 Marcus Contos and he will bring us to the dark side of physics With a talk that has a title a hybrid cavity transmitting Magnon Haloscope for dark matter detection. Please go ahead Okay, thank you. Thank you This works. Yeah Thank you very much for the invitation in this marvelous place. First of all, it's really organizers and I'm really happy to be here in person Be able to discuss in real life with everyone and so so today I will talk about some thing related to quantum microwaves, but Not well where we use condensed matter to try to build something to detect the cosmological objects and so This work has been done by my PhD student Arnautérie and postdoc William Legrand and with the collaboration with Matthew Delbeck and on the theory side We benefit from the long-standing Long-standing collaboration with Audrey Coté Okay, and so, okay, this is actually a singlet state, but the microscopic one from from like a recent Like attempt to convey more of quantum physics into the society Okay, so but this is not what I want to talk to you about today So, well, so the the idea is really to use quantum microwaves Like all the techniques which we have learned from quantum microwaves to probe cosmological objects Because in fact, there are many good reasons so with quotes for the existence of dark matter in the universe in fact if like this is like the content of Estimated matter energy in the universe and it turns out that we Like the we we think that we actually know only a very tiny amount Of we understand a very very small amount of the whole a matter energy content in the universe So this is so there is let's say essentially 5% of ordinary matter 26 roughly 26% of dark matter and the rest of dark energy and and so I'm gonna focus on dark matter and essentially the idea is that the dark matter Would have if it exists the non-zero density In all the galactic hello, so in in a milky way in our at our location But would be extremely weakly interacting with light and normal and normal matter and So the idea is to use the techniques for microwave Amplification to probe this invisible dark matter And I'm gonna focus in one specific class of dark matter models, which are called action models Okay so Okay, good Okay, so the the action Like particles have emerged in the high energy physics Context it was first proposed by Pacheon Quinn in at the end of the 1970s to solve The strong what is called a strong CP problem of the steering model Which is one term in the Lagrangian of the steering model, which is like the unsuccessful let's say term and which actually it apperently non-zero but It's since it would give an electric dipole to the neutron if it would exist and that electric dipole of the neutron is severely constrained to be Experimentally to be zero We should like Then there was a question of what was wrong and one solution which is now I mean Which I would be brought to by Pacheon Quinn and serve and further worked out by Weinberg and Vilcek is that you have a you could like this could arise from let's say a Symmetry breaking in the early universe, which would create a new Particle field, which is called the action which would be the Neville-Golson boson of this symmetry breaking and Which would essentially? explain why I mean There is this kind of term arising But in a dynamic dynamical fashion and so the idea is that the So the quantum chromodynamics Like essentially tilt this this makes it can have potential and and and give a finite mass to this To this excitation And so the action would be the mode of like the angular mode here, which goes into some place So so the the QCD tells you Like that it should be in fact so although the constraints are not very The bounds are not very hard Somewhere in the micro election vote range So hence in a in a microwave range between roughly one gigahertz and hundreds of gigahertz and so this is why I mean You can be willing to try to detect this one these these objects with microwave fields But it's Also very weakly coupled to ordinary matter or into a light and this is why such a class of Particles of fields are very good candidates for a dark matter one of the reasons Okay, and so one of the main consequence of the possible existence of the action field is that it should modify By a tiny bit of the Maxwell's equations, so it should essentially appear as a new term in the Hamiltonian of the electromagnetic field which will have this form. So it's a magnitude electric term and so Which is modulating in time? So there is the like this is the coupling strength here That's the amplitude of the of the action field and this is here the mass of the action Which should be as I told you somewhere between One gigahertz and hundreds of gigahertz, but it can be actually even lower on the RF side and higher towards the terahertz side and so this is this there are other couplings which are possible to a two fermions so they use so so they also can couple two fermions, but this is The term which is the last model dependent But then in order to still you need to do some models to actually estimate this coupling strength And it's actually a very small coupling strength So these are the two let's say like mainly used Like kind of model which which estimate this guy. So actually if you plug in numbers for like Like in the perspective of doing these experiments in microwave cavities In fact this would correspond to a shift in frequency in a Hamiltonian of around 10 to the minus 11 Hertz So you're like you're starting with something which will be having a frequency of 10 to the 9 and you want to detect something Which is 10 to minus 11 so you have 20 orders of magnitude. So that's kind of a challenging, right? So so so so now the question is how to detect such a small correction to Maxwell's equation okay, and so and so this was Okay, the priori almost a philosophical let's say question since it's extremely small like the coupling and then PRCQV the 1980s came up with a solution so this actually this E dot B term I mean is kind of Linked to this kind of triangular like Processes which are linked to the chiral anomaly and And so the idea is that if there is an action arriving and And they in the constant magnetic field in time. So this magneto electric term yields a coupling to photons in particular if the photons are The photons of a single mode of electromagnetic field that which is trapped into for example a microwave cavity So in fact PRCQV said okay Like if you now Want to detect this this this object so you need to place the whole cavity into a constant magnetic field and And if you're able to measure Very accurately the microwave power coming out of this microwave cavity you will be able to detect the presence of this term okay, but this is a Needle in a haystack problem because you don't know where the the action is right and this is a very favorable signal So in order to establish a common cavity I think it's interesting to see exactly how this comes about just to see what are the constraints and And it's it's nice to to come back. I mean to the original problem where you have here This is this extra term in Hamilton in which you want to detect That's the cavity mode here And this is the bath and you can quantize the electric field here So this is of course exactly like it's security did not do those things in this language But this is of course very completely equivalent And essentially if you write down the equation of motion of the field of the cavity And now you have the kappa here, which is connected to the bath and what you see here is that the Coupling to the action is actually happened like a showing up as a driving term of the cavity and so if you go now in the rotating frame what you see is that Essentially this means that the actions if they exist they indeed Contribute but this is a coherent term right that's that's really important. This is not Just this is more than just a power this is they contribute to the amplitude of the field with this With an amplitude which is proportional to the magnetic field. So you need a priori large magnetic fields and With this very tiny coupling strength and of course This now is a very is mostly efficient when the action mass is resonant with the action cavity So now you understand the problem is that of course as you could expect from the beginning is that if now this This guy you don't know the frequency of this guy This guy essentially if you want to optimize the cavity and your measurement setup This has to be fixed or weakly tunable. And so and so since you don't know I mean where this will be essentially you have to do many attempts and essentially you will exclude the different Thin lines in the phase diagram of coupling and mass and and this this is a Very complicated in principle And now since you want to if you want to measure power now you want to measure a dagger a and then since now you pay I mean the the price that this is this is squared So so you gain because this is b squared, but this is squared here. So that's that's again. I mean Further challenge Okay, okay, nevertheless Especially since the advance of quantum limited Microwave detection techniques, there are many people who have done a very important contributions to the to this field so so they're like This is the like some kind of the the coupling The coupling mass map in yellow here, this is That the region where QC the QCD actions would exist and here now you have these thin lines which Are actually wider than the actual their actual line with in real life And is there any graph so there is the haystack experiment And there is the quacks experiment also and so there is also very important Collaboration ADMX where at lower frequencies you could they could have to some tune ability But I think this is these are many different experimental results concatenate it and so and so they So you see this is exactly what I told us that you you you can exclude thin lines In this phase diagram, so it's a priori difficult to reach the cosmologically relevant level because this is these are tiny coupling strengths and and and Nevertheless, I mean there are many people now working on this More than the ADMX haystack quacks. I mean other also which Like I haven't cited and essentially the idea is that to use quantum resources to To go further or to speed up these kind of measurements and to go further down So for example in this haystack paper here, they used a squeeze the less states This is this paper published in nature last year Okay, but we'd like to try to avoid I mean to build a new let because this this is even with the resources of Like squeeze say they seem still extremely challenging to to cover Like a sizable part of this of this dagger of this map So we wanted to to find a different to follow a different path and this different path is actually like a very simple idea is that what if now I replace the be here by a Field which is oscillating in time with a tunable frequency so this this in fact Like in microwave engineering people know very well how to do this for passive soldiers for example the user for magnetic resonance And so the idea is to do exactly the same thing So which means that we will replace Like this is the be so the be can come from the magnetic mode now We will replace the static be by an oscillating be arising from a magnetic mode So for example in the for magnetic insulators these magnetic modes can be very well defined in frequency And so and so now the question now you replace this condition of resonance between the cavity and And the action by a three now Frequency Condition where essentially now the magnetic resonance you can just you need by just The Larmore let's say precession of this magnetization around the static magnetic field So you can continuously now in the same experiment in principle Do that? Okay And so of course now I mean I have to show you that we can actually implement this kind of stuff in an actual experimenter and So the here is how it looks like him. So we chose to work out to work with not a fair magnetic material Although we did some tests with the firm with her magnetic materials, but within that an anti for magnetic crystal So there are some advantages of using an entire for a magnetic crystal because it has no net magnetization and so this actually Like we took inspiration from this work by Everett's So this is a 3d microwave cavity. This is called a loop gap cavity. You have two kind of pillars here This is a like centimetric scale. So this is a cubic Crystal of 5 by 5 mil of 5 millimeters side and in fact since Well, I mean we like we have seen this week but I mean this this is kind of something which is now well established in Quantum amplification you need some on harmonicity to to amplify Tiny microwave signal so so we need to put some some twinkle of an harmonicity and We would like to put in on so we so the like the obvious candidate is a superconducting circuit But we want to have something which will be magnetic field resilient So this is why to keep taking inspiration from the cultural folks We opted for a granular aluminum Transmon qubit, so here this is the granular aluminum bridge here and Here these are niobium Electrodes, so we use a two angle evaporation and so on and so the two in order to make this this kind of bridge and So this is what hopefully Will give Rives to on harmonicity So essentially the magnetic resonance of this entire ferment if everything works fine I will provide the the tunability with the magnetic field and the unharmonicity of the granular aluminum transfer Will give a resource for essentially photon-to-frequency conversion okay, and so Okay, let's first see what the granular aluminum transmon Gives that like as like unharmonicity. So this is a single-ton spectroscopy of the cavity plus transmon system, sorry so um So yeah, sorry, so this is the the resonance of what these kind of Loop gap cavities have two modes. So there is one at six point eight and one at seven point four So this is the six point eight modem and what you see is that indeed you have the characteristic let's say a Duffing oscillator Line shape for the transmission when you when you drive the cavity with a large power So this is of course there is this is the power at room temperature with this is of course strongly attenuated and If now I look at the at the trend at the like the resonance of the superconducting circuit So this is at the lowest power This is this so there is a much lower transmission because it's you see strongly detuned from the cavity And what you see is that you also have the characteristic unharmonic oscillator Line shape when you put a large power At the at the at the fridge. Yeah, so this allows us to calibrate essentially the transmon and harmonistic It's a weak and a weakly unharmonic oscillator essentially So it's 180 kilohertz and this since we are strongly detuned that leads to a small Care to do for the cavity of around 70 Hertz Okay, so now in order to further characterize the transmon we can now go into the time domain measurement and so and and try to explore The magnetic field resilience of the of the of the of the qubit So this is at your magnetic field And this is the rabbi like a drive of the qubit so you see this is the now you are Like at this at the frequency I was showing you on the left your graph as a function of time and what you see that you have rabbi like oscillations and So it's kind of a truncated Chevron patron so you see it's you would expect something which goes down and in fact this is kind of So I we don't have many examples so the only example I know is Recent work in graphene transmons which look like a bit like that So so we think this is because of the weak and harmonicity and so these rabbi like manipulation So also has a kind of a different Amplitude versus rabbi frequency dependence, so we maybe see the like the two-third power law which was actually like Investigating this paper by the grown-up folks So we maybe see the two-third power row indicating that we really in a weakly and harmonic oscillator And what we see is that something which is interesting so we could push it further, but we like It's still under I mean Like under measurement so essentially we can go up to like a 90 milli tesla to do To see how this guy changes So now I mean I anticipate this is this is Actually, we don't see the the same T ones here because in this setup The cavity modes were closer because we had incorporated the magnetic crystal and so these changes The frequency of the most because these magnetic crystals has a large epsilon. So nevertheless we cannot draw like do some rabbi drive to Quite like a rather decent magnetic field for a transmon qubit and And also considering that this was out of plain magnetic field okay, and the T1 like a change from here to there is completely consistent with a Brussell effect from the cavity mode Okay So we can do also Ramsey interferometry to further characterize the the ground aluminum transmon and and see Indeed that we see the AC start shift from a rising directly from the qubit and homonicity. So now we do the Ramsey Like a sequence as a function of the power It's a third tone on the on the on the system, which is directly on to the cavity mode And so this is exactly what you would expect. I mean a qualitatively from like the effect of the of the drive I mean of the cavity to the to the transmon okay Okay, so now let's now turn to the magnetic part of the of the detector and and Let's see the magnetic crystal. So this is what you will expect from the phase diagram of the gadolin vanadate crystal So we would like to focus on the the entire for a magnetic regime With these two lines that which are the two sub lattice is of the interferometer magnet which start at around 34 gigahertz There is one sub lattice which is Going down and this is the one which we will be mainly coupled to and one sub lattice which is going up in frequency and and so and so this is Like the the main region where we would like to to look at the system and the near temperature of this of this Entire for a magnet around 2.5 Kelvin is explained. Why is this exchange interactions also a small and it's interesting for microwave Detection techniques because now you see that you can cover essentially a span of 68 gigahertz roughly With these two lines if you're able to address this line. So which is a potentially a very wide band detection Okay, so when we put everything together Here is how the the transmit the map of the transmission of the detect the texture looks like So you have the mode one here Which like goes down in magnetic field, this is the mode to her here. This is the So of course, it's so that the granular aluminum trend transform transition Which you actually faintly see up to like a roughly 400 milli tesla and and this is the magnetic mode Going down very fast and this is completely consistent with with the line going down And starting at roughly 35 gigahertz and going down with the slope of g-factor equal to So what you see that you have a very strong hybridization. This is normally because you have a microscopic Magnetic material with the mode one And so in fact, it's so strong that actually you really find the most but if so like the avoided crossing like Well, it cannot like have the same meaning as the like the well, okay it has the same meaning but it's like It's you see that you have like like a region where you completely lose the transmission and and that's on so then this the body crossing implies Like the ultrasound coupling to mode one, which the coupling strength of around one gigahertz Okay, and So now what we would like to do is to really show that we can follow because we want to have a wide band detector on a on a wide Frequency range the Magnetic mode and so this is what we did by doing two tones spectroscopy And so this is a cut this is now the phase of the microwave signal at the cavity of the mode one frequency as a function of the of the Frequency of a second tone, which is Actually added to this to this first tone and Since we have now on harmonicity We actually engineer an interaction in principle between the magnetic mode and the cavity mode And this is and this results in a frequency shift of the cavity mode as you drive I mean the magnetic resonance As you see here and this is exactly this manifest itself as this deeper in The phase and this allows you so exactly the same spirit as what you showed this morning to follow I mean so there are many magnetic transitions But we we we followed for example this green one here and you see that you can span essentially on the on the band the width of about 10 gigahertz Which is and so between and you see this works up to essentially like roughly one Tesla And so so you we can actually indeed follow Thanks to this and harmonicity the the coupling To the on the magnetic mode to the the interaction of the magnetic mode with the cavity mode and this Is actually like the prerequisite that we wanted to have to have a broadband detector Okay, so let's see how I mean this 7 like this 7.5 till 17.5 gigahertz or how it would look like at least in a horizontal Axis because we we don't know yet. I mean where we can go I mean how far we can go close to the to the yellow like in the in the coupling strength So This is under development and this is what it would look like So you would see that the this opens the the possibility to have a very broad band. I mean you see a detection Let's say Window and so and so following this kind of magnetic mode So there are many others so we can in principle extend further But it's the green magnetic mode for example will allow us to to to have a very large window of detection To enhance substantially the mass scanning window and so the first detection run is is on the way Okay, so but my time is over and so So I have demonstrated a hybrid transmit magnet photon system And so the anharmonicity plus the ultra strong coupling of the Magnetic mode to the cavity modes provides a in principle a large scanning range And maybe this is a new setup for detection of dark matter in a laboratory experiment. Thank you for your attention Thank you, Takis for the very clear talk any questions so for What do you need to do to be able to go down to the yellow region? I mean is it how long you measure? Yeah, and and and it's also it depends so in our detection schema. We use a Coherent field so we have to to put a large coherent fill in a cavity to essentially use this mixing between the two modes so in principle In principle, you just need to go further down to have a larger Coherent field But then of course if you put a too large coherent fill in a cavity at some point There will be other Unharmonic terms which will show up and so this is what we still don't know yet. I mean how far we can go This is why I mean we are still like tuning I mean the the setup to see how far we can go But in principle you just need to put a large coherent field and then since we detect the phase We just you know, this is like a ruler, right? You you can detect a tiny angle if you have a long enough ruler But you also need to measure if you measure longer. You're so it's the same right or not Yeah, it's the same but here since you want to detect that so it depends if you measure power You you have to wait for a long enough time if you measure coherently like we do here you need to measure faster than the The coherence like the than the coherence time of the of the action in the in the earth Frame and so this is sometimes some somewhere in the millisecond range, so we need to measure faster than this Thanks for the very nice talk actually we have two questions if I may So first about the anti-ferromagnet Stuff as far as I recall my solid state class is an anti-ferromagnet you have up and down domains But on very short length care while given the frequency I guess that the actionic field has pretty large wavelength So, I mean I guess there's something I don't get but naively seems like the M in your equation the magnetization would be somehow zero as seen from the from the actionic field, so what's the What is it? Yeah, I am missing you so no no this for the static part. You're perfectly, right? But when you start to to excite the the magnetic modes It's essentially you have to make as if you would have two magnetic resonances There is one sub lattice, which will have a long wavelength motion and yeah It's like a spin wave exactly. Yeah, exactly. Exactly. Yeah, and other question along the same line could you replace your Transmount induced an harmonicity on the cavity by an anharmonic a Ferromagnet or anti-ferromagnet like yeah, so thank you for it. So we actually at the beginning we were a bit Like to like we wanted to do that and it turns out that so from a nice from magnetic anisotropy in principle You also have a harmonicity which shows up but this so and this has been measured in the magnetics In fact, but this is merely hurts even at the best. So this is extremely weak. It is much weaker Than than what you can get with a superconducting circuit. Okay. Thanks Yeah, thanks for the interesting talk I had the same question regarding the magnetization and I was asking Did you think about so there are certain ways to create squeezed Magnons and for example in anti-ferromagnet? You have a two-mode squeezed state as you Might this be useful to and sometimes, you know squeeze squeezing helps to enhance the detection Efficiency or something like this. Did you think about this and in this context? Thank you, we haven't thought about it, but since you see now we turn The the magnets they become unharmonic now because they interact you see there is an interaction term with a cavity and then in fact If you should they will also be unharmonic because you really find a motor So in principle, you could also play these you could induce squeezing of this of these magnetic modes We haven't thought deeply about this, but it could be in an anti-ferromagnet The magnets are automatically squeezed without any Externally squeezed in the ground state or the ground state is actually a two-mode squeezed state and the excitations are also special So we haven't thought about it. Yeah, but we haven't thought about it without any external I see it. I see it. Okay. We thought that you have an external source of okay. I think they You're a question here. Okay, so I think we finish and you can discuss everything with Tuck is later Then we continue