 So, thank you very much for the invitation. This is my great pleasure to be here. The first, because of my wife's health, I'm cutting down my conference trips very much. When I receive this invitation for Boris, I have to come. And so I will talk about today this topic. Coherent quantum phase slip happens in Sinwire. And the same means in the order of about 20 nanometer. So very appropriate for this conference, nano science. And all this work, main part of this talk, the result was obtained about two, three years ago. And since then, recently, my lab in NEC, which I built up for 30 years, was terminated. And I am retired from NEC 100%. And the whole lab is moved to RECAN. And I am starting a new lab at the Tokyo University of Science. So what I want to say is lots of the work I want to continue, it's not really finished. I do have some new results that I can show you, some DC results. And yeah, I think Boris still, both of those working as NEC fellow, and I was functioning at SCUBA and Boris was in Princeton, but I'm retired. I think Boris still has some connections. No? Okay. Yeah. So what is coherent quantum phase slip? This is some effect exactly due to Josephson tunneling. And I can depict some concept of this. So the degree of freedom seen superconductor. We have phase and charge and everything else is mostly frozen. And in Josephson tunneling we use, in this picture, we have two superconductors separated by a very narrow gap. In this case it's a space and insulating barrier for Cooper pair. But the tunnel happens and you have Cooper pair tunneling if the gap is narrow enough. And the conjugate of that, in picture we can draw a conjugate by changing black and white. So you have superconductor two piece connected by very thin narrow superconductor wire. And now this black part is space. And one can have flux quantum tunneling, coherent tunneling, quantum tunneling through here. And so when this effect is stopped, one can have, in this case, flux quantum flowing through across the tunnel junction this way. And also when coherence is stopped you can have charge transfer in this way. And 50 years means from the original proposal of Josephson to until this experiment we have done a few years back it took 50 years to see this two effect which are exact conjugate to each other. So if you see this, this is a great wall of China and you see a lot of tourists walking around. And is this wall barrier or a pass? It can be pass or barrier. It depends on what you're, the prospect. So Josephson junction and CQPS means coherent quantum phase slip compared to that. It's a barrier for horse rider and charge and flux in these two cases. And it is the pass for defending soldier and flux and charge vice versa in this case. And the exact duality was discussed by a movie in Nazarov in 2006 that this is typical Josephson junction. And the ID curve looks like that. And this is simulation. And with microwave radiation you start to see this Shapiro step nicely. And conjugate of that is CQPS voltage can be written exactly like that. VC is some characteristic voltage. And we have sine here and 2 pi Q. And Q is Cooper pair transferred. And it's a continuous quantity. It's just a sine pi. And kinetic capacitance can be defined. Just a sine kinetic inductance in this case. And Shapiro step can be seen. And this is simulation because equation is the same. Of course you have a same result except the voltage and the current is reversed. And you see very nice Shapiro steps. And since this is a coherent phenomenon, you can drive them very fast. This gigahertz. So this can be used as a voltage standard. And this is being used for many, many years already. It's the international standard. I can discuss this later but we still don't have any quantum current standard. And this can be certainly a candidate for a quantum current standard. And duality of Josephson effect. This could be something similar. You will have a charge. This is Josephson junction. Charge transfers. And this is Josephson energy. And this is Josephson inductance. Kinetic inductance. And you have flux coming out here. And also, this is some invented sign for facelift device. And you have flux flowing this way. And you have some trace of charge appearing there. And facelift in superconducting narrow wire has been studied for a long time. Typically, the thermal facelift has been known for a long time. If you have a strip of superconductor, you drive it by a drive through this with external current. You start to see IV curve like this. At certain current, the weak point of this supercurrent, the face cannot be sustained and start to flip. And it keeps flipping. And that will develop voltage. And by passing more current, another facelift center appears. So, typically, you can observe this kind of IV characteristics. And in Kincom's textbook, it was described by... Okay, the other parameter in this thing wire is thin enough, much thinner than the penetration depth. You can see this. You can draw imaginary part and real part of this other parameter. And this axis is X. It's the space of the wire. So, face rotates, but if the current is strong enough, the face starts to wind and wind and wind. And finally, before the facelift step starts, the absolute size of the other parameter shrinks. And at this weak point, the face starts to flip to pi. And this is the picture. So, this is when how facelift starts. Okay, that's facelift. Okay, when it happens, the flux quanta can flow across the strip. And so, detect... So, this is thermal facelift, but if you have quantum mechanical effect, one should see some very small structure here at the zero current. And this has been trying to observe for a long time without success. And so, later, Moly and Hermans suggest to see this effect. Maybe we can implement this wire in flux qubit structures. And to see quantum coherence in this system. And with this method, one can demonstrate this facelift very easily. And this structure is exact dual to the charge qubit. And in charge qubit, this is island. This is visibar. It can be much larger. And 2E can go in and out in coherent fashion in making charge qubit. So, in experiment, one should see this is overlapping either for magnetic energy or the charging energy. But if you have coherence, one should see energy gap opening up here, lifting up the degeneracy. And this is the design of the experiment. So, when we designed qubit, facelift qubit, we were following the example for charge qubit and flux qubit. A necessary condition for our qubit is that Josephson energy is, okay, this is charge qubit and flux qubit. But here, for phase qubit, the inductive energy has to be, I mean, the magnetic energy of the group has to be larger than the coherent energy at the facelift center. So, this is the fundamental design of the qubit. And also, the materials, how do you, how small has to be the wire? What's the material? I thought about this with the help of Lev Yoffe and other theorists. And in, so, I guess this is, in BCS formalism, the facelift energy can be written in this way. The tunneling probability has exponential dependence. This is quantum resistance. A is the cross-section, if this is a wire, and A is the cross-sectional area. So, narrower is better. And here, down here, roll is the resistivity of the material, above TC, of course, above TC you have roll. And the larger the roll, so it's higher the resistance of the superconducting wire, namely, bad superconducting system, something close to the superconductor insulator transition. So, very disordered material. It's, it's better. That means disorders, their superconductivity cannot really, I mean, you can pass through the flux easier. XI is the coherent lens. So, looking at this, it's not, today we can make it as small as possible, which is like 10 or 20 nanometers, but we can choose roll, choose some bad material. Okay, this is Josephson energy. So, what we did was choosing the initial experiment we picked indium oxide film. This was made in Israel. And the thickness, if this film was about 35 nanometer, TC is about 2.7K. Sheet resistance is 1.7 kilo ohm, very high. And, okay, this is, yeah, this is usual superconducting phase diagram. Low field below this critical field, low temperature and low resistivity, lower than RQ, you have superconductivity. And we should pick some material right below here. And this is the material choice. And the experiment was done in this way. This is, so we put the facelift qubit, flux qubit in a cavity. So, qubit in the cavity is a very standard way to characterize the qubit. And very convenient and established. So, this is what we do. And the cavity was made of gold. And this is all gold, ground playing. And there are two center lines coming out. And there's a very thin indium oxide central wire. And as you expand that, you see this is indium oxide. And in the center we have a qubit. This is qubit line. And here's a very narrow wire, nano wire. Typically, in this case, it's 40 nanometer. And over here we put indium oxide film right on top of gold without any designed capacitance. Because sickness is so different, we have a huge impedance mismatch. So, this part functioned as a cavity. And so, the experiment is trying to see this gap in the spectroscopy experiment. What happened? Why this is not, something is wrong. Okay, so, this is the result of spectroscopy. The technique is called two-tone. You put two different frequency, and you see the transmission. And this dotted line is fitted. And as you can see, there's a clear gap about five gigahertz. And the size of the critical screen in current, or critical current, is about 24 nanoamp. And we further try to see the larger spectrum up to, like, let's see, 80 gigahertz. So, we are sweeping a wide range. For this kind of experiment, we have to use two-tone, three-tone, something fancy experiment. The signal is rather small. But the reason we did this is to see a large area all the way to, sweeping to the next charging state, I mean, flux states. There's a little dotted line drawn here. This shows, in this flux qubit line, the single wire, if it contains some occasional Josephson junction, like in grain boundary. One, so this is a Josephson effect. And Josephson effect also can have similar results. But if that is the case, it will show here something will happen here, but it doesn't. It really modeled as a charge qubit rather than flux qubit. We know this is a phase slip in this sense. And later on, we try to use other materials instead of in-jume oxide, which is evaporated later on and lifted off. Instead, we try to use harder material, which is easier to handle. And so we use titanium nitride grown at Delft, at Clapwix Group. And also we use niobium nitride from film growing in Moscow, Goldsmiths Group. And this is typical, this is titanium nitride. This is already bad. We use something like in here. This is temperature dependence of the resistivity of the different sickness. And we can pick particular sickness. I think these are, I don't exactly remember, but some of these films were used. And so this is the etched Danowire. The sickness is roughly 35 nanometer. And it's, you put the mask and etch. And as you can see, it's not exactly uniform. We have some jagged edge, which was inevitable from our fabrication technique. And this is niobium nitride experiment. We put many qubit in one cavity. And all of them has different areas. We can distinguish which one is which, and we have different size and lengths, width and lengths. And so in one shot, we can get lots of information. We have many qubit. For maybe 50% of the qubit work, and 50% didn't work. But anyway, you get lots of information. For example, here we have one, one, two, one, two, three, maybe three qubits here. And the purpose of this kind of study is to see the tonal improbability, exponential dependence of the tonal improbability. We change the width and see how consistent or how reproducible is this and see the characteristics. And this is the result. So the purpose is to see this dependence on width, average width of the wire. And this average width is in this x-axis. Y-axis is the energy that we found in this spectroscopy. And we have a rather large scattering. Of course, the exponential dependence is very hard to achieve because the reproducibility, it's not so good and also you have non-uniform wires. No matter the reason, we have a rather large scattering. We have two samples, A and B, and made in different way, but still. So then we have two, this dotted line and black line is a fit using different model. And this red dotted line is using this disordered superconductor model and this is the relationship. And the black one is using BCS like model. And this is the relation. And both of them can be fit like this. And the important part that I like, five minutes left. So including the questions? No, all right. So eta is the constant here and A is constant here. And theoretically, they are supposed to be in the order of one. And this is very close to one, unity. So we are very happy. Okay, let me move ahead. And this is another material. We do the same thing. And also we can see the dynamics, not only the spectroscopy, we can see the dynamics of the Rabi flip. So this is flipping zero and one. The decoherence time is not so long. Roughly in the order of 10 nanosecond. I suspect this kind of material has lots of decoherence source. Lastly, we try to see the DC measurement. The experiment is not finished yet. It's ongoing. And the postdoc doing this left. So we are starting, thinking to restart. But anyway, we have many different samples. This is IV, and here is many. This is the resistance of the sample. And the higher resistance sample shows blockade. And we are changing geometry. And as the resistance gets smaller, you start to see superconductivity. And this looks good. But then we try to shine microwaves. And at that time, not exactly sure, but maybe how the design was bad. Everything heats up and cannot really see anything. So this is the status of our experiment. And then, okay, let's see. So compared to Josephson electronics and single electronics, single electronics is using control digitally by transfer of one single electron. And partial, this is using small tonal junction. And so you have coolant blockade device. One, so switching time if you compare this. This is coherent device, so switching time is Rc. It's typically picosecond in Josephson device. But in the tonal junction for single coolant blockade type of device, it's a stochastic tonal improbability. So you have to wait for a long time to satisfy digital electronics requirement. You really have to reduce the error rate. That means the switching time can be, you have to wait for nanosecond or even more. The slow device, that was the basic one of the problem of this device. But since we have exact duality in the coherent phase slip device, if you estimate the switching time, it's about again, this is L over R constant, but this is older of picosecond. So it's supposed to be much faster than the coolant blockade type of device. And pumping. As I said, there is no quantum current slender, and there are so many different competing device working. I will not go into, introduce all of them because short of time. But anyway, here also this phase slip is one candidate. And if you look, okay, so we have a voltage standard, quantum voltage standard and quantum resistance standard. And so David Salas wrote a book about topological quantum numbers in non-relativistic phase physics. So at least in non-relativistic regime, these quantum whole effects doesn't have any correction. It's one minute, okay, I'll be finished. And Josephson effect, this relationship doesn't have any, couldn't find any correction. So that's why they are successful as the standard. So this is arguing that they have topological protection. And now, so if this phase slip, we have a competition, but phase slip device is exact conjugate. It should provide, I mean, it could have topological protection also and it can be a good candidate for, or best candidate for current slender in this sense. And, okay, I'll skip this topological protection. Yeah, in Josephson effect, it's also topological in time. The phase is winding in time. And so conclusion. Coherent quantum phase slip has been experimentally demonstrated and we can have different materials. DC characterization is going on their way. Thank you very much for your attention.