 also thank the organizers for inviting me and giving me the opportunity to tell you a bit about what we're doing in Munich. I'm also a bit fortunate because my talk is right after Fabrice's talk, who introduced the concept of what's possible with two electron atoms very nicely and then also yesterday we heard from Christian Goss about what's currently possible with permeonic systems under quantum gas microscopes and what I'm going to tell you is a bit of a mixture of both but I'm also not going to tell you anything because we don't really have a final experiment yet we're still working on it and that is going to be a slightly technical part of this talk and I hope I can show you a bit about what's actually involved in making these experiments work and tell you where we think future improvements can be done. So this is a slide I recycled from 2008 and the shows the electronic structure of Strontium here so the you can see it's exactly the same overall structure as Eterbium so you have a singlet first singlet excited state and the laser cooling transition which is broad that couples those two and you can laser cool atoms down to the milli-kevin regime using that transition then you typically switch over to a secondary cooling transition to the first excited triplet state which is seven kilohertz wide and that allows you in this particular atom to cool atoms down to the microkevin regime even that's one of the nice features of the Strontium atom is that this line width is actually really quite nice so and then the the transition that caused a lot of excitement which is also why I put this slide about 10 years ago or a bit more than that is that it's possible to build optical frequency standards based on the transition between the ground state here and the first excited triplet state and this relies on hyperfine coupling in fermionic isotopes of two electron atoms so in this case we have a nuclear spin of nine halves and this results in a line width that is extraordinary extraordinarily narrow and a line width of the triplet P0 state of about 150 seconds and no one's been able to resolve that yet but that's why it became very popular and in fact here are a few ancient results by now that show you if you compare this frequency standard against the definition of frequency and time the cesium clock you can measure this number and this is still the best agreed upon optical frequency to date and the reason is not that people haven't been working on it the measurements actually got a lot better but it's that the cesium standard is just not getting that much better anymore and which is also why there's been a lot of discussion of actually replacing the cesium standard at some point soon with an optical standard and Strontium is one of the prime candidates for that so because of all of this excitement today there's a actually a lot of different research that people are doing with Strontium atoms and it makes use of a lot of the concepts and the technology that Fabrice also introduced and just the little selection of experiments all of them are fairly recent and I'm sure I'm forgetting some and one exciting thing for instance about these atoms that Fabrice also alluded to is that the ground state interactions for these atoms don't actually care about the state of the nucleus so if you have two atoms at ultra cold temperature colliding what really happens is that just the electronic shells overlap you get stronger pulsing due to the poly exclusion principle and the nuclei never see each other and that's why then in these j equals zero two electron atoms you have a SUN symmetric interaction or if you want to think about it that way if you write down a Hamiltonian then this Hamiltonian will be SUN symmetric that's exciting because where sorry n is the two times the number of two times i plus one so in our case 10 and that's exciting because the SUN symmetry is of course very prominent in high energy physics problems and that's why people are very excited about using these atoms to do quantum simulations of such problems or of quantum field theory say there's also something very similar that also Fabrice showed already you can do spin orbit coupling something very different is you can also put these atoms into a cavity in the bad cavity limit and try to generate a an active laser an active oscillator based on them so with the hope that you can get a really hurts lined with a laser out of this that is not dependent on the boundary conditions here the cavity but really just use the features of the atoms there's a project that's picking up speed and flow and trex group where they're trying to develop a really continuous source of ultra cold and even quantum generate strontium atoms also for applications in oops atom interferometry so here's the first result very recent on using building an atom interferometer based on the clock transition and again here the the hope is that you can use the extremely long coherence times to make very large areas for your atom interferometer and thus get enhanced resolution people have started playing around with redbroke atoms of two electron systems and here the interesting part is simply that well if you have two electrons and you take one far away then you still have one electron left that you can use to actually trap these things so that's exciting of course if for a long time it's been possible to do photo association of such atoms and make molecules but now you can turn it around and actually photo dissociate these molecules in tanya zelevinsky's group and that's cool because it's a very paradigm paradigmatic experiment in chemistry that can now be done at ultra cold temperatures meaning you can actually see quantum effects in in such experiments what I particularly like is that the optical lattice clock is now approaching a regime where it may actually be helpful to use a degenerate from egas as a as the atomic sample in this clock and there's some very recent results from from junior school on that so all of this is enabled by the concept of the magic wavelengths and fabrice has already told you a lot about this let me just rephrase this a bit in the language that you've heard at this workshop also so what you want to do if you want to do good spectroscopy is well you would like to do this with many atoms because that enhances your signal to noise but if you want to do spectroscopy on single atoms and just use many of them you want to make them be as identical as possible right this is problematic in an optical trap because the ac stark effect that generates these traps is state dependent meaning your internal and external degrees of freedom of the atom couple strongly and that's bad and then that was solved in the early 2000s by the concept of the magic wavelength lattice where you know it's magic because all your problems go away and you just are a bit clever and you plot the polarizability as you've seen from fabrice and if your two states cross and you have the trap that looks the same to first order for both states okay and again in different language what that means is that you decouple the internal degrees of freedom of the atom from the external degrees of freedom of the atom as well as possible and you use many atoms at the same time right so alternative way of viewing this this is the very best optical qubit we have today and you would like to make a pseudo spin system so it's also a pseudo spin you take many of them you have a pseudo spin spin system and you do your very best job of not having these atoms interact because that's bad okay so but since that's not what we're doing we would like to do the opposite we would actually like these things to interact again and I'll show you a bit about what the idea is so here's our polarizability graph that you saw just to remind you is this red magic wavelengths that are near are and if you make a dipole trap out of these at this wavelength both atoms will be trapped in exactly the same trapping potential there's also one in in blue detune from the main transition of strontium and that's interesting with the again the polarizabilities cross but with different sign which means that if you make a trap the atoms actually repelled from the intensity maxima or if you make a lattice the atoms would be trapped at the where there's no light and that's interesting for a variety of reasons I'll come back to that especially because the lattice wavelengths is 390 nanometer and if you imagine making a lattice at this wavelength you would get atomic spacings of 200 nanometers that I'll come back to that so there's also anti-magic wavelengths that Fabrice showed what I'm personally excited about are these two not wavelengths so if you if you look here so you can find wavelengths where both of those states either you know are are nicely trapped or don't see the trap at all and that allows you to do the following scenario here where you can either trap the ground state and the excited state doesn't care or you trap the excited state and the ground state doesn't care and if you combine those two you get complete differential control over your system and there's a lot of great ideas that you can immediately come up with let me show you just one of them so here's a scenario that you know without thinking too much you can come up with so let's say you make it make a just a retroreflective retroreflective optical lattice for the ground state and then you say you use a high resolution imaging system and project an optical tweezer with at this ground state you not so that the trap that only traps the excited state onto this lattice then you can imagine if you co-propagate a clock laser you can excite a single atom say and then you can simply start moving this thing around and what you do there is you by our collisions you start entangling everything anything you want and you have a very good control over what you want to do you do interferometry schemes anything like that so that's our big picture goal and then as you can see though you do need very good optical resolution such that you can focus down these traps to small sizes and to remind you what Kristian also showed is in the in about 2010 or so the block group and the griner group simultaneously developed these quantum gas microscopy techniques where you could for the first time see optical lattices and with bosonic rubidium in it and resolve them with single site resolution that's cool we've heard a lot about what you can do with that in about five years later a whole variety of groups started then also um getting this to work with fermionic atoms and to remind you because again uh the um if someone is talking about fermionic alkali metal atoms there are really not many many choices there are two isotopes in the alkali metals that are fermions and that's potassium 40 and lithium 6 and they each have their own issues which is why it took a while to get to get this to work uh also the isotope that Fabrice was talking about excuse me uh this is bosonic uterbium two Japanese groups very recently also got microscopes to work for for this so if you stare a bit at the very best fermionic systems that people are generating these days what you find is that people are making mod insulators and here's a sketch they sort of look like this you get a regular red grid of of atoms and there's one atom per site because again we're talking about fermions now and the temperature ends up being something like half the the tunneling rate so I'm using little t here where Fabrice used j and then then you can get these systems and we also see that they are fairly small right so in the end you get end up getting something like 900 atoms or so about 10 to the 3 atoms roughly so this is still not all that cold and there's been a a lot of very recent work where oops where you can then play a trick that has been discussed for a while and if you simply subdivide your big system well your big system now into a into a central area and you work very hard at making this extremely homogeneous and then you use low density reservoir on the outside to dump your entropy into you can get antiferromagnets with a temperature that's the that are decreased by a factor of two roughly and then you in the Grinne group very recently they were able to realize the first such antiferromagnetic systems in 2d that actually look like an antiferromagnet but what you sacrifice here that's my point a bit is uh you make these systems even smaller so now you end up having about 80 atoms and the big motivation for doing neutral atom in a quantum simulation and as we've also heard in this conference is that uh scalability so what about scalability here so in the end we have about 80 degenerate fermions and that's great but maybe we want a bit a few more of them so how do you do that and the as Fabrice also said laser power is a big deal that the reason this lithium-6 system that I just showed is this particular size is that the laser powers that you need to do these trapping conditions and especially these imaging conditions is as large as you can buy so there is no way to buy any higher laser powers at this moment and this is exactly why the system is the size it is and the reason is that the Gaussian beam shape of the lattice beams simply defines a varying chemical potential in your system and that's why the system requires a finite size now if you can't get bigger lasers and simple idea would be to maybe use a cavity and retro reflect your laser beam many times back and forth to enhance your laser power so that's what we're trying to investigate and the reason is that if we plot something for for strontium using this build-up cavity that we have in mind we should be able to get the system that is significantly larger now even I mean there are all kinds of issues with going to very large systems then but just thinking about taking this and making maybe the blue circle even a bit smaller again then you would get a much more homogeneous system than is currently possible and that then should lead to at least it should be possible to engineer lower entropies and maybe do higher fidelity quantum simulations in that language so this is plotted for an infrared lattice but also if we then dream a bit and say this also could work for this blue detuned magic wavelength lattice that I showed you then you could get lattice spacings that are significantly smaller and you don't have to sacrifice so much in the beam size to get systems that are even larger and so how do you do that now now comes the really technical part and here's where you know you have to look a bit at how people actually do things so if you want to build a cavity around your ultra cold atom apparatus how do you typically do that well you let's say you have a glass cell this is this this half thing here and there's vacuum in here and your atoms live in the center and you have made this very nice imaging objective on top so you can actually see what you're doing and then you want to build a cavity around it well what you do is you place two mirrors on kinematic mounts around this and you align it carefully and you retro reflect your beam many times back and forth so I said these cavities are great because they give you all kinds of great features but that is really only true as long as you actually manage to stabilize this laser to the cavity resonance right if you're if I'm not on the cavity resonance and I get no laser light in and well nothing happens also means well that you know this cavity enhances power but with great power comes well great sensitivity to everything and especially to vibrations from these kinematic mounts there's also you can see there's glass in between the cavity mode and this leads to losses stress induced by refrigerants and generally also means that your cavities have to be fairly long just because you have to put it around something so people have tried this of course and it tends to not work so well I mean it works but not particularly great so the my idea or what I would like to sell you is that we can take a cue from how we construct laser cavities for these very good reference lasers for optical clocks and you just look at a list of how that's actually done and here's a sketch so you see this this glass body and then you can see these mirrors for mirrors optically contacted to it so in this sort of construction it's it's completely monolithic there's no tuning that's that's bad right so you can't really align anything like here you also have to actually optically bond these glass pieces together so this really becomes a single glass body you can't glue it if you use ultra low expansion glass materials like in these reference cavities then this can be actually quite good you should put that in vacuum and you should really worry a bit about vibration isolation and thermal management okay so this is the technical stuff so vibrations again and it's maybe form a conceptual standpoint is interesting to you so if you play around a bit with the finite element solver and and this geometry you can actually engineer this such that these vibrations which what they do right if this if this cavity shakes then the cavity length changes or and that also causes your optical lattice to shake and this heats your atoms out that has been the problem for for most people who try this but if you play around with the with the geometry and use a very high quality factor material like these glasses then you can engineer these vibrational modes the lowest one to be out of band with your system energy scales and the system energy scales that you typically have in these fermionic mod insulators are simply given by how how high can you crank the interaction energy so Fabrice also showed that the the energy scales for these systems are very slow so you can get if you're a good or and if you work hard you can get a few kilohertz maybe a bit more but that's about it and that then sets everything else because you then to get a mod insulator you want the tunneling matrix element to be about 10 roughly of this interaction energy and then this also here my j is the super exchange energy sets that as well but if you look here if we get a few kilohertz here this is much higher so there's some hope of making this work well you want to worry about how to design your mirrors the good thing is we don't have to we simply want to define a good cavity mode with that looks nice and has high enough power to do what we want and is large such that we don't really we're not really interested in doing cavity QED type experiments which means that the power buildups that we are considering are on the order of a few hundred to a few thousand only and that means you can actually design optical coatings that work for a variety of wavelengths and I showed you in the beginning that there are a variety of interesting wavelengths for the strontium atom that you may want to play with including these tune-out wavelengths here this ending magic wavelengths the blue magic wavelengths the red magic wavelengths another red magic one and even if you have a laser around 1064 turns out that works we've measured all that that that's fine um so what's difficult about this why has no one done this the the difficult part is that of course I've mentioned you can't actually do anything to it once you build it there's no tuning you have to start designing this from the very beginning because you have to put it in vacuum that's all technically challenging and so on but the real issue is you can see here how there's actually two cavity modes and I mentioned that we would like to have homogeneous systems which also means that these cavity modes have to actually overlap and that is very hard and typically people don't worry about that for optical cavity design and the reason is that the if you want to make a cavity with large modes you can think about your classical fabi perot interferometer with plane mirrors right and you know that any field configuration will fit in there it's not what we want because we would like to define a well-defined and meet Gaussian beam that we can use so that you go a bit away from that condition and you make instead of having infinite curvature on one side you make it a bit curved and if you make it you know 10 meters or 20 meters of curvature then the the the cavity mode sizes that we're going to get are something like half a millimeter width so a millimeter size size beam macroscopic things that also means unfortunately that the that the mode becomes the position of the mode becomes more undefined because the you can see here if you buy a piece of glass you have to worry a bit about the parallelism between these two surfaces and the best you can get someone to do for you is something like an arc second and there will always be a mode between those two mirrors but you can see that it's defined by the normal vector of this plane mirror and then the radius of curvature of the secondary mirror and the displacement is given by this angle times the radius not the length of the cavity which then makes it really quite challenging to not only get two modes through these holes but also then actually overlap that so that's what we're working on what's the status so here you can see our test piece the cavity spaces we have figured out that's working the coding run is also working like I showed you you also want to here in this test piece the mirrors are still glued you can see a bit of glue here that doesn't work so we have to contact them to the to the spacer which means you need to machine off a flat surface in this in this mirror that's something we've been working on for a while that's now working you have to optic to contact we think we know how to do that we also know how to measure the mode overlap in the end we still have to figure out two things and that's the remaining wedge error in the machining of this annulus and we have to work a bit on the precision with which we can do optical contacting that's also something that people typically don't don't do like that so that's the the big technical background to what we want to do and I think that's typically what what you don't hear in these talks is that all this effort that has to go into something like this of course that's not the only thing we're doing but we've also this is our vacuum system as it looks currently there's a lot of technical enhancements that are maybe not so important right now what is important is that we've measured the the lifetime in this vacuum chamber over here to be better than a minute in a magnetic trap and that that will help us to also work with rare bosonic isotope of strontium that we would like to address as well and with that I'd like to summarize so what we would like to do and and as you've seen there are there were already great introductions at this conference from both Fabrice and Christian is to combine these two fields of and try to to quantum many body physics in under a microscope with two electron atoms one thing we're excited about is the prospect of using blue d2 magic wavelengths because you can get such small spacings and that nonlinearly increases your system energies as I said that sets everything like as much as high as you can get the interaction as good year well the more you can do and there is are also two not wavelengths that we are addressing and I think would be very exciting to try something with that we would also like to go to larger systems and again the main point here is not that you really want larger systems but that if you then cut out a small part of it it will be much more homogeneous such that then you can talk about doing high fidelity quantum simulations also reduces your dependence on the local density approximation for the analysis of such systems things we have on our minds are trying to do interferometry experiments like I showed with using these state dependent traps we can easily see that as I showed you can take an excited state atom and move it around to create entanglement maybe also measure it one thing you can also do is as Fabrice said the clock transition in bosons doesn't exist you have to induce it with a magnetic field to mix the states so you can imagine actually embedding an excited state fermion in the bath of ground state bosons if that if you can get that to work and should be able to see something there and one thing that is enabled by these large systems that is really a bit unique is the an idea that one could maybe even do quantum simulation of nano photonics where the the freely propagating atoms in in say the ground state mimic the the propagating photons and if you can if you can engineer the band structure of these almost freely propagating atoms and you can engineer band structures of photons and the excited and trapped atoms would then correspond to to the vacuum and the interesting part here would be that you could reach coupling strengths and and cooperativities that are difficult to do in real nano photonics systems of course I can't do that by myself so I have a great team here and these are two grad students who are leading this research is and any park sepan is a wonderful postdoc who's also working with us and is all done in immanuel bros group and of course there are many many interns and master students who are also contributing so thank you very much