 All right, so welcome everybody to today's CCQ Colovium and it's a really great pleasure for me to introduce a speaker who is Tracy Lover from the University of Innsbruck. Tracy is doing a lot of experiments these days with cavities and ions in different configurations and also the experiments with more heavy cast particles, but I think you're going to talk too much about that today. But just to give you a brief introduction to the background of Tracy. I mean, Tracy had made her bachelor degree at the Harvard University from where she went to Caltech and worked with Jeff Kimball as a PhD student and finished her studies there in 2008. And from then on, she actually won one of these nice rate fellowships to go to Europe and to go to the group of Reino Vladimir in Innsbruck and work with the drug giants. And since then, you have got several nice reward like stypins and say, I mean, prestigious stypins to do research in Australia from the Austrian Academy of Science and from 2008 until today, Tracy has really developed her own special direction of experiments with ions in Innsbruck. And now it's a group professor there working on her own group now, and it's a quarterly Facebook. And this has been extremely successful and been very pioneering a lot of work with ions in cavities. So yeah, with this, I'll just give the word to you. We can use thank you for a nice introduction. It's really a pleasure to be here, especially after this time of not so much traveling and interaction. It's wonderful to have the chance to talk to people in person and to present the work that we're doing. And I would encourage you, if there's something that I can stop and explain, please let me know. And I'm happy to do that, especially because I know that the center encompasses a broad range of different quantum topics, not only chat ions, although, of course, you have expertise here in chat ions as well. So I did want to point out, before I start, so coming from Innsbruck, and in case people here are very beautiful, but in case you're thinking after your time here that you might want something with a little more mountains, please consider, working on quantum physics. It's not so snowy anymore right now, but it's a beautiful place in the middle of the Alps to achieve physics. So this is where we are. And as we have mentioned, I came from the US. And often when you're traveling, which we haven't done much of these days, you end up never maybe forgetting to bring this kind of thing along. So this is some kind of a classical interface, right? But it's not a particularly fundamental problem that it's solving, right? It's a problem that we came up with ourselves. I wonder about the resolution, actually. I didn't notice this before, but is it a problem for you? I don't have the right eyes for that. No, we can see fine from here. You're fine. OK, yeah. So as long as you can see fine, yeah. So this is maybe our own problem, right? We wouldn't need this. But I would say that quantum interfaces on the other hand, this is going to address a really fundamental problem. In what sense is connecting quantum systems with a fundamental problem? It's because we don't think that there's going to be some single quantum platform that lets us exploit all of the wonderful ideas that we have and applications that we have in mind for quantum systems. And so you might just have to hold out a couple of examples. Maybe you might think that trap ions or super-connecting qubits are among your favorite systems for quantum computing and maybe neutral atoms are what you might think of for quantum simulation. And I should make these examples, for example, as quantum sensors. So all of these things, clearly, you can make arguments for different applications. And I'm just giving these as examples. But clearly, I think when people talk about quantum communication there, we know that we're looking at photons traveling at the speed of light. So we have this sense that we expect, even as quantum research and technology continues to develop, we expect this to be a world where there's really a diversity of different platforms. And I would say not only is diversity of platforms, but also we don't think that they're going to be working on their own little islands. We anticipate that connecting these platforms to one another and building hybrid systems will be something of fundamental value and interest and will enable fundamentally new capabilities. So these ideas of connection is really interesting. How do we link together photons and atoms and superconducting systems? And as you know, there's efforts worldwide that are underway to harness superposition and entanglement for quantum technologies. It's an exciting kind of work on these topics. You're part of a center here in Denmark in different countries. There are various national initiatives. There's this European initiative of the new quantum flagship coming out of this kind of document, this quantum manifesto that's where this picture is from, describing a beautiful timeline of progress over 20 years that's envisioned many different applications that we can look forward to. And so I think worldwide it's an exciting time to be working on these questions and to be looking at these kind of technological goals. However, what I wanted to emphasize for this talk is that we're excited about future technologies, but also I would say for myself personally, this is very fundamental research, part of what I find exciting about interactions between light and matter at a quantum scale is this fundamental aspect that we can, with tabletop experiments, study these interactions between quantum mechanical systems. So I'm hoping that I can give you today a sense of this, a sense of the excitement in these experiments that we're doing. And I'd like to kind of tell you that in three steps. So I want to tell you, first of all, about the particular kind of quantum interface is between trapped atoms, trapped ions, and single photons. And so I want to give you two ingredients that is how we can trap the atoms and how we can trap the photons. And once we've got these ions trapped, I want to describe to you how we can use them for quantum networks. And then I wanted to tell you a story about how we've then taken two of these ion trap systems and built a link between them and recently showed that we can and can't go. So that's my plan. And I want to describe to you then that the vision here is, in terms of this quantum interface, is the idea that we could construct links between remote quantum systems. And by links, let's talk about linking together quantum nodes. So these little individual oscillators here are supposed to represent quantum systems where we can do computation or simulation or sensing. So we have the ability to prepare, store, and manipulate quantum states and, of course, read them out. And then we want to be sure that we have channels that link together those quantum states. And so this is kind of this vision of a European scale network. We can also imagine networks on much smaller scales that we could imagine, for example, for distributed computing. It might not be necessary to have a kilometer or scale network, but rather a much smaller scale network. But very broadly, the question is, if we want to have a quantum network, we can ask ourselves, how can we distribute entanglement efficiently and with high fidelity over a long distance? This is a slide from a EU flagship project that my group is a part of that's this aiming to look at this one. So I told you I wanted to give you these two ingredients. And the point of this slide is to show you that there's really a diversity of different kinds of very different-looking objects that can all trap ions. And you can, of course, see some of them yourself here in the house group. So these are, this is a kind of an Innsbruck-centered slide. These are two different traps from Ryder Blot's group. Then I wanted to sort of show you a couple of different US traps here on the right and on the left that are kind of showing that the transition to sort of chip-based traps. And this is actually also a trap that came out of NIST, but this is our own version that we've been using more recently in my group. So the point is basically to show you ion traps can look like a lot of different things, but the unifying feature for now is that this is about electromagnetic fields providing some confining potential for charged particles. So we're going to use in our case radio frequencies to confine these charged particles. What about light, though? So we want light interacting with these charged particles. How do we trap the light? Well, we use highly reflected mirrors. We put them facing each other. The light bounces back and forth. And by back and forth, they mean hundreds of thousands of times before it escapes. And so what we're doing is we're confining this interaction between a particle and the light to this very small mode volume. And this goes back to experiments from now, more than 20 years, 25, 30 years ago, from Sarah Torosha's group, working with mutual Rydberg atoms here traversing optical cavities. So in this case, you can picture these microwave cavities not optical, but microwave cavities here confining single microwave photons and atoms that are flying across. And also, here, more atoms flying through cavities in the early days of work with optical fields and non-Rydberg atoms, normal atoms, flying through cavities. And then that kind of pioneering work with atoms and cavities has since been extended to solid state systems to superconducting qubits, cobalt microwave resonators, or, more recently, Niting-Bingley centers, quantum dots, also cobalt optical resonators. So this kind of model is using a cavity to confine a single photon, a quantized cobalt to magnetization, and so that you can get engineer a very controlled interaction with single spins. And I'm going to talk about atoms and ions, but this is a more general phenomenon. So OK, we're going to trap ions, we're going to trap light, we're going to put them together. And in particular, I've described to you already what we want to do with them. We want to use that as an interface for quantum networks so that we can transfer information that we're storing in these ions to other dislocations. So that was the vision that I gave you previously. Oops, and now I pressed the wrong button. There we go. So I want to now kind of briefly come back to the topic of trap ions and point out that in particular that they have some really nice properties for quantum networks. And so I'm emphasizing networks here rather than quantum computing, because maybe that's more familiar that there's a lot of really nice gate operations that you can do with ions for computers. But ions are also very nice in a network scenario. So again, this is not going to go into much detail all about how ion traps work, but here I want you to picture that we have some different electrodes here. We're putting radio frequency on, you would say, four. But actually, we're grounding two of these, and we're only putting radio frequency on the other two electrodes. And that's enough to provide confinement in a two-dimensional pseudo-potential, so in the plane that is orthogonal to this direction along this axis, parallel to the electrodes. So that's giving us two-dimensional confinement through the radio frequency field. We apply DC voltages to these, so about N-cap voltages to the right of the climate in the third direction. And that's allowing us to trap ions in a so-called linear palm trap. This is this pseudo-potential. We're working in an ultra-high vacuum, maybe in the realm of a few times 10 to the minus 11 millivar. Why do we need an ultra-high vacuum here? We are interested in avoiding primarily collisions with background molecules that would then turn our ions into other things. We're not so worried with the ion trap about them just leaving on their own, because the trap depth is actually very deep. So the trap depth is on the order of 10 electron volts. So kind of thermally, they're not really going to leave on their own. But and trap frequencies, kind of megahertz trap frequencies. But yeah, we want them in UHG so that there's no chemistry going on. And then what's beautiful of these trap ions is that we can come here and manipulate them using lasers. And what I'm going to try to do, other groups are working usually always with lasers for some aspect, in particular, cooling down the particles, but often with microwaves for the coherent manipulation and controlling both the electronic and emotional degrees of it. So along this axis, we can find long strings of ions, which is maybe something like 50 ions spaced about five microns apart. What are we looking at here? We're looking at a camera image of fluorescence and the ions where they're being excited over and over again and we're collecting some of the light on the camera. And then this is also camera images that are showing you the emotional modes, the shared emotional modes, some of them, of those ions. So why do we think of them as coupled oscillators? Because they all see the same confining potential. But they also have this coulomb repulsion between one another. So that's where you get this kind of coupled oscillator and then these modes actually have frequencies of not hertz scale frequencies, but megahertz scale. So those are trapped ions in a nutshell. And what are we interested in? We're interested in linking between this and perhaps. And so that is something that people have done less work on. So the pioneering work has been on the past, which has been a lot of focus on competing with these systems. We're interested, however, in linking traps to one another. And what I wanted to kind of review is the first work that was done in this, which is with remote intermium ions from Chris Monroe's group, formerly from when he was at the University of Maryland. Actually, some of it's even from when he was in Michigan. So just a picture of how you can entangle remote ions. Ions in one trap, ions in the other trap. This is a picture from there, 2002, a paper published in the first work on entangling ions and photons back in 2004 and ions and ions in 2007. So here's a picture, two ions in one trap, one another. The first step is to entangle ions with photons via spontaneous decay. So here's an image of this particular intermium system where the ion gets excited to a higher line that has two decay channels, two different single polarized decay channels. And then, so that the polarization of the decay channel, that is the single photon that's emitted is then entangled with the final electronic state. So now the ion state is entangled with the photon state in both atom two and atom three. Those photons travel to a beam splitter. The beam splitter erases the which path information that's after the beam splitter, we no longer know which atom generated which photon because it could go up or down at either pace. And then at the end, there's some detectors and that detection event projects the atom into an entangled state. I'll come back to this in a little more detail on another slide, but this is what was done in this first experiment. Measurement here then prepares an entangled state. And so in particular, then you can say, well, okay, what are we talking about for an entangled state? You then compare it with respect to a maximally entangled state. So what you want to do is you take the experimental state that you construct and you project it onto a maximally entangled state. You get this so called fidelity, which would be 100% is perfect. The classical bound is 50% because it's highly entangled. It gives you also a highly entangled state between two ions, which were in this case in different vacuum chambers, like in the same laboratory called the T-bolts, maybe a couple meters apart. And so how often can you do this? You know, in the first experiments that they did it, I think it was about kind of one entanglement event every maybe eight minutes or something. And so that's a long time where you're sitting there in the dark in your laboratory waiting for something to happen. They certainly sped that up. So it's kind of, you know, once every four or five times a second. And this is really beautiful because the coherence time of the trapped ions, in this case, was longer than a second. So this is actually this kind of experiment with this remote spin entanglement has been in a handful of different platforms. But this was the first example where a remote entanglement was generated faster than you use it for deep coherence. And that's kind of, I think you can understand that it only makes sense to talk about building up these, this entanglement between more and more systems if you can pull onto it faster than it falls apart, right? If it's kind of falling apart faster than you try to build it up, then we shouldn't make it any more complicated. And so since there's been one other demonstration as far as I know with nitrogen and vacancy centers in the Neural-Hansom's group, more recently, different ion species, strontium in Oxford, David Lucas' group, higher fidelity's faster entanglement. So those two systems are currently the state of the art for these ion-tropic experiments and the two groups that have demonstrated remote entanglement. And so the question that I want to kind of answer for you today is whether we can construct an ion photon interface and generate remote entanglement with a different kind of interface, a coherent interface rather than one that's based on spontaneous emission. And then just to remind you about this spin photon entanglement and how it enables remote entanglement, I showed it to you in the context of these trapped ions in this first demonstration, but I just want to go through this again because it's more general, right? It's really a building block for how you can entangle remote spins in general in a network. So here's a picture, you have a little, you have a spin, an atom, an ion, you have a photon, and somehow if you have some technique for entangling your spin with your polarization, for example, or some degree of, yeah, here we're entangling the polarization, degree of freedom with the photon with the spin, then you send those polarized photons to a non-polarizing beam splitter because they can go either way. Here you erase that information, after that you have some polarizing beam splitters that allows you to detect different possible polarizations. So for example, here, the detection of two different polarizations on two different beam splitters will project us into the state up down minus, down up, so one particular spin state. If we had gotten detection events on opposite sides of the same output of the first beam splitter, it would have been up, down, plus, down, up. So the detection pattern tells us which particular, projects us onto, in this case one of two, two of the four different bell states. And I'm describing to you a detection scheme that's based on detecting both photons, but there's also ways that you can generate the voltage element based on detection of a single photon. So this is, again, I just wanted to kind of outline that kind of broader principle, which is not just about ions or atoms, but can be used for generally first-person systems. That brings me to the results that I want to describe to you, that we've, yeah, what we've been working on in Innsbruck with these trapped ions, again, if there's any questions that you have, please feel free to stop me at any point. So now we're gonna dive into looking at pictures of our experiment and then drawing pictures of the atomic level diagrams and talking about what does this mean. So this is now a picture of an optical cavity. It's the kind of thing that you could hold in your hand with an ion trap inside it. So this is the kind of ion trap I showed you before for radio frequency electrodes and two end cap electrodes. And it's now tilted 90 degrees in this picture with respect to the cartoon. And then the cavity that might be a little bit harder to see in the mirror here on the left and on the right. So what you actually see is kind of the aluminum or stainless steel actually holders that are competing highly reflective mirrors. And so there's light then that can bounce back and forth between these two mirrors, which are about two centimeters apart. And so this really brings us back to kind of ideas that have been around for, again, more than two decades now about how you could communicate between remote systems. So this is a paper by Jeff Kimball called The Quantum Internet from 19, from 2008 in nature, describing transfer between, again, it's exactly this kind of system of an atom in a cavity. So what's the difference between this kind of cavity-based system and the spontaneous emission that I was describing to you earlier? So the spontaneous emission is generating ion photon entanglement, which we can then use as a resource to entangle our remote systems. Here, because the cavity interaction with the ion, this is an electric dipole interaction. This is a coherent interaction. And so it offers us the possibility for a couple of different routes to linking together systems. I'm going to tell you a story also about entanglement that you could do in the same way you could do in a similar way with spontaneous emission, but cavities also offer the possibility to do something that you see sketched out here, which is to use a cavity-mediated raw wood process to generate photons that could be an absorbed by our remote systems. So what this picture is highlighting is kind of the, one of the strengths of using a coherent platform that is this cavity-mediated interaction between this dipole interaction between electric field and spin. Let me tell you a little bit more about that. And so let's kind of draw some atomic level diagrams and talk about our own process. We're going to see that what we see here is again this cartoon, we have an ion and we got rid of the blades for the ion trap. So we're just kind of remembering that's in the ion trap and we see just a little end cap electrons here and the mirrors in the field that's confiding the light field. So now we talk about some atomic physics and the simplest picture here is the picture of three levels. So we're going to picture a ground state here. This is a metastable state of calcium, but you can think of it as a ground state. It has a life of about a second and this is an excited state. So we're working with calcium 40. Why would we work with calcium 40? People have been using it for a long time for quantum computing. One of the nice reasons, actually, also for quantum computing is it has a nice set of laser wavelengths that are compatible with things that you can buy and work with quite nicely and that's even more so true for quantum communication where the wavelength that I'm going to be telling you about that we want to send over obstacle fibers is in the infrared. Not as good as telecom, which would be ideal, but still pretty good for communication purposes. So calcium 40 here, the ground state, metastable, excited state, and then I've drawn a couple of different arrows here. So the first arrow on the left is telling you about laser transition from the ground state to the excited state. The second arrow on the right is describing to you how we can couple the cavity to the, slightly to tune from the transition between the metastable state and the excited state. I'm finding this a Roman process and you might be more familiar with a Roman process that involves two lasers, but it's the same idea. So in general, when you maybe learn about Roman processes in atomic physics, you talk about using two lasers to couple two ground states that without populating an excited state. We're doing the same thing. We're interested in coupling the population between these two ground states without populating its excited state, but not with two lasers, instead we've replaced one laser with a vacuum field of a cavity. So I want to emphasize that I am vacuum field, so we're not going to drive this cavity. We're not going to populate it with light. We're just going to let it sit there, but it still has, it's still supporting the state's mode that's determined by the distance between the cavity measures. So we put an ion over here in the state, this is a little green dot. What does it mean to put an ion in the state? It means that we trapped it in our ion trap and then we cooled it down so that it was well localized. In the experiments I'm describing to you, we just need to sort of dock or cool it so that means that we take out, we get it to sort of about the lowest 10 phonons in the emotional states in its trap, and we pump it into this particular electronic state. So we've got the ion ready, and most importantly, we choose that the ion is now coupled to the standing wave, that is we really make sure that it's standing here, that it's here, just like in the sketch, that it's at a place, it's at the maximum of the standing wave of the trap so that it can have a maximum interaction. Then we turn on this laser, and because we've matched the laser and cavity fields, so the frequency difference matches the frequency difference between the left state and the right state, that actually allows us to use a photon from this laser to hold the atom from the left state to the right state generating a photon in the cavity. So we use one laser plus the energy difference to pull a photon out of the vacuum, put it in the cavity where there was no photon before, the ion is over here. What happens next? Well, that was a coherent process, so it just would go right back and forth, right? We would actually reabsorb this photon, go back over here, left, right, left, right, that would go on forever, except this is not simply a unitary system, there's also decay, and so the photon will eventually leave the cavity through one of the mirrors, that would be the best story. The worst story would be maybe the photon actually gets absorbed in one of the mirrors, or maybe we do accidentally excite to the state and we get spontaneous decay. So there is some absorption of decay, but ideally we have the photon bounces back and forth until it's transmitted through the cavity. We can tell where the ion is if we introduce another laser here, this is marked with three and eight seven millimeters that couples to an additional excited state. And so that laser has a very fast decay rate, and it couples only to this state on the left. So if we turn this laser on, then we see fluorescence that tells us, yes, we were over here in this left-hand state. If we turn the laser on and we don't see fluorescence, it tells us we were over here in the right-hand state, which doesn't couples about it, or we can tell these to the left-hand state. So we can figure out where the ion is, and we can also coherently manipulate the ion because this is a quadruple transition here, so it's dipole forbidden, but we can couple to that quadruple transition with a nice laser in the infrared that's a titanium sapphire laser, which we can stabilize to a very narrow line. So this is all about manipulating calcium ions, and in particular coupling them via a ramen process in order to generate single photons. We haven't entangled anything yet, we're just generating single photons, and so now I'm gonna describe to you how we entangle things. And before that was a story, remember about spontaneous emission, and now I'm describing to you how we're gonna do this in a coherent process enabled by the cavity. So this is the same picture that I described to you before, how to make a single photon, and we essentially double it. So what did I do? I copied the D state, and I made another state, and I called it D prime, and I can do that because this D five-and-afts state is actually a manifold of six different Zeeman states, so when we apply a magnetic field that splits out those states, and we have six different states, and we pick two of those. And they have some splitting here, some energy difference, which is because of the magnetic failure we applied. So there's an energy difference here, and now I can couple my original state to D or D prime if I choose two different laser frequencies. Why two different laser frequencies? Because the cavity frequency state the same, so the red arrow frequency is the same in both cases, so in order to match this Raman position frequency, I need one of two frequencies over here. So this is why we describe it as a bi-chromatic Raman field, and in fact it's actually the same laser that we use when we drive, and it can stop and modulate over two different frequencies. So what does this do? It means I can go from S to D, and in this case we've chosen the transitions that we generated a horizontally polarized photon, or I can go from this state S to D prime, and in that case we've chosen it so that we get an inverted polarized photon. So we have these two different polarizations, S can go to both places, we balance them, and we balance them in such a way that they're maxed, that we get a maximum entangled state. Why do we get to claim that it's maximum entangled because of the coherence of these two processes? Because there's a phase relationship, a definite phase relationship between them, and so it's not just, we don't just get to write down a sum, but it's coherent. Great, if we don't believe it, we can, yeah, write it down as nice, but what we do is we actually do tomography of the joint ion photon state. What does it mean to do tomography? It means that we try to generate this entanglement, and then we measure the ion in different bases, in three different bases, we do that by rotating the measurement basis with that 729 animated laser that I described to you, so we can rotate the ion measurement basis, we can rotate the photon measurement basis by changing the polarization in front of our detectors, and that allows us to characterize the joint state of the ions in the photons, and we can then here compare the density matrix that we create in the lab with the maximum entangled state, and we see that it is a very highly entangled state, this is primarily limited by dark counts on our detectors. So, another beautiful thing about this coherent process is that we have a great deal of control over the entangled state of ions and photons that we generate, so if you generate ion photon or spin photon entanglement against one continuous emission, you're kind of at the mercy of your Clebsch-Borden coefficients for the state that you're going to end up with. Here, we can choose the relative phase of our two components by varying the relative phase here of the two laser fields that drive it, so this is the four-quadding phase here on the x-axis, and we see that the coherences of the two components oscillate, but the fidelity remains very high, so we can choose the phase of our entangled state, we can also choose the amplitude of our entangled state because we control it with this laser where we can set the amplitude and phase. Total amplitude and phase, we can also tune a temporal weave packet of this photon that comes out of our cavity. Again, we choose that by controlling this laser. So, this is a picture of the temporal weave packet of the photon, you can see if you're, you might be surprised it's a very long photon, since this is the time is in microseconds, so it's gonna generate a well-defined cavity in terms of time, and it's generated in a well-defined cavity mode in this photon, so it's nice, it's coupled and it's not going everywhere, it's coupled into a very clear mode at the end of the path. We did an initial experiment after we'd done this some years ago entangling two ions in the same cavity, and we did that by entangling each ion at the photon, and then essentially the two photons left, and we measured them in the way that I described to you, and that allowed us to entangle the two photons in the same cavity. But really what we really wanted to do was to go ahead and entangle two photons in different cavities, and that took us several years more, because yeah, we had to build up a whole new system. That was actually work that my colleague, Bill Lanyon, has done in the past several years with his team in a different building and his work, building up a new setup. Work also that Ben's group has pioneered, so I was kind of part of this work, but this is really from Ben's team, is about showing that this ion photon interface has near optimal efficiency. So we can show that this probability to generate a single photon saturates that an analytic bound. So this is looking at, what's the chance that you made a photon in the cavity, and it can come very close to unity, essentially. And more than that, you can kind of do it repeatedly in order to make photon trains, sort of sticking out pulses of photons leaving the cavity, and that can be a nice resource, for example, for cluster states. Okay, so everything was about one cavity so far. Here comes the part that I wanted to kind of lead up to, which is how we've entangled two remote systems. So I've been telling you about work here and this system in my lab here at the University of Innsbruck. And as I described to you, my colleague's team is in a separate building about, so about 500 meters away for a long time. At 510 meters, we only recently measured it, or figured out how to, that it was written on the fiber cable of the distance. For a long time we thought it was only 400 meters. And it connects to something that looks very similar. So you may, this is the newer shinier version, it's shinier because the ion travel blades are gold-plated. And it's actually very similar in terms of the separation between the mirrors and so on, whoops. So we want to entangle these systems, what do we do? We entangle each ion with a photon. Here is the reminder, spin photon entanglement as a step to a remote photon entanglement. And what I want to remind you here about is that non-polarizing beam splitter and the fact that what we need to do is to erase information about where the photons came from. And that means that the photons need to be indistinguishable from another. So we have two different systems, but they need to generate photons that carry no information about where they came from. Why might they carry information about where they came from? Well, they are physically different cavities. And the cavity does sort of shape the photon temporally as I described. So we do have to make sure that the cavities are really behaving in an identical way. So this is kind of the first thing that we look at where we're generating single photons from the two cavities and I plug them here on top of each other. And you can see that they're not actually identical but they kind of come pretty close. You can also see that there's a lot more counts from node B, that's the one on the right hand side than on node A, because our detectors are over closer to node B and also because node B is more efficient. But we only care about sort of the absolute scaling. So my argument would be that it's not perfect, but these look pretty similar in terms of temporal indistinguishability. So that's temporal, but you might also worry about spectral indistinguishability and you should worry about spectral indistinguishability and we do. And so that was, again, back to the story. How do we find out about spectral indistinguishability? We look to the Hong-Wen Mandel effect which tells us that if the beam splitter photons are really indistinguishable, they will always leave the beam splitters at the same port, this original non-polarizing beam splitter. So both of them will go here, both of them will go there. And we won't get any coincidences between the left and the right hand side like the one I'm sketching out for you here. So is it true? We measured it. What do we see here? In the case of a blue, we're looking at the difference in detection times between the photons from the two setups. In the blue case, we're artificially making sure that they are distinguishable and then we actually get the most coincidence events when they arrive at the same time. But in the red case, we've chosen them so that they shouldn't be distinguishable, we've chosen them with the same polarization, they should arrive at the same time and we see that actually, yes, we really don't get any counts here at zero time or very few counts that are, so kind of just, yeah. So this dip here that is consistent with, right, that tells us that we have a very high indistinguishability with the beam. So that was kind of laying the groundwork to say, yes, we really do believe that the photons are distinguishable. So now we were ready to kind of start entangling things. We had to sort out a lot of, you know, check out that we could really get our timing synchronization correct between the two labs. We had to make sure that we were synchronizing the frequencies correctly by comparing classical light fields over a classical fiber, over optimal fiber between the labs. And we really needed to make sure that we had stable polarizations and you could do that by interrupting your experiments and periodically compensating for polarization rotations. So we do that kind of by every 20 minutes, we check if the polarization is rotating on top of the fiber and then we correct that. Yeah, then we make a photon here, make a photon there, send them to a beam splitter. We think we should make entanglement. How do we check it? We come back to the same concept of tomography that I described to you before. So we want to do here quantum state tomography for the two ions. So it means that every time we detect two photons, we go back to the ions in the lab and we want to say how, you know, what is our joint density matrix describing the two ions? That is, we measure the two ions. Each ion can be met, we can measure in a poly XYZ basis. So three times three is nine total possibilities. And that lets us extract the joint density matrix for the ion. And that density matrix tells us everything about the system. And so we can then use it to extract various entanglement measures. Yeah, just to remind you, what do we mean by a measurement? Measuring the ion is literally saying, do I see a camera imaged as bright or dark or in particular PMT counts that are bright or dark? That is, is the ion in the state F, or is it in the state D? So we do a lot of these measurements, thousands of them, quantum state tomography. And then this gives us a density matrix that looks something like this. Okay, what are we plotting? We're plotting the different final states here of the atom, whether it's in D or D prime. And you see, first of all, that, you know, that there's four entries. So that the ion, when one is in D and the other is in D prime. And we never have them in the same state. That's a good sign, because that's what we wanted for an entanglement. But it's not enough. We need some coherence between them. And we do in fact have that, which we see when we calculate the fidelity with respect to this target state. So this was the case where we got two different clicks on opposite detectors. We see that the fidelity here is about 83%. Again, well above a classical bound. So this is kind of this first measurement that allows us to say, we really didn't handle these two ions from both labs. We don't need to look just at this one state where we get the type of an opposite click, but we can also look at the symmetric Bell state up down plus down up. There's the different pattern that I'm showing you. So we get another different density matrix. This is actually, yeah, sorry. So the, what's different here is the phases. So you can still see that in both cases we get D prime and D prime D, but the phases of the different components has now shifted. And there we get about 89% fidelity with respect to a maximum intended state. I want to actually, yeah, clarify something that what we're choosing to do here is we're looking at only photons that arrived within one microsecond of each other. So we look at photons actually in this region here, between zero and 20, about 17 microsecond window, there's about like a 17 microsecond window and most of the photons arrive. So we look there to reduce our sensitivity to dark counts, but we also look at photons only that arrive, kind of, yeah. The second one comes one microsecond or less after the first. Why do we do that? Because if we look for longer times, there's more of a chance that spontaneous emissions occur. So this is a nice story in terms of fidelity. We can restrict ourselves to this kind of, to this case in order to get the best fidelity, but it does cost us something in terms of the efficiency of the penguin. So here's a full story. I can choose the detection of the window here, the arrival window, the data I was showing you here was at the top of this fidelity plot and as I open up the arrival window and look at more and more photons, the fidelity still stays non-classical above 0.5, but it goes down significantly while the efficiency goes up. So we have a trade-off here that comes from the fact that the Roman process isn't imperfect. There's some chance for spontaneous emission. How could you get around that? You could have a cavity with stronger coupling as compared to spontaneous emission. That was two nodes of a network. They were entangled with each other. We wish we had three nodes, because that would be even more fun. So these are the two I showed you before and it still says 400 meters there because I forgot to change it and like I said, we only figured out more recently and it was 510. And this here is another cavity system that I'm working on in my group and it's hard to see why that should be a cavity system. It doesn't look like the other picture, so let me show you a little bit more about it. So this is a system in which we're trapping an ion between two fiber mirrors. So these are little optical fibers, the mirror stacks on the end of each fiber. And we haven't yet coupled the ions to the cavity at the single photon level, so that's what we're working on now. I want to mention that we have recently used this ion photon fiber cavity ion system to test electric field noise models and ion traps. So we essentially are interested in understanding how much the presence of a mirror or a piece of dielectric in general affects the noise that the ion sees. So what we can do is we can control the distance between the dielectric mirror and the ion and that lets us measure the heating rate of the ion as a function of how close the mirror is to it. And so we were able to understand, actually, the role that this dielectric plays and we got really nice quantitative agreement with the model that's based on the fluctuation participation theorem that essentially is saying the fluctuations of the dissipation in these dielectric mirrors due to the motion of the ion then generates losses here in the, then essentially generates heating at the ion. So it gives us new insight into heating rates that are an important factor for ion trap quantum computing upon network experiments. Side note maybe for a kind of specialist in the field that I kind of wanted to mention what we've been doing with this third node and what we'd really like to be doing with it of course is linking it up to the other two. We're hoping that we can bring it online soon as a new system. Yeah, but the motivation really is that these miniaturized systems are kind of nice and scalable but there's also some challenges that we shouldn't sweep under the rug about surface-related electric field noise. That will be really pretty crucial for future computers and for quantum networks. And so that's the question that we're going to have to solve in order to bridge the gap. So this is kind of systems I showed you about, right? These are systems that you build by you, I mean a graduate student, many graduate students, postdocs working together. You build over several months. The vacuum system is assembled over years. When you step back and think about how you could scale that up in terms of having more systems it's nice to sort of think about these compacted modular systems that are based on optical fibers but one thing that we're going to have to worry about is new problems that arise, for example, with electric field. We're also working then in collaboration with colleagues in Seoul on integrating these little MEM systems for translating optical fibers. So this is a proposal that we wrote a couple of years ago and we're now setting up a new experiment to examine integrating fiber having to be surface-related tracks. So I want to just come back to this question that I asked at the beginning about connecting different kinds of systems. What I've shown you is that we can connect these ions and distant cavities. And yeah, so this was a picture I showed you also at the beginning. I wanted to point out on this scale, look these two ions in different cavities, right? You can't even see the separation at the level of this scale. And so we're really excited about this link between these systems and two different buildings because it meant that we had to operate them truly independently, running on separate laser systems, separate laboratory control systems and really establishing that we could entangle them in that way. But what we'd love to be doing is, one of them communication protocols on scales of metropolitan areas and even on scales of kind of national and international maps. And so that's gonna require different kinds of experiments. Something that's exciting about ions from that perspective. I told you that the wavelength that we're working at is the red translates very nicely to these long distance optical fibers. And you can also use frequency conversion, quantum frequency conversion to convert it to telecom which has been done also in my colleagues or in my family, they've done some nice quantum frequency conversion to ion, telecom and pangolin. So I think there's some really nice perspectives from going from these kind of hundreds of meter scale experiments to much longer distances. Let me wrap that up by showing you that the people who worked on the project and thank you very much.