 Where we study optimum mechanics or quantum optimum mechanics and particularly I work on microwave optimum mechanics so we study radiation pressure effects in superconducting microwave circuits which consist of capacitor where top membrane can freely move so it's suspended and linear inductors. So canonical model for cavity of the mechanical system is a Fabry-Perot cavity where one mirror can actually move. And there are important effects so normally it's described by interaction Hamiltonian like this which means that displacement of mirror modulates frequency of the optical mode or electromagnetic mode. And then you get shift depending on the motion and you can derive radiation pressure force so force with which radiation inside the cavity pushes on the mirror. And what's important is that when you try to measure position of this mirror for example in a LIGO interferometer or something like this there is actually back action so the light pressure changes position of the mirror when you measure position of the mirror. It happens because optical field in the cavity responds to the motion of the mechanical element with some delay which depends on the cavity bandits this cap. So if you just write a equation for the mechanical motion for this mechanical oscillator and you have all the terms and the radiation pressure on the other side and then you do expanded you will see that there is modification to the damping rate to the mechanical damping rate which is caused by light field. It depends on the detuning if you have positive detuning of the laser from your resonance frequency you will amplify mechanical motion. If the detuning is negative you will damp it so it's analog to laser cooling so you can laser cool mechanical motion or you can laser amplify it. It was all derived by Braguinsky back in 1970 and also demonstrated even before that and it was actually studied in connection to LIGO interferometer similar very sensitive measurements systems. So we switch to frequency picture and a little bit transform our interaction Hamiltonian so what we do we just linearize it around mean field in the cavity. So we assume we have coherent state of the light in the cavity with NC and cavity photons and then we only look for fluctuations of the field delta is now a fluctuation of the field in the cavity around this mean field. We can see that when our detuning is negative so we pump around lower motion sideband so detuned by mechanical frequency from the cavity resonance we can get kind of beam speed Hamiltonian so we take phonons and convert them to fluctuations of the field in the cavity always version and of course if your cavity is cold and has on resonance no photons you take one one phonon put to the cavity then take next photon put to the cavity next one and one by one you remove phonons from your mechanical mode so you damp it it becomes wider here so you start from this curve you go to this curve if you now put here laser on the upper motion of sideband so it's blue detuned to higher frequency by mechanical frequency then your Hamiltonian can be linearized like this so we only take terms which are energy conserving that's why we only get these terms and not these terms in this case because those should be rotating and we apply rotating wave approximation so on the blue sideband what happens you amplify mechanical motion it becomes narrow because you create pairs of phonons and photons and then phonons stay and you build up coherently like large amplitude coherent phonon state there are multiple cavity of the mechanical systems with different masses and different principles like the steroids which we studied a lot or photonic crystal cavities which can be engineered quite well all this microwave systems I will talk about and there are many others you can read this review it's 70 pages review which it describes most of the quantum mechanics by 2014 and on the theory side you can basically derive everything in linear regime so when you can apply this linearization by just writing down quantum Langevin equations if you can write them and solve them with all the dissipation terms you can basically describe everything okay those small introduction fundamentals of quantum to mechanics and now I will speak about the following aspect so connection between of the mechanics and reservoir engineering so our system is a following we have mechanical oscillator this yellow circle we have microwave optical cavity she's this circle and we study phonons and fluctuations in the cavity and it's it's detuned and this cavity is connected to environment waveguide and you have dissipation from the mechanical mode somewhere with rates with a thermal decaherence rate gamma m and thermal so effective rate depends on the number of phonons in the cavity and principles demonstrated in trapped ions that if you have electromagnetic mode which is a cold dissipative bus for your system of interest you can prepare states of your systems in case of mechanical motion it was you can call it to the ground state or squeeze mechanical motion or in principle do something else by just controlling this coupling G between mechanical mode and optical mode and since we use linearized Hamiltonian this coupling G in linear regime depends on the number of photons it's some constant times square root of NC so by exchanging number of photons and change the tuning of your pump you can in principle prepare interesting states of mechanics and it was first demonstrated for ions or suggested by payata strachensolar back in 1996 there was many experiments and for the optomechanics it was again suggested by Cronwald Markerton-Clerk in 2013 and most of the experiments to date they were done in this regime and this regime can be characterized by two things that to make it work you need that decay rate from the electromagnetic mode kappa is much larger than decay rate from mechanical mode because what happens when you increase this coupling energy from this mode will decay through optical mode to the waveguide and not to the direct decay channel and now the question is but can we actually make mechanical resonator to be a bus or reservoir for light can we use same system to construct interesting states of light and yes but we just need to make kappa much smaller than gamma m let me go once again so in standard regime we have our interaction Hamiltonian linearized written like this where coupling strength is G not square root of NC and then for example we cool we just take phonons put to the optical mode and then they escape and one by one we can cool photons we do it faster than this rate we can cool down to the ground state blue detuned we create pairs of photons and phonons phonons stay photons go to the waveguide much faster than we create phonons and then we basically can amplify mechanical motion because phonons will keep the face of the state in the resonator it's all when it's kappa is much larger than gamma m but now we go to different regime kappa is much smaller than gamma m then modification to the mechanical decay rate I derived on second slide should become modification for electromagnetic decay rate and in principle the roll should be just reversed you should just now amplify microwave or optical mode our damp optical mode so we derive this modification you can see it indeed from this from the series you can calculate it should get modification of the mechanical damping rate when you pump around lower or higher emotional sideband around low sideband you damp around higher blue sideband you amplify and there should be associated change in the frequency of the electromagnetic mode so you should just pull electromagnetic mode somewhere by applying a pump and overall you can derive the response of the cavity measured in reflection with modification to the damping rate and modification to the frequency and yes you should amplify electromagnetic mode with mechanics so mechanics will be gain medium for electromagnetic mode so if we try to to describe this amplifier we can just write output field as a linear combination of all the input operators and we will see that even there is also event regimes so if mechanical frequency is much larger than than kappa then it should be phase preserving parametric amplifier according to description of caves back in 1982 it should feature this this gain and on zero on resonance you gain should be 1 plus C or 1 minus C where you see the cooperativity it just shows the relative or its dimensionless coupling strength its coupling strength squared divided over decay rates of mechanical electromagnetic mode and you see that if your cooperativity approaches unity you should go to unstable regime because your game is just just just david urges and then if you calculate the noise added by this amplifier you will see that it directly depends on the effective occupation of the mechanical oscillator so if you want to create a quantum limited amplifier which adds just one half of noise quantity again according to case then effective should be zero so if you can create a cold mechanical reservoir for microwave mode you should be able to realize a quantum limited microwave amplifier if you have questions you can probably ask now because then I will switch to implementation yes up to now the insignificant but if your coupling strength is high of course I mean in some regimes your counterattent term will become important but this usually you need large coupling strength or you pump with large number of photons but then there are other nonlinear effects which which kick in like you everything hits up you should get thermal shifts and so so for most of the physics up to now it's it's insignificant but there are cases when it can be significant especially we have extremely large coupling strength for single photons yes slow well basically you don't get because of this you don't get electromagnetic damping anymore you get mechanical damping for electromagnetic mode because your the time scales changed well till your your you can describe the mechanical mode as reasonably high q which means it's not Brownian motion it should be still Markovian I believe no it's it's it's no entanglement well I mean the only thing you can entangle is a fluctuations and a mirror position and for the for the for the mean field and you can only measure mean field usually so it's not relevant here so now the question is how can we realize this this scenario I mean if you want just to make this gamma m small well we can just make low q mechanical mode but then your your thermal decaherence rate will be huge because this will be large factor and and thermal is also large factor because mechanical frequency has it's it's quite low it's in megahertz range and then you won't get the cold reservoir it will be reservoir but it will have a lot of phonons and it essentially it will be useless so what we suggested that we can couple second mode with different decay rate kappa 2 which is much larger than kappa use the second mode to laser cool or sideband cool mechanical motion close to the ground state and also damp it and then use this combined mechanical mode or reservoir to operate the first narrow microwave mode so it looks like this we have white mode we apply cooling tone with cool mechanical motion and then we apply let's say blue pump around main mode and see amplification ideal and in principle our effective damping rate of mechanics can be described like this 2 is cooperative second mode and staying in linear regime you can make gamma effective almost kappa to half so it should be much larger than kappa and in principle it's possible to to realize well this is how we fabricate our samples so we deposit bottom electrode we pattern it we put sacrificial layer we try to smooth the sacrificial layer and then we do another lithography we create sidewalls then we deposit second electrode on top etch it and then do release and we get our structure is even multiple electrodes on the part of some sort and this process was inspired by process developed at NIST Boulder back in 2010 so how can we now implement important feature we need two microwave modes coupled to same mechanical motion and efficient different decay rates to the environment I'll probably speed up a little bit because time is not infinite so we consider this circuit which has one mechanical compliant capacitor three inductors and one planar capacitor we engineer these two parts to have same frequencies so to be degenerate even right in the interaction Hamiltonian it will be like this we have two modes coupled and one mode is coupled to mechanical motion these operators be even now that we then go to the normal modes of this circuit because they degenerate we'll get this Hamiltonian so the modes will split up and down and one mode will be white and one will be narrow and both will be coupled to mechanical motion and this white and narrow is easy to trace so one mode will have current circulated around this loop so it will be strongly coupled to the waveguide and the other one will have this figure 8 current so it goes up close up here and then left and right and so these two currents will cancel each other and that's why your mode will be dark so if we just derive it we write Hamiltonian we couple to the modes in the waveguide one mode second mode has coupling rates and then after we again transform to normal modes we'll see that coupling amplitudes will add or will be subtracted for different normal modes so one will be bright the other one can be dark if you ideally match these two halves then you should not see the dark mode so this is the schematic this is actually circuit it's planer capacitor this mechanically complained drama show it is very beginning so we implemented it we put it to switch this copper box and this copper box to a dilution refrigerator down here this all the circuitry we need to measure in in in reflection or in transmission but this one was measured basically in reflection and then we can detect linear response using vector network analyzer or just immediate spectrum using electron spectrum analyzer and we can apply control pumps and probes and then of course we we heavily filter to remove the noise because we want to cool our mechanics close to the ground state so noise can heat up the mechanics again so after we cool them the structure we can see two resonances one is broad one is very narrow so it's a bright and dark mode and here's the parameters we have two frequencies 4.3 and 5.4 gigahertz to copper 100 kilohertz and 4.4 megahertz so the ratio is very large it's it's it's 40 as we wanted and principle with these parameters we should be able to cool our mechanics to somewhat half a megahertz or damp half a megahertz width which is five times copper of the narrow mode so we should be able to realize our experiment and then we apply pump to the cooling mode we see that with damp mechanics it increases linearly and we can reach this half megahertz and like this we create close to Markovian dissipative base for electromagnetic mode so now we just try to test if really we are in this revert dissipation regime if if we can see the effects we predicted so we put cooling pump and fix it forever and then we sweep another pump around low emotional sideband simultaneously recording the linear response and from linear response we extract frequency and we do see that around red sideband we see this change in the frequency of the electromagnetic mode so we pump five megahertz away and we see that frequency changes on the blue sideband we see similar curve in good agreement with the series is blue lines that fits to this equation and if you look for the decay rates or the widths of the cavities we do see that on the red sideband with damp it becomes wider on the blue sideband it becomes narrower so we just try to trace the position of this point when we change the pump power so here we fix the pump at the red sideband and we just increase power what we see that our resin becomes shallower shallower and shallower which means that we were under coupled and we get positive modification by optomechanics and we just become more under coupled if you go to the blue sideband then we see that we become deeper instead so we become more and more so we closer to critically coupled then become shallower gain so we go to over coupled regime when external decay rate dominates or intrinsic decay rate with optomechanical correction because now correction is negative then we go to the regime when our curve is flat almost it's slightly fun but we basically uncoupled our cavity from the from the waveguide so we reach the regime where basically here we have zero that intrinsic decay rate plus optomechanical correction in total is around zero and above that point when we increase pump power we get net gain so we start amplifying and you go to the to the amplification regime so like this we demonstrate electromagnetic control over the cavity damping rate so by applying microwave signal we control properties of microwave cavity we can make it under coupled critically coupled over coupled or even amplified so basically on the blue sideband we just introduce negative damping rate into cavity mode which leads to parametric amplification so we start amplifying and by this we decrease the decay rate so that was this regime so now we just monitor the spectrum emitted when we increase pump on the blue sideband you see this line becomes narrow so we start amplifying noise in the cavity and at some point we reach threshold this horizontal line and after that we see extremely bright tone going out of the cavity and we don't move our pump we just see that it goes slightly to the red sideband to towards the red frequencies by few kilohertz and if we look for this magenta line below threshold we see this amplitude above we see this amplitude which is six orders of magnetic lodging so we go to cell sustained oscillation so it's kind of a lazy regime when we create so many photons that we get lazy and we can describe this so below threshold our line narrows towards zero at the threshold and after that we get amazing so it's a first observation of dynamical detection on electromagnetic mode so it's not only on mechanics you can get the action parametric instability but also on on microwave mode or virtually on any optical mode so what did we show in principle just analog to the optical Raman amplifier slash laser so if you have an optical waveguide just a cartoon with let's say simulated Raman scattering with a brilliant scattering and you have some phonons Raman or brilliant with this with this omega phonon you put signal and pump and if you pump is tuned to signal plus phonon what happens that pump generates signals signal photons the photons of signal frequency and phonons phonons decay quickly just work as an idler mode with this parametric amplifier they decay quickly within nanoseconds and then you amplify your signal and you lose your pump and this is a classical process you can just open nonlinear optics book by Blombergen and it's described what we did we created a microwave it's not propagating photons and phonons cavity based version of this Raman amplifier and if we actually look how this amplifier works we increase pump power we see we can change gain and our gain can go high with cooperativity in principle it can with this sample it was up to 13 dB power gain and with another sample it was up to 42 dB simultaneously our bandwidth decreases and if we consider amplitude gain times bandwidth product it stay fixed for us so no miracles but in principle for narrow gain we can reach for narrow bandwidth we can reach very high gains and the noise properties of this amplifier are the following so here we plot total noise emitted from the amplifier in this chain so we have our amplifier we have some cables and other devices before we have cryogenic high-electron mobility transistor amplifier and that we measured outside so we have total noise which is noise added by the by our device plus noise of the hemp divided over the gain of our device and a little bit corrected by this insertion loss and noise of hemp amplifier is around 22 quanta and noise of our device is described by this equation which takes into account extrinsic decay rate and so on and then we see that basically we add only few phonons overall taking into account hemp but at large gains we get just below two photons of noise and this dash line this quantum limit for our device which is 0.78 so our total system noise is around just twice larger than quantum limit which we can get in our device with this intrinsic decay rate and extrinsic decay rate so from this we can extract effective occupation of the mechanical mode and it's around 0.665 quanta so we are close to the ground state and in principle this laser or sideband cooled mechanical oscillator constitutes a quantum reservoir so you can use it to realize quantum devices or demonstrate quantum effects so let me conclude so we realize electromechanics in the reverse dissipation regime where dissipation of mechanical mode dominates over dissipation of electromagnetic mode we show control over electromagnetic cavity properties using this called dissipative reservoir we showed near quantum limited amplification of microwave field and we showed the major action so more generally we realized quantum dissipative mechanical reservoir for microwaves and this is prerequisite for new class of dissipative of the mechanical interactions so using this kind of reservoir you can realize other effects you can read about this result here it's now published also in paper version and thank you for your attention