11:00:18 Our first speaker is a cola from Aalto University in Finland and he will talk on quantum key transport by microwave for them to come please.
11:00:29 Thank you David and thank thank you organizers for inviting me to give this talk. So I'm going to talk about quantum heat transport by microwave for them so it's mostly experimental work some blanks and theory towards the end.
11:00:47 So, what are we talking about in.
11:00:52 Okay, Good.
11:00:55 What are we talking about, it's in general, we looking at systems where we have.
11:01:02 We have indeed a quantum usually quantum circuit, which is sandwich between two heat bursts and then under different conditions we want to know how he does transported from, let's say hope best to the cold bath, or maybe under active operation also in
11:01:20 the opposite direction.
11:01:22 So, this is of course, kind of, under static conditions this is diagnosing the systems and maybe making some kind of heat valves and maybe rectifier devices based on quantum systems.
11:01:41 But then, in the long run, of course, this can serve as as elements for quantum heat engines and refrigerators.
11:01:44 Another aspect of all the stories that you can you can imagine that you have hit it with is coming from an assault, no unknown source or known source.
11:02:00 And then this is absorbed by an element with with with temperature you monitor, and these forms the basis for doing biomimicry or color imagery to measure small kid currents or small amounts of, of, of heat.
11:02:09 So, mainly I focused on this first system here in this talk, and.
11:02:16 And this is something that is quite on a general basis you can you can discuss this as a transport from from one bath, which essentially has a certain 10% maybe chemical potential coupled to another bath.
11:02:34 Again with the temperature and chemical potential. So if this.
11:02:36 If this connection between these two ends here is, is a, let's say one dimensional channel, then, then you can, you can write the right the current, let's say, particle currents in the case of just particles it's usually an electron current.
11:02:58 In terms of the, of the distributions of on the on in the two different reservoirs and also the, the transmission through this channel.
11:03:07 And similarly for the heat current you have a similar expressing but now of course there is an energy because but what you're looking at is the energy that is transported from one wonder I said what to the other.
11:03:18 And a special case in this case is the is the one where, where the transmission is is unity so we talk about the ballistic channel. And then, in this case, for, for, let's say particular current or trust particles, we have this conductance, which is context
11:03:37 in units of all this conductance quantum.
11:03:40 It is squared or eight, and then the thermal thermal conductance is also essentially, you can tell that this context, although you see the temperature here, so it has these multiples of, of this.
11:03:53 Quantum also conductance here.
11:03:55 So, is this only theory. Of course not. So there's there's quite a lot of experimental evidence and experimental realizations of this, of this phenomena, for example with this task particles electrons it's already known for, for 30 years or more than
11:04:14 that if you have a ballistic electron channel you can have conductance Quantcast in in in in units of, of this electrical conductance wanting to hear for the, for the Spirit.
11:04:29 And this was done by already, as I said, more than 30 years ago. Then the question is can one do the same for for semiconductors, insert systems.
11:04:39 And this is the thing that has come a little bit later. So, there are several examples about the thermal conductance quantum the different realizations, I mean, in general, these thermal conductors quantum is general for any kind of carrier.
11:04:58 So it has been verified by electrons in several experiments may be the most.
11:05:06 More recent and and and perhaps a plane experiment is this, in, in Paris where, where people could see in in in this kind of a domain here where you have ballistic context, one could see that the heat is transported in in unit in a let's say in quantity
11:05:27 of this semiconductors quantum and quite recently also going to do with the atomic level of contacts electrical charts and key transport measurements where we would verify the same thing, even at room temperature is is quite remarkable.
11:05:46 The first realization was by foreigners already 20 years ago by its weapon, Michael, Lucas, and they could verify that by, by measuring the heat transport both by foreigners was also get the best value that low temperatures.
11:06:04 We have a review that is coming up on this topic quite quite, quite swarming RMB together with my student by a parent.
11:06:15 So, what about the realization that I'm mainly interested in that these photons so let's take a system where, which is the most basic setup looks like a Johnson nuclear setup.
11:06:28 So let's say that we have a one.
11:06:30 One resistor here and another register here, and they are, they are couples Bye. Bye. Let's say electric police that do not conduct heat by usual means but just by by via their way of the electrical noise or one could also say microwave for photons here.
11:06:49 So by that quite elementary circuit calculation one can show it in a great sort derivation you can derive the expression that that when you take into account the quantum emission absorption most of these resistors you find out that the power assumes this
11:07:07 expression which is shown here. And then, if you take just the main temperature there or if you just take the linear regime between the two temperatures you find out that that the power that is transmitted between these two resistors is indeed it is proportional
11:07:23 to the, to the thermal conductors quantum times the kind of a matching factor by the of these two resistors which seems funny one. When there is unity when the two resistors are equal.
11:07:34 So it is also in this kind of a setup you expect that the thermal conductance is context in this, in this sense.
11:07:44 So, how to measure such things. so I just give you a very very brief recap of how we usually do the thermometer thermometer is of course the basic element in this kind of thing.
11:07:56 So, what we have as the as the absorbers where we measure this.
11:08:06 The seed is usually a metallic micro micro scale or nanoscale metallic conductor, which is then couple usually do superconducting least in in a second.
11:08:13 So, so this is kind of a can be copper or some other user metal, and then you probe it by a superconducting tunnel junctions here. So the electrical transport through this panel context is then depends on the superconducting energy gap here, and then
11:08:29 depending on the sharpness of that Fermi distribution in the normal metal, you will get the, you'll get the current which ties exponentially with the 10% low temperatures, so you can even have a kind of a primary dependence of this logarithmic current
11:08:43 through this thing, versus the world is with this gives you directly. the temperature slope of this panel IV characteristics.
11:08:53 So this is kind of a very basic measurements which we are doing all the time in the, in the laboratory to probe the temperature, this is kind of resistors.
11:09:03 So, and, and, indeed, this kind of a thermal conductance measurement can be done based on these photos and this is our quite early experiment in 2009, where we we had, we made exactly the setup of Johnson and nucleus with two resistors, one here the other
11:09:21 one here. And by having several of the multi probes on these two resistors, we can both control the temperature, and also measure the temperature at both ends so, so the connection between the two is made by a superconducting leaf which doesn't conduct
11:09:35 any key that the temperatures which are very much below the superconducting transition to damage.
11:09:41 So now the but based on on in fact some kind of a self cooling of this junctions by the NIS Donald Trump says we can, we can just look at the bias dependent so when you put a bias world is of course one pair of these changes here, you can monitor the
11:09:57 of this absorbing register be here, here and now if you do the local. If you do it locally in one of the resistors, you will see that, okay it's here is the local one, you see that the temperature dependence is such that first division Brooks and then
11:10:13 at the world disorder of the gap or the double gap, it reaches its minimum and then it rises, quickly, because of the job power into the lead. And then you can simultaneously monitor the opposite register here.
11:10:27 and that also, as you see, is somewhat following the temperature of the, of the first one, and the lower you go in temperature, the closer it follows the one at the distance of several 10s of micrometres here.
11:10:42 So when then takes the, the ratio of these two temperature drops here at different temperatures and plus it against the against the bathtub as you can see that there's create this a rise at low temperatures and, and if you could compare it to the prediction
11:10:57 of quantum of semiconductors, you can see that that you are pretty much cause of that so, so when can even even one country really see that, that this Johnson nucleus, but he transport This is really realized in this experiment, and some more recently
11:11:22 another group was measuring a set of very in a very similar way as shown here so there's a there's a long, kind of a transmission spoke I think transmission line is is connecting the story sisters here, and they would also verify that even when the line
11:11:27 line is several 10s of centimeters long you can you can see the same, same cooling via these microwave folders.
11:11:36 So, so, then one question is can run.
11:11:58 of these two resistors by putting in a reactive element in between them. And then, in particular, if you put the superconducting squid here, you can kind of obtain the coupling elements which is a parallel LC circuits here where you can be, you can tune
11:12:17 the chosen shipper. The choices and indicators, and this way you can modulate the coupling between the two resistors. By doing this you have a thermal model of a you have these two resistors here, and then they talk both to their phone numbers, but also
11:12:30 between each other now via this Juniper coupling here.
11:12:47 But when you go to a lower temperature, where the, where these weekly temperature dependent, put on the key transport is winning the, the, quickly when using phone.
11:12:54 And what happens is that at high temperatures where the coupling to the phone and Beth is wrong, then you don't see any dependents on the magnetic flux applied to this squid with really more or less the indicators.
11:13:01 pier with the period of the flux quantum of of this, of the squid. So this shows that you can also generate elements where you can, you can do that.
11:13:19 modulation of this heat.
11:13:20 We are doing a very now. Currently we are we are kind of going back to this experiment and and there is a.
11:13:28 There's a real system now you're using a similar squeak geometry here, and with two resistors as before. So again, the, the circuit can be described as before, and we can see that in this case when the these resistors are of the order of bend the resistance
11:13:47 is is relatively low light of the order of one kilo or below. We can indeed we can reach this quantum of semiconductors, when the when the squid is open here.
11:13:58 Whereas, when the squid is closed, we can see that that that the heat transport is really strongly prohibit the interesting thing for the moment is appearing when, when we increase the resistance by us making the resistors here out of chromium, you can
11:14:16 make this very high of hybrid system is through resistors, which means that you start to have kind of a dynamic complicate effects already in on this Johnson element here in between the two resistors.
11:14:36 In this case, this model of having having a just simple interactions in parallel with the capacitors between the resistors seems to fail. And what happens instead is that due to the strong environmental effects of this resistors here that he transport
11:14:52 through the system is not anymore, modulated that all by essentially not at all by by the presence of the chosen element, but it is it can be more frequent simply by assuming that the Johnson.
11:15:05 two resistors, with, on top of that need to be now considered as elements which are like RC transmission lines because of the week transport wire this capacity, so we can model this very, very nicely with the, with the, with the known capacitance is in
11:15:29 in this circuit that we have. So this is an ongoing work but it is, it's kind of the remaining modulation of this heat current can now be model with the, with the weather weather.
11:15:43 So good job easier.
11:15:43 So what we have in the experiment is that we have several.
11:15:46 We have a lot of possibilities of using the chosen elements for for for this heat transport. And in, in particular we are now using different types of curious, we have the transformative is, we have to ask you this, and we have luck skew it's basically
11:16:00 have all in our, our kind of the pilot of the experiment at the moment and and the difference is that the transport few bits are like a very harmonic, whereas the two other types of food is can be made, highly on harmonic in and then they demonstrate
11:16:16 more like a more quantum effects. So here is our experiment on what they call a quantum heat well it's very close to what I showed already by this previous squid experiments, but now we're employing the kind of a modern transform few bits where we can
11:16:35 again, control the heat by by applying the magnetic flux between the two to heat but here we somehow coupled to this, this great and between the resistors.
11:16:46 Why, a co planner wave resonators superconducting Copeland a resonator so we have again a possibility to modulate this heat, by, by changing the level spacing of the qubit so that experiment in this case is like a quantum heat Bob, where there's transport
11:17:02 qubit which is close to a harmonic oscillator is level spacing can be tuned, and then the heat is transported when that when this.
11:17:10 When this qubit level spacing matches with the two resonators here.
11:17:16 So in this experiment we had some quite interesting, two different extreme results. So depending on the quality factor of these resonators which is determined by coupling this resonators to the reservoirs, you can have either the kind of a local picture
11:17:33 where the bear qubit is coupled to this construction environment with Lawrenson spectrum. And in this case, you indeed have what I had in the previous slide, and you can see that the heat that is transported through is more related with the, with this
11:17:57 of this lexicon quantum matching it twice in a in a flux period. And Mark can also call this by at the distance of several millimeters. Whereas, if you have the coupling.
11:18:00 The internal coupling here, stronger, essentially, than the coupling to the best here, then you have this hybrid quantum element, which is then coupled to the past year we have, we have in kind of a global picture of the system.
11:18:15 And in this case, the experiment shows a modulation of the seed which is less Lawrence, like them in India in the first case, in both cases we could by straightforward modeling, we could see these two extreme cases and currently the interesting thing
11:18:35 is of course the crossover between these two regimes. Another important thing here is that when you put this kind of a quantum element between the resonators if you make the couplings to the two different best on equal like here, we just make the resonators
11:18:47 of different lengths, different frequencies. And if the qubit here can be considered as on harmonic element, then you have all the, all the ingredients to create a heat and thermal rectifier.
11:19:00 And this is what happens in the circuit of putting this transport in in between the two different resonators bit different frequencies, and we can see that the forward heat current and the backward his current are really different in in this experiment.
11:19:17 experiment. So when taking the ratio of this forward and backward heat currents under identical but opposite conditions we can see that there is rectification of you, about of about 10%.
11:19:30 The experiment can be and, in fact, in the future, we hope to improve this rectification factor by the lot by, by changing the, the cube is to do more kind of on harmonic elements by, by using the flux cubits and task units.
11:19:49 So, one of the goals of course in this game is to create as I mentioned, active active heat transport elements like like refrigerators and heat engines and one of the ideas is to use this cube is exactly the geometry of this previous slide the in the
11:20:07 geometry of having it between two unequal resonators. In this case, by putting an alternating flux to the qubit, you can transport heat from from the cold bath, to the foot bath under, under suitable conditions.
11:20:22 The interesting thing there is that of course at let's say courses that the frequencies of this driving of the author fridge, you will expect that the power is power is increasing.
11:20:35 So the heating power is getting more negative linearly with the frequency of your drive. Whereas if you go to very high frequencies, you start to see oscillations in this power with our kind of the quantum signature of, of, of the evolution qubit under
11:20:52 this a seed right.
11:20:55 So currently, and we are we are working on this experiment. So, we are trying to do this. Now, based on the, on this charts qubit because this is indeed.
11:21:08 As I explained more like a two level system between the reason is, is we consider the decline This for example in this first PRB here with their banker in 2016, where we looked at this, this refrigerator under different working conditions.
11:21:24 So in, in this case, this is more or less the same as with the plasma TV but now with the on harmonic task you begin between the resonators here.
11:21:34 So, this work is now in progress and be, in fact, I think we are we are very close to have some, some reasonable to cooling ourselves under this auto cycle of the refrigerator cycles and and it needs a lot of care to make the system in fact to make it
11:21:55 really an isolated to bath plus plus quantum system, but we are we are very close to that now.
11:22:02 So, and another challenge that we have at the moment is to really as I mentioned in the beginning to make these systems to be able to detect a signal microwave quanta so.
11:22:15 So we have, in a recent work, we have looked at temperatures temperature fluctuations let's say the energy fluctuations of the small absorbers when they are coupled to the phone on bath.
11:22:27 And we found out that they can reach the fundamental fluctuations of temperature on this absorber, which gives us like the base baseline of how small energy packages we can, we can expect to see when we cut all this.
11:22:43 When we cut all this absorption to the, to the relaxing qubit for it. For instance, or to look at some other microwaved photos that are are absorbed, and under the under this misery and conditions.
11:22:58 So, so at the lowest temperature is that the bV can do this experiment let's say a 10 million Kelvin, with with our thermometer still works in a satisfactory manner.
11:23:09 We expect that in this kind of an absorption. Our typical NFC or qubit we would expect that, that we would have something like a signal to noise ratio which is of the order of five or 10 in this mission, but of course this is kind of the idea of cities
11:23:40 where all the amplifier noise and now the other problems are kind of avoided which is of course, never, never fully true in, in real experiment. So, as a final slide here, I show you that there is a way with with way we try to improve this further, and
11:23:44 this is by boosting the sensitivity by by coupling this qubit simultaneously to two different keepers. So just having the same setup as before, but the pubic when it relaxes by this resonator to do the best VB instead have to essentially identical heat
11:24:03 but whose noises are are uncorrelated. Hopefully, and then the amplifiers are separate so we, we hope to see that that by, by, cross correlating the seamless of these two thermometers be the expect that the signal to noise ratio in can be enhanced quite
11:24:22 substantially.
11:24:23 This is an initial archive paper on on on this work we have. It's a, the more recent version will appear on archive so.
11:24:35 So that's all for the moment so that was what we can say about this.
11:24:40 Quantum heat transport. Currently and and and i also tell told you about our plans on doing some more active elements to study, study the heat transfer.
11:24:51 So here's the here's the group the experimental group is here. So, there's by Academy PS finishings PhD students using Chan. They have a superhero, our veterans running and and and i would say, Andrew Guthrie and.
11:25:10 And the my salary and also opened other activists currently on this project.
11:25:15 Thank you for you this.
11:25:18 Okay, thank you very much, you can for this interesting talk. So we have time for a couple of questions.
11:25:24 Nicole.
11:25:26 can you ask.
11:25:30 Erica thanks very much for the talk, it was great to hear what's been going on in your lab recently. I was wondering why you chose to realize an auto refrigerator, rather than an auto engine going in the opposite direction was the choice completely arbitrary
11:25:42 or is the refrigerator somehow better suited to your setup and was the author refrigerator is a very simple implementation in this circuit because, and because it is.
11:25:56 You can realize it basically with a single sign of sort of drive on the on the on the qubit, because by driving your qubit you can simply at different phases of the, of the same sort of signal you can you can realize the audio fatigue, these expensive
11:26:15 uncompressed and legs while the while the qubit is not in thermal contact with either of the two resonators, whereas at the end of this episode will drive you are you are connected to do one bath, at the time, So at maximum.
11:26:32 So, basically, it's kind of the simplest possible way of realizing a four stroke cycle in the single sign of soil.
11:26:45 In, Dr. I think that's, that's kind of a, maybe the basic exponent basic explanation of why we ended up looking at this one.
11:26:55 So, if you ran that backward, would you get an engine that's just as simple as well basically that it's a sign of soul drive a in this in this manner we in this is an interesting question how to really realize the engine and and where you really would
11:27:11 get the get the energy stored in this case so we have not yet even even conceptually be. We did not think of where the bucket of this kind of a engine would be.
11:27:27 Okay, thank you.
11:27:30 Okay, any other question or comment.
11:27:39 Hello, how you got, oh hey, I have a more experimental question maybe how he sees to happen to resist to resonators to the same grocery store.
11:27:55 It's very, very, very simply, in principle, so, so you can connect them.
11:28:01 You can go they connect them either in serious, or in parallel. So they, they simply test.
11:28:08 They will.
11:28:09 You can see it here. So, Basically what you need to do is test.
11:28:15 This of course exaggerated this element here, the size of this is course of course much much smaller than the resonator size here. But, but the idea is that, that you can insert a superconducting coupling between the two.
11:28:30 So it can be even the same material as the resume itself there.
11:28:33 And this is prohibiting the heat transport between the two resistors. Like I explained in the beginning about the heat transport in this resistor system.
11:28:43 And then, then. Bye.
11:28:46 Bye.
11:28:48 Kind of, yeah so if publication bias it's it's very, very straightforward, I would say. So you basically you just have to split it into two halves where where you have a superconducting element, separating them, and you can do it either borrow series
11:29:08 of course the impedance and the quality factor considerations.
11:29:13 Deeper reverses, I don't see it so for our conference.
11:29:16 I mean, to resonators not to run to resonate this 200.
11:29:21 k. Okay, I came along, as the wrong.
11:29:25 Wrong answer to another question. Yeah. So, I think, tourism is connected to one register yeah that's also definitely possible.
11:29:39 In this case, you may need to.
11:30:01 having. Essentially what you would have is that you have a small element resistive element in the middle of one long resonator and that's all.
11:30:10 It's easy.
11:30:18 Okay, you'll get answer to.
11:30:18 Okay, so probably is.
11:30:20 is a good time to stop here. So let's thank you can for his talk, and we move to our next speaker is, according to the retail.