 I'm just going to take a quick look at the organizers. Are there some announcements to make before we start the session? No, all good. And I see, hi Yuka. This is Johan Pop here. Can you hear me? Yes, I hear you very well. Can you hear me? Excellent. Yeah. Everything is good and we can see your first slide. So we are looking forward to your 30-minute presentation. Please. Okay. Thank you, Johan. And thank you for all the organizers for inviting me. And I'm sorry not to be there in presence. So I will talk today about it's a chain of experiments on volumetric detection of thermal microwave photons in superconducting circuits. For some of you, this may be partly a known story, but I'm sure there will be some parts which are new to everybody. So what is it all about? It is essentially we are interested in looking at heat transport. So as a kind of an appetizer, I just give here a brief recap about thermal conductors in quantum systems. What is sort of known over the years? So as we all know, electrical conductors in ballistic contacts is quantized in units of E squared over A's. And similarly, in these systems, there is kind of Wiedemann-Franc's law holding in the sense that thermal conductors also assumes values which are discrete. And this has been demonstrated in several experiments. And the thing is that it's known that it does not this thermal conductors quantum does not only apply for electrons, but it also applies for any types of carriers like phonons, which has already experienced for a very long time, although there are still questions about this, how to really reliably observe that. There are precise experiments on electrons and onions. And what we are now talking about is photons, microwave photons. And we have a review article with my former student by Nkarymi on this topic in the recent volume of RMB. So about the heat transported by photons, this is a kind of a simple story in a nutshell. So if you assume this kind of Johnson-Nykvist setup, where you have two resistors, which are not really diffusively conducting heat between each other, you still have the noise, the thermal noise that produces current in the circuit. And by calculation, which is just two or three lines, you can obtain the result that the heat current between the two resistors is given by this formula in the regime where the temperature difference is small. So you get that it's really governed by the quantum thermal conductance. And for larger temperature differences, there's a quadratic dependence on the two temperatures. And if the resistors are not equal, there's this kind of a matching factor, which is naturally one when the resistors are equal. So this is kind of the starting point. And how to really, now I give you a little bit of toolbox. So this is maybe familiar to some of the experimental audience already, but how really to measure the heat. So to measure the heat current. So what we typically do is that we have either one or two absorbers like this, which are like mesoscopic electron absorbers. We apply heat to one of them, and we measure the temperature usually of both of the two absorbers. And then due to the continuity of heat current here, we can find that the change of the temperatures of the two absorbers here, they obey this simple expression. It's like Kirchhoff's law for heat currents. So if this thermal conductance to the bath or the second one is known, then you can determine the unknown thermal conductance that you are interested in. But what are the other elements to do this are naturally that we need to measure temperature. So this is, of course, crucial. And the bread and butter for us in this context is to use just a low frequency, let's say DC temperature probing. And this we do with tunnel probes between a superconductor and normal conductor. So here is our typical absorber here. And when you measure the current, we know that the current between these two is depending on the distribution of electrons in this normal conductor and the density of states in the superconductor. And it only probes the temperature in this case of the normal metal if you are well below the DC of the superconductor. And in fact, in some extreme regime, or let's say in some favorable regime, you even can tell that this is a primary thermometer in the sense that the logarithmic dependence or the current on the wall has this simple form which we even experimentally can demonstrate in some cases. But in general, when measures usually like voltage at the constant current and this way you obtain the temperature of the electrons in this normal conductor here. And the other important element is naturally what I already pointed out is that this absorber here is connected to the heat bath via thermal conductance, which is usually the electron-phonon coupling. And this is something which is also very well known in literature and quantitatively known these days also from the experiments. In situ experiments, you can determine this electron-phonon coupling constant. And then you have the heat power between the two systems. And you can linearize it in some cases to have thermal conductance times temperature difference. OK, so these are the important things. And then the third element which is important here is that we need to control the temperatures of these two mesoscopic baths, so to say. So what we usually do is we use, again, a similar NIS junction. And by biasing this junction favorably, you can either cool the electron system in this normal conductor here, or you can heat it depending on the value of the bias voltage here. So if you are at the voltage, which is just barely below the gap of the superconductor, then you are cooling the electrons here. Whereas if you go above this wall, then you essentially produce a heater, which is like a joule heater or the electron gas in a normal middle. And this is something which is known also for a very long time already from the experiments from mid-90s, where I was also participating in. And it can really produce big changes in temperature locally. And the nice thing is that in these systems that I showed, for example, here, if this normal conductor here is then connected directly to the superconducting leads here, this superconductor blocks the heat transport through these wires. And you indeed have this textbook. Johnson-Newquist set up possible where you only have this radiative heat transport, and you don't have the conductance through the leads in a conventional way. So all this was already tested by us many years ago. So in the simplest experiment, what you can see here on the left, we do exactly what I was saying. We have one resistor here, another resistor here. You apply a voltage across a pair here, and you can produce the change of the temperature of that resistor, which is shown by this blue curve here. It's a symmetric effect. So with both positive and negative voltages, you decrease the temperature of the source here, which you can probe then with the other pair here. And then you can monitor simultaneously the temperature at the other end of the system, which is separated by aluminum wire, and at the distance of about 30 micrometers from this. And one can see that when you go to a slower temperature, these two temperatures start to follow each other very closely. So if you really take this ratio, the two temperatures is really related to this conductance between the two, as I showed, then you can see that this ratio is following quite closely to what you would expect from this quantum of heat conductance, not precisely because at that time, especially, we didn't have this electron form coupling very precisely measured. OK, so this was kind of nice. We could see that there is experiment by Mikko's Micromotorance group, which made things 10,000 times better. It's a wire which is one meter long, and this way they could even demonstrate it with this kind of a transmission line, or let's say the wave guide, which is transmitting the heat between the resistors quite long distance. Well, then there's a point that you can also modulate the heat by changing the intermediate impedance. So in the beginning, of course, we didn't have any. This was kind of a system where they were directly connected. But as soon as you start to play with some sort of intermediate impedance here, which can be reactive impedance, like a squid here in this case, what happens is that this matching factor is lost, and you have less heat produced in the other resistance with the same principle. And then this works as an LC circuit here naturally, so you can adjust an inductance, which is then governing the heat transport between the two. And a simple model can be done in that case also to see how this conductance is modulated by this magnetic flux through this squid. And in those measurements, we could see that indeed it really follows quite nicely. And this is the temperature of the heated electrode in this case. And you can see that there are some certain values of magnetic flux where the inductance gets maximized, half quantum fluxes. And in this case, the temperature is increasing. And we could model this quite nicely. So at higher temperatures where the electron-phonon coupling is strong, it has the T2 power 5 dependence whereas this has the T2 2 dependence. So here, the electron-phonon coupling wins. And then all the heat is really going to the phonon path, and you don't see any modulation. But at lower temperatures, the modulation is clear. So this sort of thing can be done also not only by magnetic flux. This is a more recent measurement where you can also do a rather kind of a simple setup in the sense that you have a single electron, or let's say single couve pair transistor here, which you control by gateways. And you have the two resistors on the two sides. And then this is also in a loop here. And in this case, we could not quite reach the quantum of thermal conductance. But also in this case, we could we could modulate the heat current between the two by this gate wall such that we could model it quite reliably. So more recently, or let's say in the recent time, we have also tried to implement this. We tried to put kind of modern qubits into the game. So here's an experiment which we called at the time quantum heat well. And that is formed of a standard transmount qubit, which is now between two co-planar wave resonators of equal frequency of about five or six gigahertz. And at the two ends of this co-planar wave resonators, we have this heat mass as this is exactly the same figure I had before. So it's this few microns long resistor again here made out of copper. And the same principle as before. And in this case, we have really a connection between the two, but not even a galvanic connection. It's a capacitively coupled transmount qubit in between. And this we could also model quite nicely in the sense that when we measure the power from, let's say, left to the right, where the temperature is always measuring the temperature on the right, when the temperature on the left is controlled, we could see that the power that is received, measured as a temperature change here again, is modulated such that twice within a flux quantum, there's a maximal power that is transmitted through. And then at different path temperatures, you can see differences. There is also some extra heat here, which is most likely through the substrate in this case, because the heat powers are quite small here. And then when we go to this so-called cooling regime, at what is below the cap for this actuator pair of junctions, then we can see that we can even cool down the distance source as a distance of about four millimeters without direct electrical contact in this case. And modeling this is very straightforward. We have kind of a, we have here, the power is like the difference in the distributions, both the distributions in the two resonators here. And then it is cut by the Lorentzian when the resonators are off the resonance of the qubit. There are also more involved results in the regime, where we were decreasing the coupling of the resonators to the bath, but I will not go to that here. So now I will come to some results, which are essentially they are totally still unpublished, and they came to us somehow as a surprise, but maybe for this audience, this is a little bit interesting also, because so in the experiments that I was telling you about up to now, these resistors are just few ohms. So they are like made out of either copper or out of gold palladium with maximal resistance of few ohms or let's say maximum tens of ohms. But the interesting question of course arises if you make these resistors much higher resistance, and what we did was that we started to use chromium as the source and drain in this experiment. And here is a very traditional squid in between them with small junctions. So this is kind of the setup where you can expect that the dynamic chromium blockade is playing a strong role. So you have a setup there where the well-known POV theory should work very well. And we did initially we did measurements of just the direct current voltage measurements of these setups which are shown here. So you can see that the IV curves at temp shop here just below 100 millikay. You can see that there is of course what you expect here there's some super current feature there in the center. And then outside you have the linear dependence. And if you then zoom into the central part of the IV curve here, you have something which you can really model quite beautifully with the POV theory. And if you look at the flux modulation, you also really produce something that you would expect. And in another sample which has smaller capacity, smaller size junctions, meaning the higher charging energy, we see even much more pronounced dynamic chromium blockades and still quite in quite good agreement with the prediction from the POV theory. So this is kind of a sanity check that everything works quite well from the point of view of electrical transport through this script here. I must say that here in this case, even the conditions of POV are not fully satisfied because EJ is of the overall temperature in this case, but still it seems that at least, well, with parameters which are not far from what you would expect and this partly can be determined independently here, we can have a quite good agreement between the model and the measurements. So, but the surprise came when we started to look at the heat transport. So these are now samples which are otherwise nominally identically except that they are enclosed in a loop for measurements of the heat. So in this early measurements which I showed, it we kind of realized that it is crucial to set us, put the system into a superconducting loop because this way you can close the current path which is really producing the heat in the opposite resistor. If this is just an open-ended circuit, then you close the loop by a small capacitance and this is not what produces the quantum limited heat transport in that case. So this is exactly the same, but now in a loop geometry, of course, since the junctions are small, we cannot guarantee that they are exactly the same as in the replica samples, but they are as close as possible. And then we have also this same typical setup here with the heaters and thermometers. In this case, what we see here is that now at two different values of flux, let's say the flux on nominally zero flux half quantum, we can see that the temperature, again, this temperature ratio determined the same way as before. It's in zero flux, it's following these blue dots here and in the half flux quantum, these red points here. And now you can see several lines there. So the one which is this violet line here is the quantum limit. So it seems that it is very close in this case to the quantum limit. And we have, in this case, we have been able also to determine the electron-phonon coupling of this chromium strips independently. So we kind of seem to reach really this quantum of thermal conductance here in this case. And then if we just assume that the Josson current is totally suppressed, then we get this line which is here determined only by the capacitance of these junctions here in closing this loop. So there's kind of the clear contrast which is given by a simple, this linear model here because also if the inductance is small enough, then we go between these two limits in any case. And but the problem arose there is that the limit, of course, when the only the capacitance matters is governing irrespective, essentially, of any model that you use here. But then if you use the basic P of E theory for calculating the heat transport here, assuming the inelastic cooperio current in this grid here, we see that the modulation is extremely weak. So it's essentially there's no modulation whatsoever. And this also holds for the other sample that we measured. There we can have maybe a little bit less consistency between the experiment and theory, but perhaps because we have quite small junctions there, the asymmetry of the grid plays also a role. So there's clearly a puzzle there in one case, the P of E works very well, but in the other case, not at all. And here are some of these high impedance, I mean, some of the heat measurements now as a function of magnetic flux. And you can see that the basic P of E prediction is really not showing essentially any flux modulation if you do it that way. So now we are of course discussing this heavily with many people this puzzle. And I just present here how I at least would see it at the moment. So this is of course very preliminary and not just given as a thought. So there's one consideration that one should, of course, look at is that, that if you look at the charge current through this replica sample, then we have when the current is composed of the usual Joseph current plus the inelastic path from kind of the P of E current, then the DC path disappears there because you average over sinusoidal dependence. Whereas if we are looking at heat, it's again like a comparison of current and noise. So because heat is like a quadratic quantity in current, then what you have is that the path, this non further path here is not vanishing for the high frequency transports. And you will have much more of heat current than you would expect from just from the inelastic P of E type modeling. So this may be one of the differences. So essentially heat is probing the high frequency properties of the junction whereas the DC current is just averaging this path out. Okay, so that's work in progress and we have benefited a lot from discussions with several theories locally and also with Alfredo Levy-Jeyati who is probably in the audience and his people in Madrid. So now I move from, so up to now what we have been doing is that we are looking at a flux of photons meaning that we measure like one million photons at minimum per second, whereas the goal is of course to be able to measure colorimetry which means that we would see each particular event at the time. And so the objective is thermal single quantum detection and I will come back to one of the yesterday's talks also in a second. So the objective is that we really would need to have a fast thermometer which has a low enough noise so that the intrinsic noise of the absorber is temperature noise is low and also that the thermometer itself is very non-invasive fast and noiseless. So what we would like to see is that once you have a source of heat which is for example a qubit relaxing from excited state to the ground state you obtain a pulse of heat to the absorber which then changes the temperature of this absorber by an amount which is the energy of the quantum divided by the heat capacity of the absorber and then after a while it would relax back to the temperature of the bath back to the temperature of the bath at the time constant determined by the system parameters of heat capacity and this thermal conductors. But what we are of course limited is by the intrinsic noise of this system in terms of temperature. So what we have been set up is to measure this temperature fast and with a very non-invasive thermometer. So instead of using these standard NIS probe we are using a proximity NIS junction which means that we put a clean superconducting contact in contact with the normal metal so that it uses a little bit proximity to this junction and then we have a feeble super current here which then is very strongly temperature dependent even at the low temperatures. And the advantage here is also that the impedance of this probe is not huge and also that it is not producing too much heating because it's measuring it essentially at zero bias on the x-base and what is causing something. So this work has, we have shown in several experiments that we do not have any saturation of this thermometer even down to the lowest temperatures and we can also prove that it really measures the electron temperature of this absorber. So something related to this was indeed presented yesterday by Efek Goumos where the joint in the joint work where he was presenting the work on the colorimetry of quantum facelift. So in that case one can do a repetitive measurement of this temperature and these facelifts, of course they have energy which is about a hundred or a thousand times larger than what we are after when we try to see the quantum from the qubits. So it's a beautiful experiment. However, we really have to go quite a big step before we can say that we can measure these single photos from a qubit for example. So what is the noise of this system? So if you assume that you have a perfect amplifier everything then you are still left with your thing which is here, the normal metal is coupled to its heat bath and this on top of conducting heat to the bath it also produces naturally the noise via the fluctuation dissipation theorem you can really determine the magnitude of this and it's related to the thermal conductance at the low frequencies and then of course heat capacity if you can measure the full spectrum of this noise. So this is something that we were set up to measure a year or two years ago and we managed to see that the noise when we measure the temperature in real time it has a noise which is not very far from this limit which is given by the FDT. Of course we subtracted the noise from the amplifier so this is just the measurement of the intrinsic noise of the observer that we saw. So it says that at low enough temperature we should be able to measure the photons which have energy of one kelvin or below if you are at temperatures well below 50 millikelvin which is possible with our current detection measure. Of course life is not so good in reality so that's why we have been thinking about how to further boost the sensitivity of this measurement and we have come up with an idea which we are about to test in practice now is to really connect this qubit and the resonator to not only to one absorber but to two absorbers which are thermally decoupled by for example a superconducting contact here and then measuring the temperature of the two simultaneous. So this way basically what we can do is that we can do a cross correlation temperature measurement which then gets rid of the electrical noise to a large extent hopefully but also we have some hopes to get at least part of the thermal noise coming from the phonons to be uncorrelated such that we really can improve the signal-to-noise ratio significantly. Of course from the numerical simulations things look really beautiful but in practice of course the improvement will never be that good but nevertheless this is a way we are now going and I think this is what I wanted to show today so here are the main players who have been doing let's say for the recent experiments of course Bayan and Diego Súpera and Olivier Maier have been doing these ones most closely and then this work has been really backed by a lot of collaborations and most let's say about this calorimetry part we have had a lot of interactions with Wolfgang Welzig and his Daniel Mikolić from his group and then also we discussed a lot with we had a lot of interactions with Peter Samuelsen from Lund and Friedrich Brang and also with Joachim Ankerholt here in the audience as I see and then we locally with Joachim Thomas and Dima Golubev on the theory side and then as I mentioned also with the Madrid guys on the recent experiment that are going on. So thank you, I stop here. Thank you very much Juka for this nice overview and also for sharing this exciting new results. Now the session, the talk is open for questions. If you have a question online, please place it in the chat and I will read it for the speaker or actually the, sorry, the speaker is online so the speaker can just answer it. We have a question, one moment. Hi Juka, thanks for the talk. I have a question and it's connected to this POV theory which you showed the dynamical cooler blockade. I mean, what kind of temperature do you put in the POV theory and is heating any issue at all? Sure, sure, sure, that's very, very good question because it's, in fact, if I go back to this IV curse here so we indeed we took into account the heating along the bias here so it wouldn't, we know as I said, we know the electron phono coupling so we could match it, I mean, it really, I don't have here the non-heated ones shown but definitely this plays a role at biases especially beyond this maximum of the super current here. So very good point, especially in this very resistive environment, this is an important point. So we assume that initially it's at the bad temperature and then we just consistently solve the temperature as a function of the current there so that's how we do it. I don't know, I mean, okay, all this is still working progress so I cannot say, for example, this deviation here about this maximum here in this case whether this is due to some failure in the POV theory in this case or is it because we didn't take the heating properly into account but it plays a role. Thank you. Yes, we have another question. Hi Yuka, Carla Daltimiras here. Can you come back to the modulation of the power exchange in this high impedance? So yeah, even before I think it's okay as a slide you were showing before. Yeah, this one, so if I understand well when you frustrate completely the squid you only have a capacitive interaction between the two bats. Exactly, yeah. And then you remove this frustration and you see that you recover a very efficient heat conduction between the two of them. Precisely. So I was wondering, what is the bandwidth of your RC circuit corresponding to these coupling capacitance and these resistors? Okay, okay, yeah, so I don't have the figure here but it is the RC time constant is, I mean it's, we can even figure it out here 10 to four and this is then, so it's still it is above it's, this cutoff is above the thermal frequency clearly in this case. Above, yeah. Okay, so I think that's it. I mean, see even though you have a normalization of the DC current, it comes from the fact that you have frequency conversion amongst the photons. But here, if you excite broadband and you detect also in broadband, even though photons are massively scattered amongst all the frequency bandwidth, if you still recover it, it will still be transmitted, right? I think you need a second order P of E which is capturing the frequency conversion amongst the photons and then it would give a higher frequency flux as you expect. But let's say, I didn't quite get this because I mean from the RC time constant you, I mean how is the flux modulation related to that? No, my point is that the normalization of the transport properties that you see is anomalous dissipation is that a single photon can be scattered in a continuum of photons. But if you detect the power in a large enough bandwidth so that you capture all the photons which are scattered to other frequency scales, they will still contribute to the heat which is transferred to the other resistor and since the density of states of the resistor is flat, if you just conserve the energy, you should conserve the energy flux. We have to see together more closely, yeah. Okay. But anyway, the resistance is like 10 kilo ohms, capacitance is like one tenth of a rat, so what you get from that is, let's say 10 to, 10 to the minus 11, so. It's in the giga range, so. Yes, so they are. So in Y. I think your bandwidth is so big that you just get all the photons through the system even though there is a massive frequency conversion amongst them. Okay, we should see this more closely, so, yeah. Anyway, the conclusion is that when this inductance is small enough, then it is, we are very close to this basic. Sure, there is no one. Excellent. Is there a last quick question? If not, thank you, Yuka, for the nice talk. Thank you for the questions also. Yes, thank you so much.