this result and this can be directly compared with the noise measurement so indeed we see here we achieve a quantitative agreement between two independent set of data and this comparison is even more this agreement is even more remarkable if we look at the expression so here only one quantity which is L-R enters into this comparison and this L-R has already been experimentally calibrated so this means that we indeed have a intrinsic dissipative conductance G-tort which which remains the same and linear even when the input power is reduced down to the noise limited level so then if the if the thermodynamics is correct then we indeed we should be able to have a supercurrent noise so then I will show you how I extract the supercurrent noise from from the measured voltage noise so in order to see that we have to open this black box of resonator plus the ring so here the the G-tort is a sum between a constant contribution gr coming from the resonator plus a small flux modulation and this one is directly proportional to the conductance of the SNS ring and this proportionality which which is the coupling coefficient is a small quantity and the same is applied for the for the noise so so here we also have this coupling coefficient kappa here which means that the supercurrent noise reflects into the measured voltage noise but with the magnitude kai times smaller so this is indeed the challenge of this measurement so if we do this data processing then we realize the phase variation of this super current noise start to be comparable with the data uncertainty of our measurement so to further improve that we realize that we actually take the measurement for for many frequency points and therefore if we average like several hundred of frequency points near resonance we can further improve the precision and the mean value actually shows a nice phase dependence and this one is has also has quantitative agreement expected from the Fluttersian dissipation theorem so indeed we are able to measure measure a super current noise with the precision on the order of 10 femto ampere square per hertz and also we experimentally confirm the Fluttersian dissipation theorem in this for SNS ring so now we can dig a bit deeper to see the physical significance of this dissipative conductance G which has a strong temperature dependence so here indeed we see that the this conductance depends on temperature a lot and especially this conductance is enhanced at lower temperature so this is different from what you expect for classical Drude conductance in the Milikovin range and actually this this temperature dependence has has been reported in several earlier walks and they have some like one over T dependence in the conductance so to to understand that better we need to convert and to be compared with a theory that I will describe later then we need to convert from what we measure which is SNS ring into the SNS junction so here here I I like to remind that the the susceptibility of the ring is directly proportional to the to a G-tort so in the later of the talk we're talking the language of this Chi ring so if we do the circuit analysis the the Chi ring and the Chi junction are related by this simple relation and here we have this quantity beta which is the screening coefficient which is due to the supercurrent circulating in the loop so indeed if beta is much smaller than one we have the Chi ring almost equal to Chi junction but in our case this quantity is not so small and we know that if we have some not so small screening factor coefficient beta we can have a large phase dependence in the measured Chi ring even if the Chi junction is phase independent so so if we revert our measure data into the to expose the junction Chi double prime as what we see here in the solid line indeed we have a much weaker phase phase dependence and here I like to emphasize that this screening effect is not a measurement artifact but actually it helps us to identify this phase independent contribution coming from the SNS junction which is otherwise hard to be disentangled from the phase independent constant coming from the resonator so if we plot this junction conductance as a function of temperature indeed we also have this one over T dependence and then to explain that we use the linear response theory and here as a preview to our conclusion we say this one over T dependence of G actually is a manifestation of enhanced current correlation near the Fermi level and this is due to the proximity effect so the linear so the linear is in the linear response theory so we have the AC flux introduced this linear perturbation to the both the Jens Hamiltonian and the finite relaxation rate gamma is included in this in this model by the master equation and therefore we can calculate the linear junction and here is the here is the equations so the so the junction conductance has two components the diagonal one and the non-diagonal one which corresponds to the diagonal and non-diagonal matrix elements of the current operator so physically the diagonal term corresponds to the to the time finite time needed for the system to equilibrate to its instantaneous states and it's always zero at phase zero and phase pi for the non-diagonal term it corresponds to the excitation relaxation between two levels due to either the microwave or the thermoflaturation so to numerically compute that we discretize this Hamiltonian by tight biting model and if we diagonalize it we can get the androff levels also all the current matrix elements so we first use this way to explain the weak phase dependence of G so here we have computed the the androff spectrum and here we see this for a long diffusive junction we have this mini-gap and experimentally our temperature is slightly larger than the than the mini-gap of our system and indeed if we compute the junction junction conductance then we see that the the phase variation of the diagonal and the non-diagonal term cancels each other and then indeed we are left with a much weak phase dependence and physically this can be understood that at high temperature since we basically act activate almost all the elements of the current operator and the G can be can be approximated by the trace of G square and therefore and this guy is independent phase independent sorry and then we can explain this one of a T temperature dependence of G so here since our conductance is almost phase independent then we can focus on two special cases one is a phase zero the other is phase pi and at these two points the diagonal contribution is always zero so we can only consider the non-diagonal contribution so if we transform this equation into the continuous spectrum limit then the androff level becomes the density of states and the matrix element of the current operator becomes this current correlation function so for unproximitized metal then both terms both quantities are constant and therefore we have a temperature independent conductance and this is actually corresponds to the Drude conductance in the in the classical metal so here we realize that in order to have a strong temperature dependence we should either we should have a high energy dependence either in the denser states or in the current correlation so this is naturally satisfied at phase zero since our face zero we have a mini gap and the the denser states decrease around Fermi level and so this is nothing quite special but it's more puzzling for the case at phase pi so here our face pi the mean gap closes and indeed if we look at the density of states it's almost constant so naively we would expect that this is behave more less just like classical unproximitized normal metal however if we look at the map of the current correlator then we see a strong energy variation when the energy level is smaller than the the the superconductor gap so here the x axis is the energy difference between two levels and y axis is the energy so if we do a line cut here which corresponds to the this term in the equation then indeed we see a strong energy variation so here we have several structures features so for this quasi-periodic peaks this corresponds to the ballistic thalus energy in the system and in our case this the experimentally this temperature scale is beyond 10 k so this these peaks are not relevant in our discussion however at the same time we have a high peak at Fermi level at zero energy which is broadened by the inelastic scattering rate gamma and so this means that we have a high current correlation near Fermi level even if the the gap is zero so if we introduce this this peak into the equation then after this calculation we can see that this gives us this 1 over t temperature dependence and here I like to emphasize that this enhanced correlation is not present if we do the calculation in an unproximitized metal so here is my conclusion so in this work we indeed demonstrate there is a linear dissipative conductance for the SNS junction even and we also managed to measure experimentally the super current noise coming from this associated with this conductance and we test we validate the fluctuation dissipation theorem in this system and we also identify a 1 over t temperature dependence of the conductance and this is a manifestation of enhanced current correlation due to the proximity effect and here I'd like to thank all my colleagues in the meso group especially the PhD student Xavier Ballu and my supervisor Mette Ferrier and Elaine Boucher and also my collaborators in situ and to provide us with this cryogenic amplifier so thank you thanks for me also more questions thank you for a beautiful and very clear talk remarkably clean and nice results thank you so I wanted to ask there have been a few attempts over the year to make an SNS qubit where the junction is a normal metal and people were aware of this andreive scenarios and tried to bias the qubit away from the gap but still it never worked they're always very dissipation limited so do you think your considerations are relevant for these different scenarios can you sort of outline what would make a qubit possible with an SNS junction okay so I'm not really in the qubit community so just from my background I my understanding for this what you are saying is this called andreive qubit and I think here you need to limit your level to be really to have only two level but if you have an SNS junction then you have a like huge number of levels and I'm wondering whether you can really operate the qubit in that way but I think that goes to the the first example that I introduce here where you have superconducting qpc and therefore you can only have like a very small number of channels and here I think the thermal noise that's what I'm talking about might not be very important because you know this to have a thermal noise we need to have the temperature scale to be comparable with the smallest gap in the system and if you have a little imperfect transmission then then this gap might be large and you can actually use the high frequency to operate your system without without this thermal fluctuation problem so that's my understanding yes yeah and I guess in this case maybe you need to tune the family level of the nano wall to be like close to like a depletion region where you can only have a few modes in the system okay thank you I was wondering have you tried maybe driving and measuring the noise just to see if you can do like excite some levels and then you know create a non-thermal non-equilibrium situation where you can maybe even see the yeah this is a yeah it's an interesting question actually we have another related work that we measure the this linear dissipation by putting a pump and we indeed we see a enhance so here I can maybe show you it's another paper it's another paper and it's not here so so what basically what we measure is not the noise just this and here without the pump we see the dissipation is slow it's low at phase zero because we have a largest gap but if you're adding a pump then you can see this guy goes up so to then you can yeah you introduce more excitation by the pump and this actually we it's not really the object of of this measurement but we this is something that we can measure but I think we need to still improve the precision of the data because in the entries we are even we are almost at the limit even to resolve this but if you have a pump then you have even smallest smallest signal so in the systems in which you have very few channels like superconducting atomic contacts or nanowire junctions there is super current noise due to quasi particle poisoning so how is it that you can neglect that here so this I'm not very familiar and I think in terms of experiments we have we can detect in the same way we just because experimentally I just get all my noise and the end is how we extract so that depends on the physics so I think for to answer your question I not really familiar with this quasi particle noise but maybe I think we can so extract all the other like noise contribution from the amplifier from the other thing and then we can check in the end what we are left and compare with the theory but experimentally this can be I think this we can use the same technique to do that if the signal if the signal is large enough