 Do we have a pointer? Oh yeah, that should work there. The button is going forward. Okay, so it has a funny color, but it works. Okay, let's go with the funny. It can be seen from Zoom as well. Okay. You have the floor please. Alright, let me just... Alright, so good morning everyone. I'd like to thank the organizer for letting me do this talk instead of Max of Fines, who was originally invited but couldn't make it unfortunately, and with whom I work at the University of Sherbrooke at the Institute of Quantity. So I'm going to talk about voltage bias Josephson junction again, and I'm going to focus on the results we add on two different devices using this. So mainly it would be an amplifier and a photo multiplier that can be used as a photo detector, both based on this so that it could be prepared internally. So first I'd like to acknowledge the people who really did this work because I just started my postdoc with Max, so most of the work has been done by the ESPHG students in Grenoble and more recently in Sherbrooke by Joelle Grissmar and Ulrich Martel who is a master student. We also had a nice collaboration with Joelle Pagan-Gas for the description of the photo multiplication. So I first described quite quickly the concept we already talked about quite a lot this week and basically we're using Josephson junctions and we all know Josephson junctions. Usually if you want to make current devices such as a qubit, that is basically just an harmonic system, you will use the Josephson junction in a zero-voltage state where you can take advantage of this bearing potential to realize your two-level system. But if you increase the current inside the system and even when you go above the critical current of the Josephson junction you will be in a place where a voltage will start to develop around the Josephson junction. Then you will start to lose your currents for your system and something you don't really want in devices such as qubits. I really like this picture to describe this phenomena. If you think about the Josephson junction that is residing on this flat earth picture you can think about the horizontal axis as the current and when the phase particle that is the junction goes above the critical current it falls inside this monster of instant currents. So when the junction is in this voltage state we don't have this interesting current behavior but we have other interesting things. So as we already discussed and especially on Wednesday morning if we look at the IV characteristic of a single Josephson junction biased in voltage well we do not see anything in this voltage state but there is still the presence of an AC excitation which is mainly the AC-JSN effect and if we add an environment in this system then we start to have interesting phenomenon happening. Usually when the voltage the voltage bias will be chosen so that the Josephson energy the Josephson frequency sorry is chosen so that the real part of the impedance of the environment is non-zero then we'll have inelastic Cooper path to learning for the junction and we'll have the apparition of a DC current inside the system that we can measure basically the power is going through from the Josephson junction to the environment and can think about that as dissipation another way to see that and it was already described on Wednesday again we need to think about it as a Cooper pair that has additional energy because of this voltage bias and can tunnel through the junction because there is no states in front of that and when you add an environment you add a channel for this energy to be dissipated and then the Cooper pair can tunnel through the Josephson junction by emitting a following at this particular frequency the signature of this phenomenon those bumps in the IV characteristics it has been measured in 1994 and more recently in an experiment by Max Ofain we have Fabien Portier in SACLE an experiment that was already mentioned by Denis Villon on Wednesday morning when they did the same setup it's basically the Josephson junction coupled to a Coplanar waveguide resonator that acts as a single mode or multi-mode environment we were resonating more at 6 GHz they will have been able to measure the current quite precisely going through the DC current going through the junction and the number of photons that were coming out of the system what they measured is here on the right is the rates in red Cooper pair tunneling through the junction and in blue the rates of photons being emitted and they showed that these rates were non-zero where the impedance of the environment was non-zero as expected the interesting thing here is that the rate of Cooper pair and the rate of photons are exactly equal that means a Cooper pair of energy 2 EV will produce one photon of the current another thing they saw and it was a bit more interesting was at the voltage bias that it was twice the value for this original peak and they also saw photons being emitted at 6 GHz with these voltage bias that means the Cooper pair gives rise to two photons inside the environment so more generally speaking if we have a Josephson junction we can generate for example in the form of the color and get the composition for resonator we can create a Cooper pair tunneling through the junction will create an ensemble of photons and the rates of tunneling for the Cooper pair will be it will depend on the Josephson energy but also on this delta function and the Cooper pair can tunnel only if the sum of the energy in the system is zero and that means that the energy 2 EV has to be divided inside several photons inside the different modes of the environment if we look at just two modes inside the environment we can go a bit further inside in this description and look at all these photons will be created and we end up with those amplitude here the mn of k that are described here is the coefficient alpha k that is basically just the reduced impedance of the mode so the impedance of the mode divided by the superconducting quantum resistance describes just the coupling of the mode with the junction so we see that in an experimental for an experimental system this is quite interesting because we have two different variables that control this process one is the value of the impedance of the environment and this we can control as much as we want and the other one is the voltage that we apply to the junction and again this variable can be controlled quite precisely and this makes this full platform really interesting for experimental devices so using this platform we talked on Wednesday we talked about using this to create sources to create photons and a high number of photons you can also use these systems if you add inside your environment alongside your single resonating mode you can add a capacitive term in the form here for LCS circuit you will then prevent subsequent tunneling of group repairs because of discharging energy and then you will end up with a single photon generating device something that was measured by max and the group of that with max a few years ago in the opposite scenario if you have two modes inside your environment you can show that if you bias your junction so that the energy is equal to one photon in each of the modes you will have pairs of photons that have non-classical properties and that was again shown in the work of Fabien and Amboise Peau, his PhD student in SACLE the measurement side of things kind of so basically we are making two devices at the moment one is an amplifier and the other one is a photomultiplier I will start by describing the result we have on the amplifier and then we go to the photomultiplier and hopefully I will have enough time to describe both of them so in the case of the amplifier we have again two different resonating modes inside our environment and we bias our junction so that we can spontaneously create a photon inside one of each mode but this time we also send an incoming signal that we want to amplify and basically this is going to trigger simulated emission inside the system and we can consider this device as a parametric amplifier and that means that theoretically we can achieve continuous limited amplification so our measurement setup is going to be here and the device is over there with the Josephson junction as a form of a squid so we can control the Josephson energy and a Coplanar waveguide resonator that is around 6 GHz that is the same device as I talked a bit in the beginning of the talk and we can measure this device using homodyne detection using a VNA or we can measure the noise of the system using power spectral density measurements at the same time we apply a voltage bias to achieve these processes so what I am showing here is one of those measurements so here we have this device and we apply no input signal so we are just looking at the spontaneous emission of the device add a function of the voltage bias we apply so we are measuring the power spectral density between 4 and 8 GHz to increase the voltage bias well we can see here we can see different things we see this line at the bottom that is basically the Josephson frequency of the junction that means we are emitting photons inside the environment and when this line crosses the resonant frequency of the environment around 6 GHz we see interesting things start happening so basically here the bias equals exactly the resonant frequency we have the emission of one photon each time it could be compared to next through the junction but if we increase this bias by a factor of 2 we see we can achieve the generation of 2 photons inside this mode and if we increase it even higher so this time at 4 times the original value for the bias we have other things happening and we start to excite one photon inside the fundamental mode of the Coplandi wave resonator and one photon in the third mode the third harmonic of the environment and we can go even higher to the fifth harmonic and so on but we stopped at 45 GHz for experimental practical reasons if we take the same device and we now send an incoming signal that we want to amplify and this is what we see here in this color plot we've in red the gain that is positive and in blue the gain negative so losses and we have the same kind of lines for the gains for the same processes as described just before the one photon process the two photon process and the two photons in two different modes process and those processes are associated with gain we have an amplifier that provides gain at those points the gain can go up to 10 dB for this particular device but what we also see in this graph is those blue lines we count those as losses but it's not really losses per se it's just frequency conversion means that at those points the incoming photon energy corresponds to the Joseph Cooper pair energy to create a photon in one of the higher order harmonic mode if we look a bit more closely on those curves we take some cuts inside these 2D plots we can have those more classical curves where we see on the left the gain of the device as a function of frequency and on the right this is the noise of the device as a function of frequency so first thing on the left we can now measure the bandwidth of this amplification process it's the order of 100 MHz for this device but what is more interesting is those dash lines that we plotted here were calculated using a POV calculation for this device and we see why we do not have quantitative agreement the qualitative picture is quite close they're quite close together of course we know in those devices the Josephson energy is higher is quite high and we know we cannot really apply the POV theory so that's why they're not close together on the right here we have the added noise those noise added by the device are referred as the input of the device and we see that for the case of the blue line so this particular cut here we have a noise that is sitting at twice the value for these dash lines the dash line here represents the quantum limit for the device so the quantum limit of noise added at the input and we see that for this device at this working point we achieve something around two times the quantum limit which was pretty nice to see at the time and that was using one of the first devices Max ever made in Grenovo of course he tried to improve that in the past few years and quite recently we measured a new device that had quite more interesting performances and this device is summarized here in all those points so each of these points correspond to one working point so a set of voltage bias and frequency for a single device so for a single device we can choose where to work, which voltage to use which frequency to use, which process to target and this results in different performances for the amplification so the gain will be different the bandwidth will be different and the noise will be different this is all summarized on those two plots on the left you have the bandwidth of the amplification as a function and on the right we have the added noise divided by the quantum limit as a function of the gain so the first thing you can see is on the left here the maximum gain we can achieve is now around 25 dB which is more than twice the amount we had on the previous device and is more in line with what other amplification devices propose but for those high gain we see that the bandwidth is limited by 1 MHz and we feel limit ourselves to the 20 dB gain which is more the reference to compare amplifiers we have a bandwidth that is around 10 or 20 MHz if we look on the right now at the noise and again around the 20 dB mark we see that we have two working points that are really close to the quantum limit and in fact they are below 1.5 times the quantum limit so for these new devices we improve both the gain and the noise of the amplifier and we start to have really really nice performances really nice characteristics of course I have to compare our device with other devices and our device being DC powered I need to compare this device with the DC powered amplifier the first one being the Mth of course is widely used and the other two are two different propositions to use Josephson Junction to realize DC powered amplifier the first one is a superconducting low undulating galvanometer and the second one is a single Jackson amplifier if we compare all those to the Josephson parametric amplifier of course we have to compare ourselves to the Josephson parametric amplifier we can see that there is a main difference that is the power source the devices are using a DC bias that is their main advantages because it's easier to control and to implement a DC bias there is less components involved while the Josephson parametric amplifier use an RF pump if we look at the noise though we see that of course the Josephson parametric amplifier is still the best that we still have not beaten that result but we see our noise is now really close to the Josephson parametric amplifier and the noise level of our devices is way lower than what other DC powered amplifier are putting forward and we think this is the case because in our device we have a dedicated electromagnetic mode for the idler in this parametric amplification process so that will be all for the amplifier so as a quick summary we have a device that has noise below two times the quantum limit we have around 20 dB of gain I didn't really talk about it but the saturation power is our minus 125 dBm close to what Josephson parametric amplifier would have and our bandwidth would be between 10 and 100 MHz the main advantage as I said of those devices is that we don't need a microwave radio frequency pump of high power so one of the drawbacks is that we don't have a phase reference inside this voltage bias so that means the phase sensitive regime will not be accessible in those kind of devices as we make them so I will not talk about the other device we are making in Sherbrooke and that is a photomultiplier basically it can be the exact same chip as the amplifier but used slightly differently so now we are still using two different modes in the environment but we bias the junction so that the energy to EV plus an incoming photon will be equal to the energy of several output photons in the blue mode here this is basically frequency conversion and if we choose the parameters correctly theoretically we should not have any spontaneous emission but we see we do have some still because the value to EV here is not equal to any of the modes in itself it needs the complementary energy from an incident photon to create several photons inside the output mode using the work of URI Pagangas we could characterize or calculate the Josephson energy that would be needed to have a perfect conversion in those process basically using input output description for the system you can show that for any characteristics for any frequency any bandwidth for the resonators and for any value of N where N is a multiplication factor you can find Josephson energy that would provide the system with perfect conversion efficiency meaning every photon that we come in the system would be converted this value again depends on those coefficient alpha so the reduced impedance of the modes and to have a low enough Josephson energy so we can manufacture the device we would like to have these those alpha to be higher to be close to one so the device I will show you the result on is the same actually as the last amplifier device and is basically again 2 resonating mode 2 LC resonating mode 1 at 5 gigahertz and 1 at 6 gigahertz because of manufacturing reasons the impedance of those modes was limited to below 500 ohm so the alpha coefficient is around 1.2 in this device so we we measure those device by sending us a weak incoming current signal and measuring what is going out of the device at the frequency of the output mode by doing so we can calculate the probability at the different probability of the system so either the probability of the photon being reflected at the entrance of the device or the probability of the photon being converted so here reflected is in blue and here reflected is in orange and we also have spurious processes that we don't really want to have but we still have because it's experimental realisation and there is the direct transmission of the incoming photon through the capacitance of the junction without being converted here it's in green and the the last spurious process we have here is the photon is converted then reflected inside the device so the frequency changes but it goes out from the wrong way from the input of the device so we see that here those probabilities are the function of the flux so as a function of the Josephson energy we see we have a certain value for the Josephson energy that enable us to have a perfect not a perfect conversion but to have a zero reflection inside the device at the same time we have conversion efficiency that reaches 75% and the other spurious processes are still quite have a quite low probability but at the same time we see that the total probability here in black is not equal to 1 is below 1 means we have losses inside our system somewhere we don't we don't know yet we don't understand really well or at least we didn't measure at that time the last information we have on this graph is this gray curve here and this gray curve is the dark rate so the emission of photons by the system when no input photon is sent to it that's a limiting factor in here for this particular working point where a dark rate of 410 megahertz theoretically we should have no dark rate but we still have some because that's an experimental realization and if we look at the same results but this time as a function of the input frequency we have the same kind of curves and we can measure the input bandwidth of the device that is around 100 megahertz again the input bandwidth is mainly fixed by the the width of the input resonator and here it was around 100 megahertz the maximum efficiency was 73% so this is I forgot to mention it was for the 1 to 2 photon conversion and we can now look at the same curves but for the 1 to 3 photon conversion so we have a slightly different voltage bias so that we achieve a different process and this time we don't have a reflection probability that goes to 0 it goes quite low for a certain value of EG but it doesn't go to 0 this time the value for the Josephson energy has to be higher because we are going to higher a number of photons being created as we discussed in some previous talks and we still have a conversion efficiency that is close to 75% exactly 75% and this time the dark rate in gray is way higher because we increase the Josephson energy so the other system can couple to more superior modes especially in low frequency modes and that generates a lot of unwanted photons because of that and this time it's around 400 MHz which is pretty high for this kind of device again if we look at the same curves at function of frequency we have again the same bandwidth and we have this maximum probability of 75% though we can look at what happens when we increase the input power so the number of photons we send to the device and of course after a certain number of photons at the input we will start to have a degradation of the other performance of our device this is what we see here and what is summarized in the inset where we plotted the conversion probability at 4.74 GHz that corresponds to the maximum of the resonator and we see that above minus 120 dBm we start to have a quick degradation of this conversion efficiency meaning we have a saturation power around that point this corresponds to around 6 photons in average in the input resonator which is not that high but for a photomultiplier that is aimed at very low power because you want basically to multiply a few number of photons but if you use an amplifier for that it's not such a problem and actually one of the usage we try to realize for using those devices is in the case of single photon detection basically if we take two of those devices and put them one after the other using a single mode as the input mode for the first stage we can have what we call a cascade photomultiplier basically one photon would be in the case of one-to-three conversion would be converted to three photons that would then be converted to nine photons and as soon as one of those photons is emitted inside the transmission line for further measurement and detection the reverse process cannot be achieved that means we can find as before a value of EG that we enable theoretically a perfect impedance matching and a perfect conversion from the one photon to the nine photon the two advantages of this system compared to other photo detectors using qubits for example is that this system is number resolving we can send several photons at the input and we get the same number multiplied by nine at the output as long as we stay below this saturation threshold I talked about before and for these kind of devices we don't have any dead time so with that I will conclude with one last information, one last advantage of such system is that the physics of these processes is valid up to the frequency corresponding to the gap of the superconductor for aluminium that means frequency up to around 100 gigahertz but if we switch to large gap superconductors such as niobium we can hope to use frequency that we go in the terriots regime that is basically what we are going to try to do in the following years lastly I mentioned that while we understand quite well what is happening we don't really have a good understanding of some strange processes and especially we observe some non-linear amplification where several input photons would be involved in the parametric amplification we don't really understand those processes and our description is based on the POD theory and input-output description so we like to get further than that if we want to have a very open system with large less energy with that thank you for your attention if you have any questions I will try to answer them as best as I can Thank you very much Nikola for the nice presentation I have a question which is maybe trivial but what actually limits your conversion rate the optimal point somehow is the point where there is no reflection so all the incoming signals are sucked by the system but it's apparently not converted to 100% so what limits the conversion? One of the first trivial answer would be as per use processes for example we have direct transmission through the capacitor for the junction it's something we are going to try to eliminate by reducing the size of the junction we add at one point some noise in the system that would also reduce the efficiency because you would kind of see an average around the peak of maximum conversion so you reduce your conversion efficiency we reduce that noise quite well but we still have a voltage noise on the voltage bias of course and you can see here the total probability is quite well below one so we still have volumes going somewhere else maybe in other frequencies for other processes or previous modes inside the environment that we still do not control perfectly things like that first part regarding the comparison with the POV theory I'm surprised that I would expect the opposite that essentially the width is not matching well whereas the height seems to be better I would expect the opposite because the width normally you know it better and then the height is related to the coupling so I would expect the opposite would happen so why is it a little wider I mean the POV theory it's a prediction I'm afraid I will not be able to answer this question I did not do the calculation myself all I know is they use the POV theory to calculate the admittance of the junction and they fit that inside the linear of circuits to calculate those gains we are not that far I would say from the applicability of the POV theory that you have some energy is not that it's higher than what it should be for the POV theory it's not that high we have other problems appearing at higher radiation energy as we saw in different talk there is some amplification problems and all that and we see we cannot use all devices in this high radiation energy regime okay thank you thank you just an experimental curiosity how do you measure the dark rates more specifically we just use these we measure the POV spectral density basically here it's on the boundary for 400 MHz we integrate all the energy basically to count the number of photons without any signal at the input okay it's just a spectrum analysis measurement but then you have 400 MHz bandwidth and 10 MHz dark rate right so you're like measuring a fraction of a fraction of a photon as PSD sorry I didn't really understand that because at one point whenever you measure your power you need to divide if you divide by the bandwidth you get an energy and if I so it gives you a very very small energy and you can still resolve that in your measurements I would say yes I didn't do the experiment but I would say yes the averages is on a quite long time with on-off measurements and all the calibration is quite well done for all those measurements okay thanks alright since there don't seem to be more questions let's thank Nikola again we'll have a coffee break