 Hello? Hello, yes. Hello. I want to start, of course, thanking the organizers for giving me the opportunity to present our work here. I come from Germany. I'm at the theory division of the Max Planck Institute for the Science of Light. And I will be talking about cavity optomagnonics, and this is in a nutshell how collective magnetic excitations in solid state systems couple to light. So I think this doesn't work. So I think given the name of this workshop, I don't have to convince you that we are living in very exciting times in which we are going from processing and processing information and communicating information in a classical way to doing it in a quantum manner. So here I chose to picture one of the best candidates so far for processing quantum information, so superconducting qubits. So we would add, of course, an optical fiber, so we would like to communicate information and then optical with light. Why is this? For example, if we want to process information here, we will be doing it a microwave regime. This requires low temperatures, but we would like to communicate the information not at low temperatures, so this is best done with light. So we would like to design systems that are able to, we would like to be able to prepare states to process information and to communicate it. And for this we need a hybrid, what are called hybrid systems, a system that combine different degrees of freedom to perform these tasks optimally. So I chose here a collection to show a collection of the systems that are being studied nowadays. And they all share a common quality which is these are systems at the micro scale or at the nano scale and they use collective excitations. So what we want to do is to design the system so that we can use these collective excitations. So for example here is a picture of a photonic crystal where the light can couple to the vibrations in this crystal in an optimal way. This here shows a suspended nanotube in which the electrons can couple to the collective vibrations of the nanotube. This is a similar setup here but the vibrations couple to electromagnetic fields at the microwave level. And the last picture is, the last picture is a very new addition to this collection of systems which is what I will be going to talk today. So these optomagnonic systems in which light couples to magnetic excitations. So this is a picture that I will be going back later but then we go to the outline of my talk. I will be giving very briefly an introduction of mannus and actually the mode that I will be talking about which is the Kittel mode. And then I will show that these excitations have been coupled to microwaves and then I will be going to the coupling to light and I will show how Kanwe could one use light to induce, to control the spin dynamics in the system. So let me start then by telling you what a magnon is. It's an elementary magnetic excitations as already said. So it's the quantum of the spin wave analogous to the phonon to the mechanical vibrations. Why would we be interested in using magnets where there are collective excitations which are robust. There are two levels for example in frequency and they can have very low power so they are useful also in terms of energetics. So the Kittel mode which is the mode that I will be talking in the next few minutes is if you take magnetically ordered material and you consider that all spins are locked together and then you can excite a mode in which all spins are locked together and they precess in phase. So it's like they are forming like a big macro spin. So this is a homogeneous magnetic mode. It doesn't depend on space. So we can map all these spins as a big macro spin which is precessing with some frequency. This frequency in general is controllable by an external magnetic field and in the examples that you will be seeing later you will see that for example for a 30 milliteslas magnetic field this frequency is in the gigahertz range. So if we now take the spin and we want to see how the dynamics of the spin is and we can use an equation of motion which is the Landau-Liffchitz-Gilbert equation which is the equation that you see here and what it's telling you is if you have the spin that can rotate there is some external magnetic field that will make this spring precess around an axis. In this case it's set axis so this is a usual larval precession but then there is a phenomenological damping term that we can have to do with the properties of the material that will damp the precession of the spin to its equilibrium position eventually. So these are all elements that we will need for later but let me now tell you a little bit about the experiments that have been performed in the last years in this kind of systems and now three years ago it was demonstrated that these magnets and in particular this Kittel mode can be coupled strongly to a microwave field so the picture that you are seeing here is a microwave cavity and which as sphere of ferromagnetic, a ferrimagnetic material is put in one side of the cavity and it couples to the microwave field in the cavity. This is what you are seeing there, this sphere is actually yig, it's Ethereum iron garnet it's one of the best materials for this kind of magnetic uses. This is a ferrimagnetic material is insulator so it means that the spin waves have low dissipation and it's transparent in the infrared which will be good later if we want to couple these excitations with light. So as I said in this experiment they show that they can couple strongly the magnetic excitations in this sphere that you see here to the microwave field so if you look at this plot you see that the microwave mode will be here, the Kittel mode will be here and as the external magnetic field is swept and the two enter in resonance there is a splitting of the modes, there is a hybridization of the modes and this splitting gives us the magnitude of the coupling. So this is a resonant coupling, a magnum goes into a photon, a photon goes into a magnum it's quite strong in this case, it's around 50 MHz for this setup and that means for the experts the cooperativity is quite high, so around 10 to the 3. So this is the ratio of the coupling to the dissipation in the system. So this was a performance I said three years ago in the lab of Nakamura in Tokyo and also in Hongtan's lab in Yale. So once one year after the group of Nakamura showed that actually they can also put a superconducting qubit in the cavity and via the microwave field in this cavity they can couple the qubit to this magnum excitations. So this provides the first strong motivation to couple magnums to light or to try to couple them which is if we would be able to couple it so we know it couples to the microwaves and if we would be able to couple it to light then we could have a wavelet converter so a transuser of information from the microwave regime to the Terahertz regime. So this brings me to the subject which is optomagnonics and first of all how light couples to magnum, this is quite old effect if you want so Faraday already few years ago made the first experiment of this class in which he took a light from an oil lamp, he polarized it by reflecting in a glass and then what he observed is that as this polarized light was going through a material here he put a polarizer and if it was observing it like this there was no light but if we would put a magnetic field now then there would be suddenly light so that means that the plane of polarization of the light was rotated and what he measured is and he did this very, very, with a lot of details he tried very different materials, very different ways of putting this magnetic field he was very conscious and what he proved is that the rotation is proportional to a quantity that is a characteristic of the material which is the Faraday rotation this theta f that you see here and is proportional to the length that the light goes through the material so just to give you an idea so this is the original paper of Faraday this was the first demonstration of a direct relation between light and the magnetic and electric forces this was around 15 years, 15 years before Maxwell equations so one can have an expression for the electromagnetic energy that takes into account the magnetization in the field and in the material so actually what one sees is that this magnetization in the material modifies the electric permittivity of the material and one goes to an expression of the energy, classical energy that looks like this so there is, if you see here this energy is proportional to the Faraday rotation it's also proportional to the magnetization density in the media and it's multiplying the optical spin density which is this cross product between the electric field so this is what is called the spin of light and if you have circular polarized light if you take this cross product it will give you basically the helicity direction of light so what we did was taking this energy, this classical energy and quantize it so you can see that the magnetization goes to a spin operator the electric fields go to photon operators and you see this is one spin operator and two photon process so this is what it's going to allow and you will see after that the magnetization dynamics the spin dynamics is actually in the gigahertz regime but we have photons in the terahertz and these two photons the parametric process is going to compensate by this energy mismatch and now this expression actually if we want to go to a quantum model then we run a little bit into a trouble if we want to consider the most general way in which the spin would depend locally in each position so what we did is to take this Kittel mode as I was introducing before so we considered the magnetization to be homogeneous in the sample and we can replace this by a macro spin which has a dynamics in the block sphere so what we realized with this is the optomagnetic Hamiltonian which tells us the coupling between photons and the spin operator so you see here I have two photon operators I have a spin operator and this G here is when it's giving us the coupling which we calculated to be this expression here so you see that it's proportional to the overlap of the electric field modes functions it's proportional to the faraday rotation as I said before and importantly it's inversely proportional to the number of spins so that means that what is important for us is the density of magnetic excitations so if we have one magnetic excitation in a smaller volume it's better as to have it dispersed in a big volume so actually the coupling between optical photons and magnons was demonstrated last year again in Nakamura's group in Hong-Tang's group in Yeh and also in Ferguson's group in Cambridge how do they do this? so they take this X sphere that we saw before and they couple a nano fiber evanescently to whispering gallery modes that are present in this sphere so these are standard wave modes like if you would have a linear cavity but these are in this spherical symmetry and what we have to take from here also is that a cavity will actually enhance the effect because the light goes many turns in this cavity before going away that means that the length of... so the faraday effect is also proportional to the length in which the light goes through and here this length is increased in the cavity so what they observed in this system is that if they measure... they throw a light in, they measure the light out and they see side bands in the light at the frequency of the magnon excitation so what we did actually is to take a toy model to see what can we do... to study the spin dynamics which is induced by the light and what kind of effects we can expect so we took a simple model in which we have the Kittel mode that I've mentioned before and a single optical mode which is circularly polarized in this plane here which is the Y set plane so that means that the spin of light that I mentioned before is pointing in the X direction so in this system the coupling takes a very simple form so we go from this Hamiltonian to a coupling that looks very simply so simple we have two photon operators here from the same mode and the operator is... because of the geometry we chose the X direction the rest of the Hamiltonian I'm in a rotating frame so this will give me... if I drive the system with a laser this gives me the detuning between the laser and the resonance of the cavity and this is the term that will control the frequency of my spin by an external magnetic field so in this simple example one can calculate the coupling constant G it takes also a very simple form as you see here again you see it goes as one over the volume of the spin one over the magnetic volume proportional to the faraday rotation and if we go to the diffraction limit and we take a sample in which will be one micrometer cube this will be around one hertz for you to have an idea this corresponds to an optical magnetic field density which is quite small it's 10 picoteslas but this is per photon per micrometer square so this will be for example in a cavity enhanced by the number of photos in the cavity so what can we do with this? sorry we can calculate the... we can explore the dynamics of the spin given the coupling to the light and driving it externally with a laser and we decided to do it first to explore the classical dynamics of the system so this is the classical equations of motion that one obtains from this Hamiltonian so you see that we introduced also a cavity decay rate and here is the detuning this is how much so the amplitude of the driving and we see that the equation of motion for the spin which we saw before the Lipschitz-Landau-Gilbert equation is modified by a term which couples to the light so you see here already that the light is acting as an effective magnetic field we can go further with these equations in the fast cavity limit where the light is much faster than the dynamics of the spin one can integrate out this photon field and obtain an effective equation of motion for the spin and now you see that really takes shape which we saw before so we have an effective magnetic field that controls the spin and interestingly we get also a dissipation term caused by the light so this is due to the retardation between light and spin fields so we see the effective field here it's proportional to the amplitude of the laser and also we can control it with the detuning and interestingly the damping we also have an analytical expression and you see here that we will be able to change the sign of the damping by controlling the external laser drive so now we can see what kind of dynamics we can obtain and so this is in this fast cavity limit and we see that in the case in which we are changing the sign of the dissipation in the system we are basically changing what is the stable equilibrium of the system so if before the stable equilibrium of the system was the north pole now because of the change in sign of the dissipation we are bringing it to the south pole so this is basically we are changing if you want information from 1 to 0 in some sense also interesting dynamics can be obtained such as self-sustaining oscillations in which by a strong drive one can bring the system into limit cycle behavior I should say this kind of physics is also realizable in cold atom systems and the group of Stanford Kern in California they show this kind of behavior by so magnetic switching behavior in their systems so if one goes to the full non-linear dynamics and not beyond the fast cavity limit that I was studying before you can see that the non-linear dynamics is even richer so by increasing the laser amplitude we can go from this limit cycle behavior that I showed before then one would have a period doubling of this limit cycle and we could enter a zone of chaotic dynamics and even coexistence so this shows that in principle we can have coherent optical control on the spin dynamics such as magnetic switching self-sustaining oscillations and scales and this I should mention is a collaboration with Florian Marquardt in Nell Langen and Hong Tang in Yale so let me go in the last five minutes to an outlook and summary so this is all very nice but there is a problem in the current state of the art in these systems in which the optomagnonic coupling is actually in experiments too small so the coupling for photon is around 60 hertz that means that the cooperativity which if we want to do for example quantum state transfer should be bigger than 1 in this system is 10 to the minus 7 so if we go one step back we can let's go back to this Hamiltonian that I showed before this coupling Hamiltonian if we consider now instead of considering the non-linear dynamics of the spin I consider small oscillations of the spin around its equilibrium position then we can use Holstein-Premacov transformation to put this spin operator in terms of bosonic operators then we obtain a Hamiltonian which for those familiar with the subject has a form which is also the form that the optomechanical Hamiltonian has so systems in which light couples to mechanical vibrations and so now our coupling constant will be this g times s square root of s over 2 so it's actually enhanced by a factor of square root of s and this means this is the fact that we are working with collective excitations and we are taking advantage of this magnetic ordering and this we can if we can now take the sample of one micrometer cube then we see that we get a g which is around 0.1 megahertz this should be compared to this g that I have here sorry I didn't put the g not so this tells us that if we go to smaller samples then we can enhance the coupling so if you go if you look at this figure actually the sphere that I have been using in the experiment right now they are around 1 millimeter in diameter so they are pretty big the other problem with this system is that the overlap of the Magnon mode with the light is actually not that good because this Kittel mode is in the whole bulk of the system while this whispering gallery modes live in the close to the surface of the sphere right so there is a whole there is a lot of coupling that is lost in this suboptimal overlap so ways of overcoming this and this is something that we are working right now would be to go to smaller systems one and also to try to design systems such to obtain better overlap of modes so the thing is if one goes to smaller systems something happens which is actually very interesting but makes the problem as usual richer but more complicated and is that if one goes to the micrometer regime one starts to get magnetic textures in the system so for example this is a micro magnetic simulation that shows that if we take this and we let the magnetization evolve to its ground state it will form a vortex so this is something interesting and this is something that we are working right now how the light field interacts with this kind of magnetization textures so in this I should mention one also gets this whispering gallery modes for the optics the other interesting thought and the other line that one can think about is to improve the overlap of modes take as an example the successful example of optomechanics in which they use they design crystals such as to obtain optimal overlap between optical modes and mechanical modes so can we do the same with optomagnonic crystals so these are two things that we are exploring right now so I will finish with summary as hope I convince you that cavity of antibiotics is a promising new field and that using collective magnetic excitations is a promising path also because they are robust they are designable and in principle they can also be quantum although I didn't talk about that today and I will finish advertising a little bit I will be starting my group in January at the Max Planck for the science of light and there are open positions for phd and postdocs so thank you very much