 I would like to thank the organizer in particular of Burizio for setting up this very nice workshop. It is a great place in Vatime and giving me the opportunity to speak. Sort of the third part of this mechanics session, I suppose. And, okay, I seem not to... Oh, no, it works. And, yes, so I'm working actually not at the University of the Basque Country, but at the Donostea International Physics Centre, which is an independent research institution, and I'm employed by the EcoBusK Foundation, which may advertise its offering tenure track and tenure positions to all fields of science every year. So have a look in next spring. The next offer will come out, and we welcome applications from everywhere. So what I want to talk about is a particular implementation of QIP in the solid state setting, and I'm not talking about five-nines or six-nines like we heard in the previous talk, but we'll see that there are actually some surprising connections between this solid state implementation and the field of trapped ions. And the work I'm presenting has been on the last couple of years together with several people, the group at the Max-Machs-Branck Institute for Quantum Optics of Ficknathio-Sirak, where I was working previously prior to my present position, and it was led by Martin Schütz, who is now... who was at M.P.Q. and is now a postdoc in Misha Lukens' group in Harvard and by Yannis Knauzer, who is a PhD student in the Max-Machs-Branck group. And we also collaborate heavily with Leven-Fundersite Min Delf. In our talk, our surface acoustic waves as a tool for quantum information processing in the solid state setting, and we've just had a very nice example of a talk that shows how important bosonic fields and bosonic modes are in quantum information processing. The trapped ions were the first system in which the mechanical mode where the ions oscillates were used as a quantum bus, and of course lasers are used in all the manipulations one does for the... or now microwaves of the internal states of the ions. And also in many other approaches, circuit QED, all the quantum optical approaches, we have bosonic modes which play a crucial role. In the implementation that tries to use a semiconductor nanostructure, similar to quantum dots, there is no such natural candidate for a bosonic mode. Of course, one can also use light and one can try to use circuit QED, but these are not natural to the system. They have to somehow attach, have to be brought in. And so the talk today will be about a bosonic mode that is right present in the system and so far been in use and that we tried to make use of and turn into an asset. And this was motivated by recent experimental successes in using these surface acoustic waves to for, at the moment, not yet coherent quantum information tasks like moving electrons between separate quantum dots, loading and unloading them, also trapping excitons in lettuces and studying the interaction of these excitons. And recently this field has also been explored in the context of superconducting qubits placing... in a surface acoustic wave cavity and demonstrating cavity QE effects and single phonon coupling and the like. And so the aim of this talk is to introduce surface acoustic modes and indicate that they can actually play a useful role and might be able to play a successful role as a quantum bus in between quantum dots qubits and also as standing waves that could provide the basis for acoustic lettuces and trapping of carriers charged and uncharged carriers in semiconductor structures that could lead to interesting applications in quantum simulation. So I fortunately don't have to talk much about spin qubits and quantum dots because we had a very nice presentation on this topic by Daniel Loss a few days ago and so I will just briefly remind you because it's sort of the motivating setting. I will not talk much about quantum dots in the later part of the talk but the motivating setting is that we have these semiconductor structures, hetero structures where the interface between two different semiconductors to the electron gas is formed which we can manipulate by applying gate voltages to the top of this structure. Thereby one can deplete the 2-deck in many places and the remaining puddles of 2-deck contain a finite number of electrons that can only tunnel out of it and whose number one can by now control very well so down to the single electron level and these are the electron spin qubits that were the basis of Daniel Loss's proposal and of many experiments in Delft and Hobart and Copenhagen and many other places and that are the objects that we would like to address with the surface acoustic waves. The spin qubit QIP proposal is one of the oldest around and while one has a number of advantages like the closeness to the semiconductor technology like the high compactness it's probably among the smallest qubits of good isolation from especially charge noise and fast gate speeds and while a few qubit demonstrations have been achieved one is the field is actually quite behind the trapped ions and circuit QED settings in there but one still talks about 2-3 qubits and 90% or maybe 90 something, 96% fidelity. There are two bottlenecks or two outstanding challenges where many ideas exist but not really an accepted solution. In this field it is how do we couple across longer ranges not just neighboring quantum dots but dots that are not directly interacting that are far from each other and also how would one build structures that go beyond the 1D setting so arrays of dots there is a very clear path to it but 2D structures people have ideas but there is no very accepted approach and as I like to indicate maybe the surface acoustic waves can help in both of these challenges. So the outline of the remainder of the talk what are surface acoustic waves and what may they be useful for so I will give a very brief introduction only on the surface acoustic waves because what I'm really using is just their bosonic nature and particular aspects of how they couple to spins or to charges mainly charges in semiconductor structures and the applications that I want to discuss and this will also be rather a brief both of them will put the emphasis on the last one so this could form the basis for analog to cavity QED can build resonators for the surface acoustic waves which can serve as a quantum bus or a means to mediate coherently interaction between several qubits in this structure or to convert stationary qubits into flying qubits that move them with the speed of sound in this material and the new result and the one that I would like to advertise more is this idea of using creating standing waves of these waves and trying to trap electrons in a periodic structure with them so surface acoustic waves just a particular type of a problem that propagates close to the surface as the name says and that is sort of these are particular solutions to the wave equations that appear because of the boundary condition at the surface that there is kind of a stress-free surface there is no force acting there and this leads to these solutions the most well-known modes are the Rayleigh modes there are others the nice thing about them is that they are close to the surface that they are confined naturally to within a wavelength of the surface so if one wants to couple strongly there is already one dimension we have to worry much about we get a natural we get directly one of our confinement to within one wavelength and also they can be addressed, guided, created by surface patterning so they are accessible to us more easily accessible than for example bulk waves would be and only their properties can be rather readily augmented creating heterostructures of materials that have particular properties in their reaction to mechanical stress so active materials in particular that will lead to the fact that then these mechanical oscillations are accompanied by electric or magnetic fields depending on the material we use and that makes this a system that can be fairly universal because you can design it such that it carries magnetic or electric or mechanical or all of them and that allows you to talk to many different things and may also make this an interesting system to build hybrid systems and then clearly they can play the role of optical fields and modes in this solid state setting so the analogy is very clear one can try to transport electrons like one could thread atoms in an optical tweezer one can use them to drive gates of qubits one can think of acoustic lattices in an analogy to the optical lattices and one can build coherent modes, study coherent modes and they are interacting, interaction with qubits and so do an analog to cavity QED and so people talk about quantum acoustics now in this context so this is an ugly slide and I will remove it right away I just want to show these waves follow rather in the end rather simple equations so you describe them by just the wave equation at the surface the black thing is for non-Piazzo materials it's just the wave equation for the elongation u from the equilibrium position and then in Piazzo materials there is a linear coupling between an electric potential or electric field to these mechanical elongations and the back action that is described by the Piazzo electric and the dielectric tensor of the material and apart from these wave equations an important aspect is the surface boundary condition that they have to satisfy and that leads to the solutions that we will be using but I don't want to go into these details here what I want to emphasize is that in these Piazzo electric materials not only is it interesting because we can couple then if the electric wave propagates to charges easily but we can also excite these waves and detect these waves easily by their electric fields or all electrically and this is used also in many devices that most of you have in your pocket in cell phones so if acoustic devices are used as bandpass filters and the like and the workhorse of all of this is the so-called interdigital transducer which is an array of gates on top of the structure with a particular periodic spacing if one puts an alternating voltage on this it excites the surface acoustic wave or if one takes off the voltage or if a wave propagates towards this structure one can read off the amplitude intensity of the wave from the voltage and this plays a role of a laser or of a microwave source in this structure in addition to this one can also pattern basically create break reflectors for these so long arrays of grooves on the substrate that will reflect particular wavelengths and this way people have constructed high quality surface acoustic wave resonators high quality in this context means up to Q-factors 10 to the 4, 10 to the 5 and which we'll see is good enough for strong coupling to qubits and one can also by placing material on top of the surface of the structure prepare guides channels in which the surface acoustic waves can propagate while they are being constrained by the changed boundary conditions due to the heavy material that you put on the surface for example and just to show how these things look in papers published on that subject here is by the Oxford group they studied surface acoustic wave resonators in the quantum regime and you see here the IDTs to create the material here the periodic mirrors in order to catch them and to contain them and here is an example of such a wave guide also this is from the Grenoble group similar types of extremions are also done in Oxford where again an IDT creates the surface acoustic wave and it then travels through this channel in this case the interesting thing is that it can pick up electrons and carry them through this channel and actually carry them back and forth many tens of micrometers without losing them okay so I want just to give a few numbers sort of to sketch the ball parks of the structures we talk about so these frequencies can be a couple of gigahertz maybe up to 50 gigahertz energies of these waves we typically talk about tens of microEV which means in order to be in the ground state of these oscillators these resonators we would need a dilution fridge temperatures which are well regularly achieved in quantum thought experiments speed of sound the lowest of the slowest of these waves in typical materials like gallium arsenide is three kilometers per second and the wavelength we talk about are fractions to several micrometers and so one nice thing about them is that they are actually much smaller than the comparable microwaves are because of the slower speed of sound that means the structures that one can get are so you can feel more compact so the... okay so I think I will actually be very brief in this discussion on the quantum acoustodynamics or the Q&E analog because it's the only important point or the only question about this was do the numbers kind of work out so do we couple strongly enough to or can we couple strongly enough to an interesting qubit in order to reach a strong coupling regime between this two level system and resonator once you have this you end up with a Rabi model or a James Cummings model and you basically can repeat all the stuff that people have been doing in cavity quity with these so this is that I want to only indicate that one can actually find a number of variety of systems in which this nice regime can be reached so the general setting that we have in mind is an artificial atom typically placed between such mirrors in which of a finite quality factor we will have losses that go out into a quantum channel so that leak out of the cavity in order to propagate and others that will leak out into the bulk of the system that are truly lost so we have two types of losses in the system and we want to we think of coupling this here and using an output mode in order to communicate possibly with other nodes of a network and I point out, I mean I will not pursue this but since we had trapped ions in this session these electric fields accompanying the surface acoustic waves they extend to outside of the material as well and so one actually can create oscillating fields or coupled to a mode with charges that are several micrometers so up to the surface and so this may be an interesting way to couple solid state and quantum optical qubits so the system that we have looked at so we always think of mostly think of piezoelectric material like calium arsenide as a standard example and we think of, so then it couples very strongly to a charged qubit but charged qubits don't live very long, I mean we saw they have only nanoseconds of coherence time and so what we are mostly interested in for this coupling is actually a double quantum dot spin qubit in which one has the capability to shift between charged at mixture and a purely spin setting depending on what one wants to do Daniel Loss mentioned this in his talk as well, you used a singlet triplet state of two electrons and double quantum dot but then you change the bias between these two dots and that will sort of give a higher weight to the singlet state that is localized in the lower energy dots and thereby your spin qubit acquires a small charge contribution and this is what we use to couple to the surface acoustic waves and in that case one can, if one orients the quantum dot properly with the geometry of the surface acoustic wave when it can achieve coupling strength in the order of tens megahertz and cooperativities for currently used resonators that can reach 100, so that's about 10 minutes so then I will go over several slides now without showing them well in this case maybe I go with this one Kirstof here or somebody who, sorry that I didn't touch it, okay so I didn't go into the details of these cavities, if there are questions you can ask them later or in the break and the idea that I want now to advertise and I will actually have to rush this a bit is could one also use these things to replicate the success that people had trapping atoms with laser light, can we trap electrons or other quasi particles in a quantum well in a 2-deck using these surface acoustic waves I find this, so one thing that I find interesting from two reasons, first that you can study for example the Fermi-Hobart model using these electrons in a regime that is very untypical to you can choose a length scale that is on the micrometer range, you have very light particles, very strong charge and so it's a different regime from the one that can be probed in atomic systems and you will have not only these electrons but you have a whole bunch of quasi particles available that you can in principle, these can be electrons that have an intrinsic spin orbit coupling, these can be particles that are in a quantum whole system and carry a flux, it can be particles that have a very strange dispersion relation if you put them in an unusual band and so you get a new zoo of particles to play with in this creating a periodic structure in which they are trapped and in which you can study their interaction hopefully, so the thank you and but what we have to see is whether we can trap any of them at all and I think this is all that I will be able to talk about now the basic idea is that we shine in a surface acoustic wave that oscillates rapidly, thanks a lot, thank you very much and so let's talk about electrons for the moment, so there is an accompanying electromagnetic field that kind of accelerates the electrons back and forth and so at first idea is not why should they stop but the idea is actually the same as is used in trapdions but in a very different parameter regime that you try to do this so fast that the particle is too inert to follow and that it simply cannot decide anymore, it sits at the note of the electric field and cannot move from there as the field oscillates very rapidly and okay so something is really bad, I didn't know that PDFs could be so harmful okay I have to reboot it yes there is another copy actually on the stick but I can't open anything ah there is a computer I didn't know that okay so okay I think maybe I try to convey the idea without pictures and formulas so we have this so this is now we apply a periodic field or periodic potential to these particles and so that's the normal setting of the in which one can use the floquet formalism and in order to understand how the how these okay so you again use the dangerous one probably, could you use the file 3S without 2 because maybe there is something wrong with that can we open a different file? no because this is the I think the one that didn't work so this other one the lower one it's basically the same there is only the wave equation is not there yes to the conclusions yes okay I think I have to I don't know what I did wrong there is nothing bad in this file so what okay what we have is we have this the position of the so what I'm looking at is the position of the electron as it is exposed to this file to this field or this potential this will be maybe I should sketch things here our today here in this area the electron sits a surface acoustic wave passes which has a which comes with an oscillating potential we consider one standing sine wave and so we would have here and say W okay good can we could we go directly to the to this acoustic lattice but I don't want to take people's break away okay okay then go to the conclusions which are there and can I go back okay then I okay I'll try to I'll try to do this so we have a we have a standing a standing wave that is time dependence and spatial periodicity and that that's sort of the the coupling to this electron comes from the fact that there is an electric field that oscillates in this way and the range in which we want to work now is the one in which this is a large number so that this ponder emotive trapping works and if one and basically one can now do okay theory and go into the if okay if we have something like this a theorem quite close to the broad theorem holds so the solutions will be can be written as a product of one quasi energy that and a periodic solution and periodic solution will be a high speed solution will come will oscillate with this so this is the time scale we are not interested in we kind of want to average this out and we are interested in these quasi energies and that's what we are what we are looking for so we would like to obtain the effective time independent Hamiltonian by sort of considering slower slower time scales than the one than the one given here and if one if certain conditions hold like for example that this square is smaller than one and that this is large and that this here is not is not too strong one can okay well one can obtain an effective effective time independent potential that is that is just a sine square one can I've written our classical equations of motion one can do the same thing using a Hamiltonian going in a rotating system and expanding the effective Hamiltonian and different in terms of omega over one and then keeping the lowest terms and then one gets exactly the same thing one gets a sine square quantum potential and d square divided by 2m kinetic term and so and now okay what we want now what one has to study is when does this separation of time scales really work and I think I will only try to sort of convey the numbers that become important here so here there is the mass of the particle that is standing there there is the frequency and the k vector of the surface acoustic wave from this we get the speed of sound which is another important parameter and we actually see that we can get here for this effective potential some small number times so if I'm now looking at a single site expand around the center of the site I get a harmonic potential with a particular trapping strength here where this ES is the kinetic energy this particle that we tried to trap would have if it were moving with the speed of sound of this wave and this number is kind of a very important material parameter that is governing these conditions that I'm putting here on the first slide that I can show again which so can I take two minutes or so which is sort of the chain of sufficient conditions that we've derived in the pages that are not shown in order to see that the particle is not only trapped but even if assuming that the particle is there is still suffering from dissipation it is still not heating up even though it is moving very fast due to this high speed driving it is moving with such a low amplitude that it is not heating up so this is the gamma is the dissipation and heating rate that we have to deal with and we need this dissipation to be slow compared to the correlation time of the bath in order to make the Markov assumption which is in there that's the first inequality the second is that we will create in the end from this here a trap that has a trap depth of or a trap frequency of that we call 0 so that's a slow trapping frequency of course this frequency should still be large compared to the temperature that we work at otherwise we will not be able to the total ground state so second inequality third inequality is that of course this frequency should be very slow compared to the driving frequency in order for our separation of time scales to work and for this potential to apply and so they can neglect all the higher order terms and finally that's sort of the constraint that will if this large frequency would not still correspond to an energy small compared to this kinetic energy here then the particle would just move too quickly and we would not have a single bound state in the potential that we create this way and so we have a pretty tough number of constraints and I will not go through the numbers that I'm estimating here for a typical gallium arsenide system just to say that all these inequalities can be nicely satisfied if we find a system that in which this ES is on the order of 100 microeV and so now comes the first dollar is that in our favorite system of gallium arsenide this is unrealistic so their speed of sound is too slow the electrons are very light for electrons in gallium arsenide it will not work this way but there are of course ways around this so we have to look for materials and for particles which have a larger mass a larger speed of sound this can be done both by looking at materials or by building heterostructures in which we can enhance the speed of sound and we have here investigated a number of options where you see that this important figure of merit can reach up to several thousand but one has to admit none of except for the silicon and the gallium arsenide none of these are sort of routinely used materials so these are 2D materials these are holes in gallium nitride and so on so I think I'm so we looked at what kind of quantum simulation for how that model this would allow but I will not be able to you can get numbers that are these are all microeV energies so you can get in the range where you have particles that are deeply trapped in this 1 or 2D array and interact with where the tunneling strength can be comparable to the onsite interaction and so it might be an approach to studying well-controlled, tunable, movable many-body quantum systems that can then also be moved next to a single quantum dot or quantum point contact which would allow you to read out probably a single side resolution these structures so I apologize for not showing you the slides that I wanted to show I don't know what went wrong but the summary I want to say is that these surface acoustic waves I think provide well I mean a versatile and promising new tool in the toolbox of semiconductor quantum information processing even in gallium arsenide you can couple strongly to spin qubits and you're in principle capable of doing high cooperativity cavity QED type experiments and classical strong classical fields would be able to trap move and couple qubits electron spins in sufficiently engineered materials or heavier particles like trions like excitons or even in gallium arsenide if you apply a strong magnetic field maybe I say this as last you make these particles in principle the particles of the quantum hole effect are in principle infinitely heavy particles so they have a flat dispersion relation and those can be trapped in gallium arsenide at the fields of futep tesla no problem with this approach so that's all I want to say here I thank my co-workers again and I thank you for your patience and your attention