 Na moment. So, good afternoon. My name is Josef Fasalc, I come from the University of Catania. And I will speak today about a diabetic manipulation of multilevel artificial atoms, presenting some recent result we got in our group. It's a pleasure to be here in Trieste and I thought the organizers to be invited, je to veliko zelo, da je tudi prizvom, da je tudi vsevsto, Boba dešel, in, da, svoji, tudi smo se spravili o kvantom vzelo, da je Boba dešel ljudjo, ne za ljudjo, nekaj ljudjo, But then it was a flurry of physics. And one of these branches has been quantum computation, and quantum bits in solid state devices. And here in this audience there are Yuri Pashkin and Professor Tsai, which made a great breakthrough in this direction. And since the conferences called fronteers of nanoscience. One of these frontiers is building quantum coherently hybrid networks. So this is my personal roadmap in short. And today I will be concerned about artificial atoms, which are basically solid-space state mesoscopic devices with functionalities of atoms. And superconducting-based artificial atoms are quite a well-developed class of devices, which present definite advantages with respect to natural atoms, so some flexibility of design, which allows several the same solution to be implemented. And the fact that it is easier to integrate such system and, for instance, couple these quantum bits with cavities and then thinking to more and more complicated architecture. And other advantages are listed here and tunability, stronger couplings. And the fact that one can use these cavities means that signals can easily produce detected. Photons can be confined in one dimension, so there are many, many advantages. Disadvantages is the coherence. The coherence in such devices can be due to several sources, which depend on which kind of device we are considering. Let's say there is usually a dominant source and a subdominant source and a noise is broadband and colored with low frequency part, which is almost 1 over F and high frequency quantum noise. These are general characteristics. And the major drawback for these systems is the coherence, as I was saying, but tremendously, figures tremendously improved in the last few years. This is basically people were able to fabricate highly noise-protected qubits. The recipe is that suppress the low frequency part of the dominant source of noise. This is the main reason. And to do that, one design a Hamiltonian with certain symmetries. And in recent years, these also subdominant sources, which are responsible for spontaneous decay, this action has been limited by the use of suitably engineered environment, which in particular, three-dimensional cavity design. And the improvement in figures since 1999 in figures of noise has been several order of magnitudes. These are the coherence times from the first experiments to the most recent one. OK, this is the summary of this part. The point is that all these advantages cannot be combined always in an easy way. And there are things that may give some problem. An example is the so-called lambda network, which will be concerned in this talk. The lambda network is a system, the easiest realization is a system of three levels, which are connected by two lasers in this configuration, which is called lambda. The important fact about this kind of system is that it displays interference effects in that population is trapped despite the lasers. Kamp population in this level 2, the population is trapped in this low-energy doublet, since amplitudes, if this system is in a particular state called dark states, amplitudes for transition interfere destructively. And this phenomenon is the basis of several effects in atomic physics. And these effects have been observed recently in individual atoms. And some of these effects have been observed in multi-level artificial atoms. For instance, this is the opening of the ultralar tones splitting in a three-level phase qubit. The motivation for studying this phenomena is that these physics may give advanced control tools for quantum networks. And the perspective is to use them in highly integrated systems. What I will tell you today are two applications. One is so-called 2 plus 1 stirrup, which may allow to see some three-level coherence, important three-level coherence in a highly protected system. And that the same physics can be used to amplify the detection of ultra-strong coupling with an artificial atom to cavities. So, I will mainly apply this tool, which is called stirrup. And it is as follows. This is the Hamiltonian of a three-level system driven by two atoms. And if this field of tuning is zero, this Hamiltonian supports instantaneous eigenstates, which are called dark states, which are a superposition only of state 0 and 1, so the population is trapped, is coherent population trapped. If we let evolve adiabatically the system, for instance, by varying this amplitude in a sufficiently slow way, we can change the dark state in the bare basis. And by shining a sequence of pulses in this order, we can, for instance, completely transfer population from zero to one, we never occupy in two. This protocol is called stirrup, and it is known in atomic physics since a number of years. The main advantage of stirrup is that coherence makes it robust, being sensitive, basically, only to the two-photon detuning, which is this quantity we would like to have equal to zero. If this quantity fluctuates, then one may have a decrease of the efficiency. This is the efficiency. And if the two-photon detuning is larger than 0,2, 0,4, this scale, then the efficiency drops down. While this is the single-photon detuning, which may be large two or three times this scale, so it's not sensitive to this other parameter. One has to say that this phenomenon stirrup is quite interesting because this population trapping, even if it is easily understood with a picture of the dark states, it is stable because of coherence and because it involves several coherent effect in three-level atoms. This is why demonstration of this phenomenon could be important in artificial atoms since stirrup is a benchmark for multi-level control in artificial atoms. Another point of interest is that since it is operated by two lasers, it is an absorption emission cycle, so it is a building block for processing in architectures. OK. The point is that stirrup in artificial atom in lambda configuration has not yet been observed. The fundamental reason is the following, that in order to get large decoherence times, one has to bias the Hamiltonian and some symmetry point. For instance, this is an external parameter and these are the energy bands of this device, which are symmetric with respect to this external parameter and this is the facing rate, which is minimal at this point. But at the same symmetry point, symmetry may cancel couplings and indeed it cancels the coupling needed to implement the pump pulse. So, I mean, the system is clean, but we cannot drive it. So, which may be the solutions to this, the way out to this problem? Of course, the first thing is breaking parity symmetry, so work with an asymmetric device. The point is that as long one breaks parity symmetry, then one pulls inside noise. So, in a sense, one has to optimize this symmetry breaking and if you look at a valuable device, you can get perhaps 70% efficiency. This calculation was for a charge qubit, for flux qubit, it's basically the same discussion. Sorry? Qg is in case of charge qubit is the gate charge. In the values implementation is an external parameter that you can bias and you can choose this external parameter in order to have a device with symmetry or not. If you work at symmetry, it's clean, but you have no couplings. So, this is what I will look here is a proposal to work at a symmetry point where there is not such direct coupling and see whether we can, in a realistic device, implement this coupling with, for instance, a 2-photon pump. This scheme, which is called 2 plus 1 stirrup, is known to yield poor efficiency, at least in economic physics. What we will show is that if we combine this scheme with some advanced control, then we can have nearly 100% efficiency in highly protected devices nowadays available. So, I mean, this is a bit the story of 2 plus 1 stirrup. So, what I have a device and I couple a field with three tons. This is the stokes AC field and this is the pump. The 2-photon pump pulse and I allow for some slowly varying parts of these pulses. So, the Hamiltonian is something like that and the selection rule tells that this is zero, whereas I would like to have something different from zero here to implement lambda stirrup. Then the goal is that how can we find an effective Hamiltonian H3, which is equivalent to the lambda scheme. So, I mean, which has an effective Hamiltonian, which is the Hamiltonian we like. So, we work under some standard hypothesis for the drive and if we do that, we can derive an effective Hamiltonian technically by a magnus expansion and derive a structure that is the same structure of the desired Hamiltonian. In particular, here you find that one has an omega p and omega s, which are these matrix elements. It has the same structure with some effective 2-photon pump and something appearing on the diagonal of this Hamiltonian, which is related to dynamical start shifts. So, if we use somehow these two pump paths to have stirrup, we will not have stirrup at all. This is the population in the target state, which goes to zero. This is the population on the initial state and this is the population on the state 2, which should be unpopulated. The point is that the protocol is really sensitive to photon detunings and start shifts yield dynamical to photon detunings. So, how can we do? We just study, try to find a phase modulation, which makes zero these entries, in particular this one and if we do that, we recover 100% efficiency for stirrup. The nice thing is that this phase modulation is pretty easy to find, it may have in simple cases an analytic form related to the pulse shapes I'm working to and more importantly, in practice it can be easily implemented in the microwave domain and it has actually something similar, a kind of control with the same numbers have been implemented in last year in a paper of the VALLAV group at ATH. So, I mean, this protocol can work in principle. Let's see if it works in practice and let's try to study, for instance, a flux qubit, having in mind the numbers of technical yield is a four junction flux qubit and we take into account many levels, some decoherence but the point is that effectively one can find large transfer efficiency in such devices in requiring times which are well below the decoherence time of the device. Another appealing option is to use really high quality qubits nowadays available, the so-called transmon to achieve such a result. The point is that this system have a nearly harmonic spectrum. It means that I'm never sure to address the right transition and the technical point is that since I did some large power to address the two-photompom transition I will have to take care of all the start shifts I can produce but this is exactly the same discussion as before. It is simply more complicated. I will have to take into account some more. I can calculate the effect of Abiltonian. I would have to take into account some more complicated structure of two-photompom pulses and dynamical start shift but the result is that one can again find a scheme, a controlled scheme yielding 100% efficiency in a transmon. Here times are 1.5 microseconds, whereas decay times are much larger. So again it is well inside. These times one can also feel to repeat this protocol. So I mean this is the first message. We can use highly protected qubits and control put together to get nearly 100% efficiency for such a kind of three-level protocol which I think it has some importance in manipulating multi-level structures. Another issue we studied with trying to apply this physics is the detection of ultra-strong coupling of artificial atoms to cavities. So ultra-strong coupling is a regime of coupling of an atom to some harmonic modes which goes beyond the James Cummings model and presents also counter-rotating terms. And these counter-rotating terms cannot be neglected when this coupling constant is of the order of the cavity frequency which is also of the order of the atomic splitting if you work at resonance. The idea is that this is the scheme of the level scheme of a two-level atom coupled to an harmonic oscillator with zero, one, two photons. And the James Cummings model mixes these doublets here, whereas in the presence of these counter-rotating terms, there are other couplings, these lines here, which can come into play. So I mean, a characteristic of this model of ultra-strong coupling is the, so to speak, the ground state is not anymore the zero-photon state, but contains photons, as components, for instance, with two photons, with four photons, with one photon, three photons, and so on. So this is quite hard to obtain in natural atoms, but it has been observed in artificial atoms where some spectroscopic detection of this coupling so of this structure of energy levels that has been obtained in, basically, in superconducting artificial atoms and in semiconductor quantum wells. And recently there has been a proposal to try to observe these effects in a different way. I have the third level, so I consider a three-level atom, and then I excite the system. And if this ground state is connected with other states, I should observe decay, in particular this decay from the state 2 to the state b, and then I will, the state 2 will contain two photons and I can detect two photons in the cavity. So if I excite from the b state, this system I should observe in pratics two photons, and there has been a theoretical proposal on that in 2013. The bad point of this proposal is that this probability, which is related to the amplitude of this state in the ground state, is very small, so, I mean, the effect would be blurred. So, I mean, our proposal is that we can, can we amplify the output signal by coherence. And basically the idea is, sorry, the idea is looking at this same scheme, but in the perspective of producing some coherent population transfer, some syrup from here to here via this intermediate state. And the point, if one tries to write a simplified Hamiltonian for that, for this process, this process will take place if I will have some component of this state 2 on the ground state of the cavity atom system, and so this component, I will have if I have a substantial ultra-strong coupling. So I can have coherent population transfer is a smoking gun for this coupling. The point is not only a smoking gun, it is something that in the best instance gives me 100% population of the target state, so a high output. So, I mean, it's a very effective way to detect this ultra-strong coupling. And since, I mean, I can address the transition in a faithful and selective way. Of course, also here I will have problems with dynamical star sheets. And in practice, the point is that since this C02 is pretty small, is pretty small, because even if a large coupling can be built, this is limited to a fraction of the natural frequency of the resonator and of the atom. And this means that this C02 is something like 0.07. So one needs a large-stokes field to induce enough transfer. And this large-stokes field induces huge star sheets. But we know these star sheets can be compensated with suitable phase modulation. This is in a three-level, three-four-level perspective. There is something which is even nice if I really consider more and more levels of the atom cavity system. And these are all the couplings I need to consider for having all the couplings which enter in the dynamics. And most of them produce star sheets. But most of them produce star sheets, which are auto-compensated. So at the end, if I do nothing, if I do this simple protocol, I will have a really decent result. If on top of that, I'm able to do some control as the one I showed before, I can get 100%. Another problem is that how to produce stronger couplings in such system. Of course, there is a recipe which says if you can couple a single atom with a decent coupling constant, then if you are able to couple more atoms, this coupling constant will scale according to this rule. According to this rule, n is the number of atom-1 couples. And here one see the spectrum of two different systems. One with, I think, four atoms and g, which is half. One with one atom with a certain g, which is here. And then with four atoms with a g, which is half. And the spectra are pretty similar, unless they deviate at this level. But we are interested to this region of this diagram. So, I mean, this scaling, it's pretty OK. And indeed, we can try to work out easily the case of stirrup via two intermediate levels. Actually, this is the Hamiltonian. I have these two atoms, which are connected with these two intermediate levels. And these two intermediate levels have the full Rabi ground state with one of the atom and the b state of the other one and vice versa. If I really make a transformation on this Hamiltonian, what I can realize is that I can transform this h in a nature, which is effective, three-level, but with the square root of two amplification factors. So, I mean, if I'm able to put more atoms, integrate, say, 16 artificial atoms in a cavity, which is pretty feasible, I can have a coupling constant, which is four times larger and guarantees me an observable effect. However, this generalization to many couple of atoms is not trivial, because one may have new transition and come into play, and one may realize several of the situation in which instead of having a lambda system, one has a so-called tripod system. And this completely spoils the app. But one can operate with the tuning just to manipulate this transition in an effective way. What can detune this one, keeping this resonant? And on top of that, this effect of auto compensation of start shifts, it's quite fantastic in that even if I do not, even if I do not operate any compensation of any adjustment, I can get 92% efficiency just taking all the matrix elements with all the higher energy levels. And this is 92% efficiency of transfer. The huge problem for this proposal is the fact that somehow we cannot choose to couple E and G and not to couple B. So, I mean, if we have a three-level atom, both may be coupled. And if they are not separated enough, then the new coupling opens a James Cumming channel for the process 0B to B, which is our smoking gun. What I mean is that if I have, if also the third level is coupled, the stirrup is not anymore a smoking gun for ultra-strong coupling. And one can see that this G prime is the straight coupling. If I have a G, which is the good coupling, equal to 0, and G prime different to 0, I have already 90%. So, it is not anymore a smoking gun. The point is that to be, in order to be the main transition, I have to satisfy some condition on the spectrum, which actually is never met in superconducting artificial atoms. However, I mean, these conditions are that basically this coupling has to be large and this has to be small. And usually, this is a flux qubit, exactly the opposite happens. Or these, and these two frequency have to be very different. And if you look at another example, which is the transmon, which is promising for observing that, you see that this other condition is not met. However, one can look at this, at a different scheme of population transfer, which is the V scheme. So, instead of adding this third level on the bottom, add it on the top, but this is the level scheme with large coupling here. This is exactly the level scheme of a flux qubit. In this case, this population transfer for this state to this occurs via an intermediate state, which contains these two photon components. And the important issue is that this is a smoking gun for ultrason coupling. So, if I have not ultrason coupling, I get this rabi oscillation. So, if I have ultrason coupling, I get population transfer. With no ultrason coupling, the population on the target state will be zero. So, again, this transition is detected with nearly 100% efficiency only in this situation. And, OK, I think I said what somehow I had to tell you. And as a summary, just I would try to show that multilevel coherence in artificial atom, it's quite important because it may allow quantum controlling complicated architecture. And that stirrup is a benchmark protocol for that. And stirrup in lambda configuration can be observed in highly symmetric protected superconducting artificial atoms using a kind of control, which is quite easy in the microwave domain as opposite of the optical domain. And that some new physics can be studied as the coherent amplification of ultrason coupling of the temptation of ultrason coupling by stirrup in with electromagnetic cavity. So, this is a final part of the talk, which is some congratulations to Boris in Italian, which is Cento di Questi Giorni, which is typical for birthdays. OK, thank you very much.