 Last session of today. The first speaker is going to be Francesco Giasopto from Colón Normales Superiores de Pisa. Francesco, what do you want? Thanks, Alfredo. Good afternoon, everyone, and I wish, first of all, to thank you for having invited me here to present some brand new results on thermal transport in superconducting systems. So today I will talk about a very basic structure in proximity systems that we named the thermal superconducting quantum interference transducer, so the T-squint. Let's see the outline. So I will start the talk introducing some motivations and the mission of this research. Then we'll introduce some background about proximity effect in hybrid systems and the impact on the density of states. Then we'll show what is the concept of the electrical superconducting quantity of proximity transistors and what is its predicted thermal behavior, okay? So I will show the realization of the thermal script, so how it is realized, what are the expected performances, the results and comparison to theory. In the last part of the talk, I will show how it is possible to use one of such kind of thermal transistor. In order to implement thermal memory cell with topological protection. So the argument that I am treating now deals with what is known as coherent power electronics, so the complementary of coherent electronics. So the idea is to phase manipulate and master, let's say heat transfer in a fully solid state environment and to provide the original novel approach to realize another thermal device like heat transistors, splitters, diodes, refrigerator and exotic quantum circuits that take advantage of these above mentioned building blocks in order to enhance the functionalities. Last but not least, to address and understand some fundamental problem in physics related to energy and heat phenomena. For instance, query dynamics, heat interference, time-dependent effect, noise, the problem of the coherence, quantum thermodynamics, and so forth so on. So in a nutshell, so the main goal of this caloritronics at the nanoscale, so mesoscopic caloritronics, is to develop quantum technology for managing heat in nanoscale circuits. So the physical basis of phase current caloritronics can be easily explained with the aid of this very simple cartoon on the top. So since we are dealing with solid state systems, we will be interested in quasi-particles and electrons and phonons, and so the phase current caloritronics deals with envisioning novel physical mechanisms which are able to control tend to the mesoscopic quantum phase, typical of superconducting circuits, the manipulation of the heat current flowing from hot, let's say, electron reservoirs to colder electron reservoirs. Toward the sense, we have identified basically three more relevant routes in order to manipulate heat in nanoscale systems. So the first one is, the first toolbox is basically the exploitation of the Joyceon effect, so superconducting tunnel junction, a particular temperature bias, the Joyceon tunnel junction, where we have an important component of the heat current which becomes phase dependent, and thanks to this we can realize quite efficient thermal modulators. Then there is another interesting route that is that one based on the proximity effect. So the idea is to use the proximitized layer, so let's say, novel metal of superconductors that have acquired the superconducting correlation thanks to the intimate contact with the nearby superconductors, and so this, let's say, S-prime artificial superconductors, they are characterized by interesting properties in the sense that they are key properties like the denser states, the electron phonon coupling, the entropy, the specific heat, they become all phase dependent, okay? So they can be, in principle, manipulated thanks to the phase. Then there is the third route that is the middle, that is basically the study of how is it possible to control the heat flow between body residing at different temperatures that possibly are not even in galvanic compass, so maybe they are just coupled to quantum circuits, so quantum resonators in the form of squid or whatever, and then so to use basically the electron-photon interaction. So by tuning the electron-photon interaction, in principle, it's possible to control the amount of heat flowing from, for instance, the left reservoirs to the right reservoirs. So now in the following, I will show the first effective implementation of a proximity-based thermal quantum transistors that allows sizable temperature modulation implementation of this first memory cell. So as I was saying, we are dealing with metallic contact between a normal metal and superconductor, so where this is, I mean, this end part can be a short, let's say, metallic piece or even a short metallic superconductor. And we know that in this system, I mean, the charge transport occurs thanks to under-reflection, it's the process for which, I mean, an electrical incident from the normal metal for energy smaller than the superconducting gap is retro-reflected along the incoming electron time-reversed path while at the same time it could prepare condensate the superconductor. So this mechanism allows the propagation of charge, let's say, from one part to the other, but not the propagation of energy, okay? So below the gap, basically, under-reflection prevents the flow of heat current from one side to the other. So now, I mean, if we connect such two of these blocks on the left to realize an SNS junction, for instance, so the electronic correlation due to under-reflection will extend from one side from the other side from the left and right inside the normal metal, and so this will, if they overlap sufficiently, they will realize a novel kind of state inside the normal metal, say, the normal resonator, okay? In particular, I mean, they create the so-called undrived bound state which are responsible for allowing the flow of dissipation and superconduct across the system. So typically, I mean, the system that we are using, at least what I'm going to show are metallic systems, so diffusive systems, disorder, maybe disorder metallic-themed films, and they operate in diffusive regions. So in quasi-one-dimensional geometry, diffusive means, indeed, that mean-free path is much smaller than the characteristic length of the system, much smaller than the phase in length. Relevant parameter in this system are the diffusion coefficient, the superconducting gap of the superconductors, phi is the microscopic phase of the other parameter, and then there is one important scale, energy scale, that is a tau less energy, that is basically the typical, let's say, energy of a disorder coherent conductor. So a system like this can be very successfully, I mean, treated from the theoretical point of view with, let's say, quasi-classical equation. In particular, one class of this is called the Housel de l'équation. This is a sort of, let's say, diffusion equation that allows to calculate some key properties, like, for instance, the denser states in this normal metal. Not only, I mean, the super current spectral density and so forth, so on. We are, in this moment, particularly interested to describe the denser states of the metal because this one will be absolutely relevant for the calculation of the heat current flowing in the proximity metal. So the key properties of the denser states are that is a symmetric function of the energy and possess a gap, so a forbidden region for quasi-particles that can be controlled thanks to the macroscopic phase of the two superconductors, okay? So by changing the phase difference across, let's say, the junction, the SNS junction, we can control the amplitude of the net gap from the maximum value that depends on the length of the junction to the meme that is almost zero when we are at pi. So it's interesting, first of all, to understand what is the impact of the proximity effect on the denser states of the proximity metal of the superconductor. So here on the left, there is a calculation from Kuevas and coworkers showing the denser states versus energy as a function of the length here on the upper panel and the position dependence in the lower panel. So in the upper panel, we see that by changing the length of the junction, so when the junction is very short, with respect to the coherent slender superconductor, then the system behaves almost like a BCS superconductor. So it means that the interlayer acquires the same, at least theoretically, I mean, in this limit, the same properties as the parent superconductor which is giving rise to proximity effect. Then by making the junction longer and longer, what happens is that this artificial superconductor becomes weaker, so the mini-gap becomes smaller and smaller, and eventually when the junction is very long, I mean, this tends to the denser states in the normal state. Is it possible to see what does it happen as a function of the position? So, I mean, if we move along the wire, basically with the denser states as a strong position dependence, okay? Although the gap is position independent. So even more relevant is how we can control at will the amplitude of these denser states, okay? This can occur thanks to the phase dependence. So for instance, if we suppose to change the phase difference across the superconductor from zero to pi, we can see clearly that we can continuously change the amplitude of any gap from the largest values up to zero when, I mean, we close completely and the system resemble a normal metal. Now, I mean, till now I have shown what is expected. So let's see what was shown. So this is a very nice experiment that dates back to 2008 from the Sackley group where they realized aluminum, silver, SNS proximity squid, several different devices with different length of the junction, and they probed with the STM the denser states in this proximity metal, let's say, as a functional position and for different length. And so for instance, if we look at the upper, sorry, the upper left ring that possesses the shorter junction, we see that there is indeed a very nice mini gap developed within the wire. And we see the amplitude of the mini gap is almost constant moving along the wire as we were showing before. Then increasing the length of the wire in another screen, we see that there is less and less pronounced up to the very end where, I mean, for this ring here, we have a much reduced effect by some induced coloration inside the SNS rings. So this is not the full story. The full story is that then it was possible they have shown for the first time that it's possible to manipulate this denser state with the phase. So since this proximity metal is embraced in the ring by changing the magnetic flux, piercing the interferometer, it's possible continuously from zero to pi to go from a situation where the mini gap is fully developed to a situation where at pi it's fully closed and then if you want, you go back in a fully reversible shape. So here on the right, there is a comparison. For instance, just to recall the effectiveness of the quasi-classical theory for treating this system, comparing the experiment, okay, a differential conductance that they obtain as a function of different fluxes piercing interferometer and the comparison with the theory. So the agreement is indeed very nice. So starting from this idea, we almost 10 years ago, maybe even more, we started to work on the possibility of implementing, let's say, a fully solid state, a device-like version of this experiment with the STM. So the idea was indeed to obtain artificial superconductor times the proximity effect and the phase control to the magnetic flux and then the detection through tunnel junction implemented directly in the proximitized weak link. And this, in principle, can give rise to very high sensitivity for flux detection. So this is the idea of the superconducting quantum theory as proximity transistor. So we have this sort of AC squid with the proximity metal in the middle and then there is the tunnel junction connected to this green part that allows to make the tunnel spectroscopy. And so this has been proven in different sources, let's say, to be a very nice interferometer with very nice and very low, let's say, flux noise. So these script setups have been realized in several shapes and materials. Typical aluminum is used as a material for the ring because it possesses pretty low kinetic inductance. And for instance, in this case, the probe can be even normal metal of superconducting. And as we are saying, the weak link can be normal metal or even superconducting. So each of them has its own advantages and drawbacks. So if we look, for instance, at a script with an end probe, I mean, when they say the nanowire is fully proximitized, it will make the spectroscopy to the junction and the standard junction is normal. So the system will evolve from a superconducting like SIN junction to NIN junction when we close the mini-gap, so a fully straight resistive line. And so, and this is the corresponding threshold conductors on the bottom. Whereas for a superconducting probe, this will evolve from an SISS prime junction where we have, in addition, the presence of the supercurrent around zero to a NINIS junction when we close the mini-gap of the superconductor. So this is just to make some history of the properties of this interferometer, okay? So then the question was, okay, now that we are more or less understand how we should behave an electrical interferometer based on proximity effect, the question is, it is possible to use this for very effective heat current manipulation nanoscale circuits, okay? And the answer is yes. So the idea is indeed to create the heat counterpart, the thermal counterpart of the circuit, okay? So a thermal superconducting quantum interferometer proximity transistor, and this is something I would say very, very, very simple to conceive. So as here in this sketch, we have just the superconducting loop with the link in the middle. On the right, we have a normal metal of superconducting probe. They reside at different electronic temperatures. The idea is to study the heat current flowing through the system. So a very simple, let's say, basic understanding of the devices can be gained if we sit and if we suppose to be in the linear response regime in temperatures. That means that the temperature in the two system is the difference between the two temperatures is pretty small with respect to the average temperature of the system. And so in the linear response regime, we can define the thermal conductor of the system. Basically is the convolution of the density of states of the proximity nanowire, the probe injunction, and the squared of the energy, okay? So, I mean, if we study the thermal current, the thermal conduction to this system, here on the left, on the right, top panels for end probe and an S probe, we see that, I mean, the thermal conductor here is shown as a function of temperature for different values of the flux. So we go from the blue, deep blue, where the gap is fully developed, and we see that for low temperature, there is a dramatic retaction of the thermal conductor with respect to the normal state. This is expected because for very low temperature, I mean, it's very gaped. And so, I mean, this is calculated for in the regime of short junctions. So the density of state is almost that one of a BCS superconductor. And then by changing the flux, we just reduce the mini gap inside the proximity wire. So the system will tend to conduct more heat current in the system. But you already see that in a system like this, there is a suppression in principle of several orders of magnitude between close gap over gap. Something similar happens also for a superconducting probe that is here on the right that, of course, may provide an even more isolation, but the drawback is that since one of the two electrodes still is always superconducting, so this means that at the end, the full heat transport in the system will be limited by the remaining superconductivity in the superconducting probe. It's also important to analyze what does it happen as a function of the length. So as we are saying, the longer the junction, the less proximitizes the junction, so the less modulation in term of heat we can provide in the system, okay? So in principle, if we want to operate one of such interferometers, the idea is to realize a system with a very short junction, the shortest possible, so a tau less energy that is large with respect to the gap or comparable to the gap, so that we can achieve this efficient suppression like in the dashed line that corresponds to the very short junction limit. So the idea was indeed to realize a sweep very short with a short junction of the order of a few coherence length at most and then to prove it is possible to achieve this effective manipulation of the heat current. So on the left top, we have the thermal squeeze structure scheme, okay? So let's say this ring embracing in this case a superconducting weak links, so it is an aluminum-aluminum contact. So it's a very short and narrow wire. The wire is typically 400 nanometers. The idea, I mean, if we look at this structure here, if we suppose to heat the normal metal electrode that the red one that is connected to the script, that is a normal electrode, as we are saying, because it provides advantages. If we suppose to give a fixed power to this electrode here, then we study how it does evolve the heat transport across the tunnel junction versus the mini-gap existing in the proximity wire, we see that indeed by reducing the mini-gap dramatically increases the power transfer, and the heat power transferred from the red electrode to the rest of the structure, okay? So here, when we go to 80% reduction in the mini-gap, it basically corresponds to almost four orders of magnitude of variation. Basically, this is given by the amount of residual states, let's say the Dynes gamma inside the system, okay? So a very nice junction or tuning of the environment, of course, to reduce the residual state will be beneficial in order to have this on-off state for heat. So here on the bottom is just a pseudo-color image of one of such structure that we realize with conventional electron billetography, three-angle shadow-mask evaporation, and basically, you see, I mean, the face of the loop, the interferometer, in the middle, we have the small superconducting aluminum and wire, then there is connected aluminum manganese probing electrode, and then we connect additional aluminum probes here on the right, operating as heaters and thermometers in the structure. So what we do basically is that we heat the system, we impose some stationary, let's say, power in the system, and then in real time, we measure the electronic temperature established at the state in this normal metal electrode as a function of the flux appears in the interferometer. So for a given power, of course, what we expect that change in the mini-gap will change the amount of heat flowing out outside, and we can make a modulation of the temperature thanks to the, let's say, control of the spectral properties of the metal, because, I mean, what I didn't tell before is that till now, I mean, we were pretty effective in controlling heat current, but thanks to the interference of Johnson-Cutting, okay? So here, I mean, in some sense, is not really the first time, but maybe the first time is pretty effective in the way of controlling the spectral properties of a metal in order to control the several key parameters, thermal and electric parameters. So in the case, what to expect in the electric behavior of the thermal script? So here is shown. So here, so we have just to resemble a few concepts. I mean, when still we are dealing with the superconducting weak link, in the case that superconducting weak link is short, I mean, it possesses a sinusoidal, sorry, I'm making a mess, a distorted sinusoidal current phase relation, okay? Distorted because, I mean, if it is short, I mean, one, it is predicted that it is a non-sinosoidal, basically. And so this means that we apply a voltage bias across the script as we see here. We can basically, I mean, for fixed voltage, the current will be a continuous function of the phase. So you see that when the mini-gap is closed, there is low current and then we will maximize that for half integral values of the flux. Here we are in a different regime where our nanowire is longer than the superconducting current slank is of the order of six, size zero. So the current phase relation is already intermediate regime long is becomes completely hysteretic, sorry, becomes hysteretic. And this means that because basically there is the nucleation of a slip in the structure. So I mean, and these two branches that we see this, you see it is completely straight, so the path depends on if we are moving forward backward in the system. And these two branches correspond to different, let's say topological phases or let's say different branches characterized by the different part of the logical index that represent the phase of, let's say, the winding number of the phase, okay? And so, I mean, in this case, what is interesting is that what is expected that basically the current for fixed voltage will reflect this exactly this hystericity, okay? So first of all, I mean, we can characterize the IV characteristic of the script and showing that it can possess basically 50% modulation and indeed also the current behaves as a sketch here. So there is this jump in one side of the other side going backward and forward in the system. So now let's see what is the expected behavior. So as we are saying, I mean, the experiment is performed by heating, giving some power to the central part and then simply by reading the electronic temperature and equilibrium. So what is expected that when there is, there are integral values of the flux, we can close, sorry, completely open the mini-gap so there will be stopping of the heat current flowing from the normal metal to the weak link and for some integral values, there will be a larger flow. So this is shown here in this temperature versus flux. You see it reflects in the same way what we are saying before. So for zero, there is integral values of flux. There is a stopping of heat. So the island is more heated. There is a maximum temperature. And then when we go around half integral values, there is this hystericity thanks to the presence of this, let's say, multi-valued current phase relation in the system. I mean, we have characterized the valve or let's say the transistor for different injected power. So from low to high, so you see that increase in the power increase at the average level because we are increasing the temperature in the system. And then this sort of butterfly that presents the hysteresis is almost or less constant. So what does it happen? Indeed, if we collect just the delta T, that is the maximum duration temperature, is that we can achieve a maximum of 16 millikay of swing in temperature that corresponds to 1.7% at depth of temperatures. And that the average temperature, indeed, increases with the power as expected. Here on the right, there are just a comparison with a simplified thermal model that takes into account the main relaxation mechanism, escape heat escape mechanism present in the structure. And it is able to provide, I would say, your reasonably good behavior that is in a reasonable agreement with the system. So let's see what is the impact of the bus temperature. By increasing the bus temperature, it's interesting to see how does it relax. So we see a low temperature by increasing up to 800 millikelvin. I mean, the effect is present. And basically, the hysteresis reduced. And also, the swing is reduced. The swing is reduced thanks to the increase of the electron phonon coupling in the normal metal electrode. And the width of the butterfly is reduced because by increasing the temperature, we reduce the proximity gap. So this increases the coherence length. And so the junction goes towards the limit where it's less hysteretic. And so we can see here that already the delta T, so the swing in temperature for temperatures of the bus approaching 1K, is still around 20% of the maximum. So we can say that up to 1K is possible to observe the behavior of the reduced of our system. So now it's just the very last slide. I want to show the first implementation of a thermal memory. So as we are seeing, the temperature, since it shows this nice hysteretic behavior, it can, in principle, be used as a memory. So these two different branches are completely, in some sense, separate. So if we think to fix for some fixed reference bias, let's say flux bias, at some point, we can define two positions in this temperature to flux phase diagram. So we have 0 and 1 that correspond to different states. So they can low temperature and high temperature. And then they can encode information. So 0, 1 are categorized by different topological index. And that is discriminated by the parity of the winding number of the phase. So this means that by giving a pulse on the positive direction, for instance, we can make the writing process. And giving a negative pulse, we can go on the other state, erasing. So if, for instance, here, the readout is given for some fixed power, you see a positive bias, we achieve the state 1. Negative bias of the pulse, we achieve the 0 state. This can be repeated continuously with very repeatability. We have then analyzed the stability against flux fluctuation, adding some oscillations on top of this system here, modulation of the flux, in order to show that the system is very stable indeed. And then what's interesting is that this memory shows a fully non-volatile behavior. So this means that we can put the memory in one state. And then we can depower the electrode. And then we can repower the electrode, obtain the same state. And this is because there is this protection. For we, the memory is just given by the circulating current in one sense or the other. And these two states are protected by the very large barrier that prevents stochastic phase leap from one side to the other side. So here, this non-volatile behavior is shown here, as you can see. So when we give power to the system, heat in power, we read, in this case, 0. Then when we are in the other portion, there is off, one, off, one, off, one, off. So photo on, I mean, in time, this is very stable. And I mean, the different temperature of this memory is apparently pretty low. It's 4 millikelving, but I mean, it's very repeatable in time. So in some sense, it's an interesting concept. OK, so these are just the conclusions. So we have demonstrated phase tuning of thermal properties of nano-size superconductor. And we have shown a sizable temperature variation in the high flux to temperature transfer function with the operation up to 1 Kelvin. We have shown probably the very crystallization of the first tunable thermal memory where the logic state can be encoded by the temperature that has shown robustness against fluctuations and non-volatility. So at the end, I believe that this object can be relevant, or at least is the first step in order to realize some technological application, like energy harvesting, general heat logic architecture, thermal amplifiers, or non-volatile data storage units, and the end, maybe also heat engine. So with this, I have concluded. And I thank you very much for your attention. Thank you, Francesco, for this very interesting talk. And there is a question there in the back. Yeah, thank you, very interesting results. So I have a question about the last data that you showed about the memory encoded in the persistent currents. And I was looking at the X scale and its seconds. And I can tell you that we see something on the time scale of hours, which I'm wondering if you also see. So on the time scale of hours, we see that ionizing impacts in the substrate actually reset these currents. I agree with you, if you do the phase-slip calculation, these persistent currents, they should live forever. Yes. But they don't. And I think what we have concluded by going to Gran Sasso under the mountain, where they do live forever, where forever means three days. Cosmic rays. Yes, there. Well, ionizing radiation. But mostly, you want. So do you see that? Because here, the time scales are still under long, but they're just tens of seconds. Do you see something on the hour? Yes, this is tens of seconds. We have another experiment where we measure the electrical part where it is several hours also. And you don't see anything unexpected? No, we don't see anything. No. You don't see anything? No, no, no. Well, maybe there is a reason. Because the energy barrier for this phase-slip barrier is so huge here. And if you calculate this, the rate for escaping from, let's say, the topological index one to the other is of the order. I mean, the rate e to the minus 280. So it's 70 seconds. So it's absolutely suppressed. Unless you are very near to the switching, OK? Yeah, yeah. Because it's a pretty short junction on this. So I mean, let's say that the corresponding tau is energy is pretty large. Good. Well, that means we might learn something from this geometry. If you don't see this, in our community, we might learn how to suppress. Well, maybe we can make one of these rings put under the mountain. Well, if you don't see escape now, you will not see it under the mountain. Well, maybe there is more interesting. Because if you want to make the qubits, maybe it's more interesting. And this is just a modest, let's say, thermal device. All right, great. Thanks. Another question? Just about the process for the cooling of your device. So I understand that when the gap is smaller in the normal region, it's easier for a quasi-particle to tunnel in. But then, how do they escape from the normal region to the superconducting electrodes, which have still the big gap? I'm not sure that I have understood exactly what you are asking me. Sorry. So I'm trying to understand how the heat is transported through the superconducting part. OK, OK. So you are saying, basically, that I'm injecting, you are injecting a quasi-particle above the mini-gap. Yes. But the mini-gap is a local property, and within the ring, which is here in blue. So you are asking me, how is thermalizing, let's say, when goes, let's say, inside the S-prime part in the rest of the ring? Yes. I would say, I mean, basically, first of all, because the heat that is injected is small. So maybe there is sufficient time in order to evacuate sufficiently. Because I mean, the ring is big. There is a very nice contact to the same material. It is true that there is a slightly reduced mini-gap, but it's an S-prime junction. So some heat, for sure, will go. So basically, it's this, I would say. So there is possibility. So I mean, the experiment is showing that, in principle, it's possible to do this. I agree with you that it's not the perfect evacuation in general, because I mean, the. When you do the calculation, how do you model this? OK. Yes, the calculation is pretty simple. We have a few slides here. One slide to show you this. Yeah. So basically, I mean, is what we use typically for analyzing this kind of system. So we have basically three different boxes. So electrons in the proximity wire, its phonons and the phonon in, sorry, this is in the island. So it's not in proximity wire. In the proximity wire, we have considered everything resides at the same temperature. And by using simply the fact that there is a dramatic impact of the capyta coupling in the system, because it is a very narrow and long wire. So here, apparently, I mean, is we are working at sufficiently high temperature. It is 800, 8,000 Kelvin, 900,000 Kelvin of electron temperature in this long island, where everything is capyta limited. So indeed, the regime where there is capyta limitation or electron phonon limitation is around 700,000 for this kind of structure here. And so I mean, there is nothing complicated. So basically, we solve a system of thermal balance equation, so no linear, let's say, integral equation that states that all the current heat current going inside and outside is equal to 0 at the end. But here, we assume that the weak link has the same temperature as the rest. So it's at the above temperature. So I mean, if we look at the, if you remember, if you want, I can go back to show you the agreement. So I mean, it's a very simple theorem, but it allows to grasp what is going on in some sense. So in this sense, I would say that I agree that in S prime, it's difficult to evacuate. But if, I mean, the time adjunction is 60 kilo, it's pretty opaque, I would say. So at the end, the amount of heat that is going through is not so much. Maybe if we want to make a very effective heat modulator with tens and tens of millikai like we did with the squids, maybe it's more difficult there. So there, maybe we have to think a little bit better what is going on. But for instance, for a memory, it's nice this. We don't care too much, you see. So these two states, four millikelvin of difference, can be exceptionally well resolved and maintain time. So, but the question is, who is going to make a thermal computer? Nobody. So. Sorry, I think we are running out of time, so let's... So as far as I understand correctly, that the hysteresis is like the squid, typical squid hysteresis where you, you know, change the number of flux corner in the loop. No, this is not new to the screening parameter of the squid. So there is a substantial difference. So what you are talking about is when you have a loop, when you have a loop and the screening parameter due to the kinetic inductance or dramatic and that sort of the loop is sufficiently large. This is very small. So here, I mean the screening parameter that is basically the ratio between the screen, the total inductance of the loop and that one of the weak link, here is much smaller than 0.1. So it's very small. Here, the hysteresis stems from the fact that S prime is a long junction. So the current phase relation of a superconducting quasi one-dimensional Joyce-on-junction is, becomes strongly skewed and non-hysteretic. When the length is larger than 3.5, say not. But it's still the squid, the flux in the squid and the current phase relation that does it. It's not the temperature per se. Exactly, yes. Yes, for sure. So one might say that instead of, that you actually encode your memory into the flux degree of freedom and not to the temperature, but you use temperature to read it out. Exactly, exactly, absolutely. Indeed, the first step of this was done on a... We need to move on. I have to escape. Yes. So thank you, Francesco, again. Thank you again. Next speaker.