 old faces and to share some of the projects we've been doing on this also together in collaboration with Joachim's group. So it's really been a lot of fun and some things are coming up now that are new. And I'll be hopefully spending a little time talking about the outlook and less on older stuff. So let's see, does it have the range? Nope. Okay, so nope, yes, slow. Okay, so the group does a bunch of things, fabrication of devices. We also have optics and atomic ensemble experiments. In general, we work on quantum optics and electric circuits, which is sort of a motif in this meeting. So it's really great to see sort of a sub-community emerging of more fundamental research along with the sort of applied quantum computing effort, which is ongoing. We've been studying also coupling to atomic systems similar to TLSs, also some hybrid, more explicit hybrid projects. And in general, I'll be talking mostly today about this sort of multimode photonics approach, which is an extension of the quantum optics scenario. And because time always runs out, I want to say a special thank you to all the people who really do the work. And it's really inspiring to have a small but very, very dedicated group of people who really, you know, they spend the extra hours in the lab and doing the simulations and really thinking about what's going on to get things understood. And there's also, of course, the broader perspective of friends and collaborators and funding, which we gratefully acknowledge. So because time is short, I'm going to just jump in and talk about what is the motivation of this particular line of projects. And it's the story of photonics and optics. They have a very long tradition of routing both fundamental and applied photonics down to the single photon level and turning this very technical capability into both basic and applied research and the beauty of photonics and mode shaping and space and time is part of what is really lovely in optics. But for microwaves, we have superior on-demand capabilities, much better than the optics. And we can design our circuits. We have more engineering freedom than they do. Our sources are relatively more stable in terms of the classical phase noise of microwaves and intensity noise, especially as something that the laser people can just look at in awe. But we have a problem, which is the problem of scalability. And that has to do with some very basic, the very basic and trivial issue with the wavelength of microwaves in free space is about 100,000 times longer than that of light. And when you try to put that on a chip, it just doesn't, not that many modes fit. So you can sort of like wrap things around and you can lump element them. But in the end, if you want to do these sort of photonics propagation itinerant traveling wave stuff, you just don't have that much room on a chip. And unless you want to go really bulky, sort of like the Yale attitude of these huge, insane arrays of, well, they're not insane because they work, but it's really, I admire that sort of direction of these sort of scalable, very low temperature arrays of cavities. It's very interesting and we'll see how that emerges, but extraordinarily difficult. So we want to talk about high kinetic inductance and microstrips as a combination which can really help achieve some interesting things in this direction. And we already saw in the talk a very nice introduction of the idea of kinetic inductance as a useful non-linearity and actually linearity starting from it. Well, I'm going to spend a little time on the basic physics of it because it's just fun to look at. And it's something that somehow for sure solid-state physicists don't always recognize its importance. And I think it's emerging also, especially in 2D materials, the concepts of how microwaves couple into these things and kinetic inductance as a critical element of describing them and the wave functions of the electrons confined to that extreme make it also interesting. So the standard description of kinetic inductance has to do with the fact that we usually ignore when we talk about the Hamiltonian and talk about the pre-factor of current squared, we talk about the magnetic energy as the dominant representation of that aspect of the Hamiltonian. And that's because it's at least 12 orders of magnitude dominating over the kinetic energy of the charge carriers in almost any normal scenario except in plasmonics and in the superconducting amorphous materials I'll be talking about and we already heard about some. So those are two extremes of nature in which kinetic inductance can actually dominate and it can be even 100 or 1000 times larger than the magnetic energy. And mathematically it's very, very simple. We're just talking about here the linear approximation of current as some sort of average velocity, drift velocity, multiplying a charge density and a mass and you get an expression when you lump it all together which has a kinetic inductance term which could be contrasted with the magnetic B field inductance. And this can be compactly lumped into being proportional to geometric terms L the length of the wire and A, sorry it's not marked here but L is the length of this wire and A is its cross-section and we have here a material property which is just the London depth of the superconductor. And why does this work in superconductors? Because we've basically swept away the resistance and in order to make this significant effect we actually have to work with nanostructures in which L over A or especially A is small so these like nanowires just like we saw in the previous talk but also really lousy conductors in terms of amorphous materials where the effective carrier density is very low and that by being one over raises up the kinetic inductance. And there's also a nonlinearity so let's call this kinetic inductance to have some sort of linear low current sort of linear limit but then there's a quadratic correction which gives us an interesting nonlinearity, interesting and useful nonlinearity. So yeah if someone can move that window away that would be helpful thank you. Great thanks. So here for example is an experiment you just do on a resonator and you measure it's you know as a function of power and you see this sort of duffing like softening and even if you go even higher bifurcation of the response of that resonator. And if you want to ask where this nonlinearity coming from I won't spend too much time on it and there's sort of like a Ginsburg-Landau intuition and actually if anyone's aware of a more in depth BCS calculation I'd be happy to see it it's kind of hard to track down there's a lot of perturbative stuff but when you go to higher power approaching the critical currents to really track down the nonlinearity and the low temperature limit is a little fishy. There's analogies to Josephson junction arrays which are of course relevant but again those are a limited validity. So I'd be curious to see a lumped element calculation if anyone has it I'd like to know so please approach me in the break if you know of it. And the short version of this explaining this nonlinearity is that high currents, high relative to or on order of the critical currents suppress the gap. You suppress the gap that reduces the superfluid charge carrier density and if you insist on having the same current that means they have to move faster. In order to achieve the same current with a lower carrier density you have to move faster i.e. more kinetic energy, kinetic inductance is appropriately boosted by this nonlinearity so this I0 is going to be on order of the critical current of the actual wire so in typical regular rectangular wires it's usually a factor of three of the critical current. Again being a perturbative term you can of course drive more current than the actual critical current. And this gives rise to the sort of nonlinear wave equation where the inductance depends on the current and that of course gives the possibility of wave mixing phenomena so initially we started out by looking at four wave mixing where you have a strong pump and a signal which is added to a weak signal will get amplified by the four wave mixing phenomena of course you need phase matching and all the machinery of quantum optics again in a classical nonlinear wave but we're hoping to reach single photon noise limits and there's obviously an idler which is being created by these sort of parametric activity with this sort of dispersion. And the popular implementations by far are Josephson Junction arrays and the so-called Tupas and the significant disadvantage aside from having a huge advantage of actually working and being relatively low loss you have to say something about a disadvantage of being scientists and always looking for something new and being critical people so we have to say what's wrong with them and that was mentioned in the previous talk is the low dynamic range. On order of a few tens of photons going through these things they start saturating and behaving in all kinds of strange and also heating up in modes and it's not a regime you want to go to if you value your qubits. Kinetic inductance and nonlinearities have sort of an engineering limit of being very very impedance mismatched and it's related to the Josephson Junctions but the Josephson Junctions are sort of lumped element and it's kind of easier to deal with them and the kinetic inductance is more of an intrinsic element and it's a bit harder to get a 50 ohm transmission line out of this thing and some attempts were made with coplanar waveguides and just to remind you of especially the theorists in the audience is that when you have any sort of transmission line you talk about a typical impedance which is the square root of the ratio of the inductance per unit length that's the little L here and capacitance per unit length that sort of ratio gives you a typical impedance and our electronics for relatively fundamental reasons is 50 ohms it's sort of an interesting compromise of the impedance of the vacuum and dielectrics and it's an interesting story but 50 ohms is a standard electronics that's what we're coming in with that's what the hemp amplifiers want to see and not having that in these traces is going to be very problematic and for the kinetic inductance amplifiers this is barely feasible to get enough capacitance to make this close to 50 ohms actually it typically fails and what you do is you do these clopsin steam tapers in order to transition adiabatically within a certain bandwidth to much higher impedances and that actually significantly extends these amplifiers to be chips of a few centimeters with lots and lots of coils and a lot of microwave engineering there's all interesting fractal capacitance work that was done in various places also in Chalmers and these are barely feasible it's just very hard to accumulate the proper parameters for this and you get these highly rippled gain curves because of this and we went for something which in the end it's sort of obvious but it has this elegance to it the idea of having this kinetic inductance trace but a very very narrow dielectric gap to a ground gives you a huge capacitance per unit length and we're talking about something quite extreme so this dielectric is just going to be a few nanometers sometimes we even go down to 10 nanometer barriers over centimeters of trace so it's a regime which experimentalists are a little less familiar with because usually you don't have that smaller gap we talk about hundreds of nanometers of dielectric that's a more comfortable regime and we need this because we want a very large capacitance and that's what's going to give us the interesting 50 ohm response of the device now there's another bonus to this is that we get a very very slow phase velocity it's shockingly slow in the sense that the phase velocity is one over the square root of the multiplication of L and C just like a resonant term with per unit length it becomes a velocity and here we have something which is 300 or even more times slower than the speed of light that's a huge effective index of refraction it's not a group velocity it's actual phase velocity and that's an interesting behavior and now going to the non-linear wave equations this is kind of standard envelope equations with the non-linearity added perturbatively you make assumptions of the usual undepleted strong pump you define the phase matching mismatch and the parameters of this sort of non-linearity scaling function and here it's a four wave mixing process and you get these are just classical amplitudes which of course transition into operators with the standard notation so and you see here these are the usual parametric processes with the pump again as a classical amplitude and these idler and signal as quantum operators and the fabrication is relatively simple you start out with silicon you grow this here we're working with amorphous tungsten silicide so this is a sputter target that you order with the proper stoichiometry and you sputter it after optimizing the conditions and the nice thing about adding this aluminum layer here we add the ground on top so it caps and protects everything and it also allows you to have really good launchers because one of the things you realize with these materials that they're kind of thin and nasty and again the experimentalists are nodding because they know what I'm talking about and having this nice aluminum tungsten sort of interface and launching into that and then going into the material is pleasant and we do this one tone how much time do I have? where are we standing? okay that's great that's where we want to be so we do a one tone experiment and we see immediately that we have serious dielectric issues here and that's going to plague us and that's something that will remain till the end that the transmission actually becomes pretty smooth relatively smooth this is after we impedance match everything so there's some rippling but it's not horrible indicating that centimeters of this wrapped transmission line on a 6mm chip are pretty close to 50 ohms but you see that at low power there's significant absorption and that's coming from the amorphous silicon that we deposit so amorphous silicon is a pretty good dielectric but it absorbs and it's TLS is in the dielectric and again we're looking for better dielectrics and the critical current of the wire is in the few tens of microamps that's a nice place to be if you want it to be a weakly non-linear system and we get a huge linear phase going through this device because of the slow phase velocity and a significant non-linear phase which accumulates because of the pump and this is sort of a conclusion slide in the sense that we see that it amplifies on order of 20 something dB and it's a pretty good amplifier even with the loss so it overcomes the loss which is a trivial, uninteresting TLS loss it overcomes that partially because the pump is sitting right there in the middle has a huge power broadening and it's saturating these TLSs we can talk about the heating effects that causes but as a linear amplifier this behaves quite nicely and we end up with a very respectable and broadband and relatively smooth gain of this amplifier it has a nice dynamic range and if you think about how many photons you're sending through so here we're scanning something like 50 dB from the single photon in the wire at any given time out to many photons and it responds quite linearly and here using a signal to noise backtracking technique we can estimate the noise temperature and because of the standard uncertainties of a few dB in the amplification chain we have a relatively large uncertainty in the effect of noise we didn't go beyond that with single photon source measurements of the noise but it's a respectable low temperature amplifier with just a few photon or even close to single photon noise added in a relatively large bandwidth and I mentioned dielectric loss I'm gonna jump over this and this we sort of optimized for it you know it's in terms of you have like a trade-off of length versus non-linearity and it all adds up and then you wanna be here so we thought about loss characterized it and optimized accordingly but let's go multi-mode and this is when we approached Joachim and started asking what can we do together in terms of more complex structures because this is a platform it's a photonics platform let's just put the numbers out there the wavelength is 200 in the extreme case the wavelength is 200 microns at 5 gigahertz that's sure you can put a lot of those inside a usual chip so let's do that so wait I skipped over something I think well maybe not so here for example are these sort of devices we have a bunch of ports going in and I'm gonna be talking about two kinds of traces because what we wanna do is we wanna have basically a linear trace with a very slow phase velocity and short wavelength going through so these are like the broader green curves here and then we wanna add these we call them inductive couplers super inductance but it's a large inductance very impedance matched coupling between these 50-ohm traces so we're gonna call these couplers and those we're gonna call waveguides so it's just a name in the end it's the same material same fabrication just you cut it down here to a few hundred nanometers and here it's say three microns so there's that difference both in capacitance and in inductance make these say just an appropriate mismatch so the main flow is along the waveguides and there's these periodic couplings wherever we wanna put them along the trace and we're gonna be talking about three sort of devices we made with this sort of strategy so the simplest one is just let's call it a hybrid coupler or a two rail system in which you have two input ports and two output ports and coupling periodically placed along the trace and then we went to something more complex with seven coupled arrays and we couldn't resist and we made something also resonant as well something with resonant mode so here this actually if you tilt it and distort is actually a square lattice we have to think about it for a bit what's going on but in the end if you look how many neighbors does each one have that's a square lattice sorry so I'm gonna rush through the results it's in our paper from a while ago in journal physics so here's the coupled waveguides when you look at it with low power so again just as a linear element so it's a remarkably compact hybrid you know if you guys know the microwave element called a hybrid it's this so it's you couple in and there was really a beautiful description that the Ulma guys and all of them put together of symmetric and anti-symmetric modes and the dispersion relation of this multimode structure to describe how the waves propagate and it just works you measure the transmission so the ones without the prime are the inputs the primed ones are the outputs so you measure what goes from one to one prime and you calculate it and even the subtle everything here it all matches really very very nicely and if you go to higher power you start to see it's a transmission amplitude here it's actual I should check that that seems a lot I'm gonna check that that's an extreme number here I should check that it's a little weird I'm gonna get back to you on that okay so if you go to higher power and you start saturating actually the interesting thing is you saturate the the couplers whereas in photonics they usually saturate on-site interaction here we're saturating the couplers so it's an interesting non-linearity theoretically just looking at the seven coupled waveguides we see more complicated transmission patterns again you say injecting in four and looking injecting in four and looking what comes out and then looking at all the related traces we see these oscillations which initially you wanna understand what they are but if you let's just skip ahead so this is just a coherent walk system which the photonics guys have done years ago but now we have it also in microwaves so you inject here and actually this is what's happening along the position a few millimeters and it's doing these coherent back and forth of course nothing quantum here yet but if you start pushing the power and checking exactly what's going on you see that because the couplers are small structures we have significant non-linearity at the level of few tens or maybe a hundred photons so we can push on that a little and go down to potential single photon levels with I guess less pain than the photonics people than the optics and then looking at the lattice of this square lattice we can really see so I get confused I guess this is the data and that's the simulation and again just calibrate the behavior of the traces and then just simulate it from just a simple tight binding model and it really works and it's very nice to see that you can get this complicated structure and each one of these resonances has a duffing like response which is non-linear I'm going to skip over this propagation movie it's a nice simulation of how the multimode states evolve and walk inside this lattice but I want to show you something so this is work in progress I promised I'd show you some new stuff so this is unpublished and we're inspired by work that was done of course in traveling wave parametric amplifiers and published recently but also things with kinetic inductance and in general parametric amplification and Kazimir effects also from Chalmers and even going back to say older history stuff is measurements by the Wellef group of quadratures so the project is to do broadband itinerant two-mode squeezing so that's the bottom line and just reminding everyone that we have these sort of quadratures the I and Q which are you know the combination of creation annihilation operators in the single-mode representation and there's just standard uncertainty relations because it's an electric field and you have a resonant parametric amplifier that's what I showed you earlier and you can operate it in degenerate mode where you look at say half the frequency or you can look at off-resume signal idlers this is what I showed you earlier and actually from the quantum sense they should be squeezed and two minutes away so three-mode mixing is actually a more a better way to work because you have less background so you push the pump you have to add a DC bias but it works and for example classically characterizing this amplifier we get almost 60 dB of contrast between the stretched and the squeezed mode and that's kind of a world record for these things and if you start looking at single-mode and measure the I and Q of an ensemble then you see this nice squeezing and this of course is measured through a hemp amplifier chain so it's convoluted with noise but you see that like the blue stretched one is not significantly expanded actually it shouldn't be much narrow because there's the hemp width it should be very slightly narrower just a few percent so that's all the hard work of measuring a lot of data and very carefully fitting everything in order to check if it's really squeezed so in order to measure these wideband correlations there's a nice trick because it's exactly half the frequency you can use these nice room temperature frequency dividers this is for the experimentalist and then you can just with one IQ mixer 200 megahertz of bandwidth of squeezing just by doing Fourier transform on the heterodyne signal so you don't have to measure just one or two now of course if you want to go broader you need a faster acquisition card but at one gigasample you can see a nice bandwidth of squeezing and simultaneously over many modes and this is the raw data you know so here it's well it's clipped and this is the I plus and the I minus plus and minus are just signal and idler you know the plus frequency and the minus frequency around half the pump and so each mode is just thermal noise but the correlations are strong and in order to see this sort of squeezing the hemp amplifier adds about 30 photons of noise so it's a huge amount of squeezing to see it on a 30 photon smearing but there's a lot of squeezing going on here and so again because time is running out you have to really carefully calibrate everything you have to check you've overcome all the biases there's IQ asymmetries absorption asymmetries phase noise all kinds of drifts and again there's a nice quote Andreas posted that if theorists want to sound smart and impress their experimentalist friends they should ask them have you calibrated your IQ mixers and the answer is always not enough even if it's a commercial system with automatic aberrations we're never happy there's always more to do there okay there's beautiful tests for Gaussian states the Simon's theory of partially transposed modes and just to get to the bottom line we see even with very very conservative error bars including all systematics and having tested this for months and thermal scans we're convinced we see a very large multi-mode, two-mode squeeze state with at least 7 or 8 dB of squeezing and actually it's much more but we're limited we're being conservative in that statement and this is sort of like a correlation matrix so again skipping to the end it's a platform for collaborative sources, couplers and interactions it's an exciting time for microwave photonics and integration with single photon sources is definitely interesting it might open up again options for interesting hybrid systems because of its small dimensions the capacitance can be more effective inductance again there are interesting trade-offs you can think of it as sort of like an impedance transform to atomic systems better than before and the open issues are again these dielectrics, what's going on with quasi-particles and heating in these systems higher order harmonics, non-local effects, there's a lot to talk about and a lot more to do and thank you for your attention, sorry for stealing some of the coffee time thank you Nadev, we have no time for questions Yuan hi, great, thanks this is very interesting try how do you know that it's the dielectric loss, have you checked that's limiting you have I mean I think it's very likely true but have you checked the Q factor of resonators without the ground so because time was short we have a paper in which we just measured coplanar resonant structures and we saw Qs of 100,000 there and that is easily limited by surface preparation of our silicon and some residual stuff there and this was like with the dumbest process possible, you know you do a wet edge and you still get a Q of 300,000 low power, single photon level Q's, intrinsic Q's of 300,000, 150,000 depends on the frequency, we made a really long resonator so we were able to measure multi-mode starting from 170 megahertz all the way out to 5 gigahertz so we got a whole slew of these to measure their Q factor and that was and that convinced us the materials intrinsically pretty good and it was completely comparable with the same aluminum process, we made the same chip with the same physical design of aluminum and it had a different frequencies because of no kinetic inductance in the aluminum but the losses were about the same at the same frequency so again it's the material itself is pretty good I think we have a question in the chat, repeat it so from Thomas Ramos the question is in the setup with coupled microwave wave guides what are the possibilities to couple single photon non-linearities like two level systems so right now the two level systems fabricated two level systems like qubits are a natural implementation to couple into them but maybe atomic systems we'd still need some sort of resonant enhancement just running through the numbers it's still not enough to reach the limit in which photons travel through and you get enough of a field from a single photon to talk to a two level system at that level but with a resonant enhancement we think we can do very nice atomic system couplings we have some preliminary work with actually with all kinds of deposition of cold gases cold crystals growing on the substrate trying to couple them to these wave guides but nothing to show yet the numbers are interesting and different from what's been tried before as far as I know at some point you said that in the photonic devices you could reach the quantum limit I understand well that you can reach the quantum limit even with those electric losses yeah so that's a very important point you're saying wait you're losing all this stuff how can you still be quantum squeezed et cetera interesting because these are Gaussian states and things are being created along the propagation Gaussian states are more robust to loss and along with the fact that the states are not being created at the beginning but also at the end of the wave guide you can get enough squeezing for it to work so you can run through and actually we depreciate some theoretical support on these correlations of both multi-mode and lossy non-linearities et cetera to try and estimate what's the limit of squeezing we can achieve there so the experiments were sort of drove us to a low frequency regime where the losses are less impressive and we think that's ultimately what limits are squeezing you know if you had the classical squeezing of 60 dB 60 dB relative squeezing between the quadratures you should get that much quantum mechanically if it's quantum limited on order of so the losses are bringing it down significantly but hopefully we can push on that and better dielectrics are always something useful okay thank you very much for the very nice talk and for the question session yeah so thanks again I think it's now I think it's now time for coffee break and we should come back at