 Welcome everyone to our special film, today is slightly unusual time, but it's my great pleasure and honor to welcome Arno Außenburg, who visited us for today from Berlin. I think many of you know Arno from the pioneering experiments he has been doing over the years and inspired a lot of our work. And let me just say a few words, so before he did, Arno actually studied physics at several universities, as I just found out at Düsseldorf in London at the Imperial College and at the University of London. And then right after he again moved place and he went to Paris to pursue his PhD with a group of searchers, where he actually worked on some of the experiments that later were awarded with the Nobel Prize to search. And since then, basically Arno had, between 2005 and 2017, he was holding several professorships like Michael Mainz at the University of London and then in the end at the Technical University in Vienna. And since 2018 he is now at the Humboldt University in Berlin, where he is still now holding a chair for optics and electronics. And so there's a list that I'm not going to hear of national and international awards that Arno has been receiving for his research and for his results. So I think like most recently it's the Humboldt professorships, which is kind of the most prestigious award for international scientists that we have in Berlin. I'm looking forward to hear about your latest results and as I said, it's fair to say that Arno is a true pioneer in our field, so he has been setting the stage for this field of nano fiber optics and nano fiber optics. Quantum optics, so I think even back in mind, he had this brilliant idea to pursue this idea of pulling fibers to these extreme scales where they become like the thickness of just a few nanometers or thinner than our hair. And since then he has been doing a lot of inspiring experiments and led to many ideas like for fundamental science but also for applications and I think still continues to amaze us. So I'm really looking forward to the award. Thank you Tomas for the kind introduction and thank you for having me. It will be a dense day and I already learned a lot of interesting things and so interesting things. I'm looking forward to seeing more of you and your work and I'm very happy to show you some of ours this morning. So the title of the talk is pretty generic but it has ended what we are essentially working with or have been working with for more than a decade now, which is waveguide coupled atoms. And since I will be talking about several experiments, I just put how a simple quantum optical system can amaze you. And simple it is as Tomas said because it's just a waveguide with atoms coupled to it. And I say amaze you because I tend to be amazed, I hope that you won't be bored. And I would also like to start with a disclaimer. So some of the things I will be presenting I have never talked about, I mean I have never given a talk about. So if you feel like I'm not explaining it well just ask questions. I'm very happy to stop and spend more time on things and I don't have to get through all the slides. I think this could be a good setting also for just having an interactive seminar. I would be happy about questions during the talk. One thing that unites the experiments I will be talking about is that it's about collective interaction of emitters with a single field mode. And to introduce this topic let us just imagine that we are looking at the emission of radiation by two emitters which are separated by much less than the optical wavelengths. In that case we can actually say that these two emitters interact with the same electromagnetic mode which in the Hamiltonian is just written here hand-wavingly with one annihilation and creation operator and the two atoms here coupled to this mode. And in the Hamiltonian we don't assume any atom-atom interaction. And then when you look at the single excitation regime so either one of the two atoms being excited and no photon being present or both atoms in the ground state and a photon being present. Then the basis states that we find are actually a superposition of E and G where we either have a plus or a minus sign on depending on whether there is a plus or a minus sign here we refer to these states as being super radiant or sub radiant. And the reason is that if we look at the transition rate so of the rate of decay rate of this excited atomic state then for this super radiant state with the plus sign here the coupling is twice as large so the decay rate is twice as large whereas the sub radiant state here has actually zero matrix element with the atoms having decay to one photon being present so it does not decay. And usually when it refers to the super radiant state also as the dicker state and we can generalize what I explained here to n atoms by just writing sum over all possible states of one atom being excited. And the only difference then if we deal with n atoms is that this transition rate here n is then sorry this transition rate is n times as large and we have now n minus one sub radiant states but all of them in principle do not decay. But here of course there are two things which in the experiment are not so readily realized one is that the emitters are very closely spaced and the other one is that there is no atom interaction even though the emitters are so closely spaced and the typical situation in experiments is that the distance is larger than the wavelengths. And then we can have states or excitations of these n atoms with single excitation where if the atoms are excited with propagating light with a wave vector k then we still have a dicker state which looks exactly the same as before so one atom being excited however now we have a phase factor here which corresponds to the propagation phase of the light from to the position of the nth or kth atom here so we have this e to the i car i k r j and this state still exhibits a super radiant decay rate however the enhanced spontaneous emission will now be directed because we have here imprinted this propagation phase so our ensemble of atoms will predominantly decay for example if it's excited from the left with the propagating photon it will emit to the right and what we now do is explore such collective effects in a close to perfect one-dimensional setting where we define this propagating mode using a wave guide which couples to the atoms and there's related works by Charles Adams Antoine Brouves and T. D. Toshikatori so check out their work on such phenomena and finally I would like to say that in the introduction now I was only talking about this single excitation regime here the situation can of course be generalized to more than one excitation being present but it turns out that then also the dynamics even on the theoretical level becomes harder to describe and to understand and we will also explore this multi-excitation regime so the outline is that we will talk about the collective radiative dynamics of such waveguide coupled atoms and one thing that we saw and we could actually see experimental evidence offers that in this time-dicker states there is a coherent coupling between the sub and super radiant states so such a sub radiant state will not stay sub radiant forever it's just a momentarily sub radiant state and also the super radiant state will actually evolve into sub radiant states then we will go from here these two are in the single excitation regime we will then go to the situation where we have more than one excitation and even close to almost inverted ensembles of atoms coupled to the waveguide and if I have time I will also then talk about the transport of light through this ensemble and how it modifies the photon statistics of the light that propagates through the ensemble so let's start with the collective radiative dynamics but before doing so I would like to thank the people who really did the work so first and foremost I have two senior coworkers Philipp Schneeweis and Jovi Foltz who supervised the sub-project on a daily basis and then the experiments were done by a post of my Ph.D. student initially which is Ashlyn Johnson and Martin Blauha Ashlyn is now with Markus Aspermaier and now the experiments gradually were taken over by the post of Ricardo Penetta and the Ph.D. student Daniel Lechner so I very schematically sketch our experimental setup as Thomas said we are working with ultra-thin glass fibers they are made by heating and stretching an optical fiber until the waist of this tapered optical fiber is thinner than the wavelength of the guided light in our case here 400 nanometers and if you now launch light into the fiber and you squeeze it into this very thin wire here then there's an evanescent field surrounding this nanofiber and if we now prepare in the first experiment simply a cloud of laser-cooled cesium around the waist of the nanofiber then this light couples to the atoms and what we then do is we launch resonant light which is resonant with the two-line transition of cesium which is pulsed so we actually use an electro-optic modulator to make pulses of say 150 nanosecond length and then we analyze the light transmitted that's the transmission of this pulse through the ensemble and we can also analyze the back reflection of the light and detect in both cases with single photon counting modules the pulse rise and fall time here is much shorter than the lifetime of the atom while the pulse length here is much longer than the lifetime of the atom such that we should see both transient dynamics after the switch on and switch off of the pulse and we should have a kind of steady state of the atoms at the end of the pulse before switching off so how do we now model the transmission of light through such an ensemble of fiber-coupled atoms for this we assume so-called chiral coupling meaning that the light that propagates through the waveguide from left to right can be absorbed by the atoms but then the atoms only emit into the direction of propagation of the light and there is no back reflection of the light I won't go into the details but indeed this is something that can be realized thanks to special polarization properties of the guided modes of nanofibers but it turns out that even if you start by assuming the chiral coupling you will find out that also if the atoms can in principle backscatter the light in general it will be enough to consider chiral coupling to learn about the transmission of light through the ensemble we can talk about why but take my word for it that if you want to know what is the output pulse after sending it through an ensemble of atoms it's enough to consider that the atoms only emit into the forward direction if they do emit into the backward direction it could be integrated into the loss so into the emission into free space under most circumstances so that's what I said here that it also describes the system dynamics for the case of symmetric coupling and in this case it's very simple to compute now the transmission of light so the amplitude transmission of light through the ensemble as a function of detuning of our light piles from the atomic transition frequency because it will just be given by multiplying the amplitude transmission coefficients consecutively of all atoms one after the other and the expression for this transmission coefficient per atom is given by the interference of the incoming light and the re-radiated light by the atoms and here we have this so-called beta factor appearing beta is the fraction of light that is emitted into the waveguide if the atom decays so beta is just the probability for an atom emitting its photon into the waveguide and 1 minus beta will then be the probability for emission into the radiation modes and gamma naught is just the free space decay rate and if we now want to know the temporal shape of the transmitted piles then we just have to decompose our input piles into its Fourier components then propagate all the Fourier components through the ensemble by multiplying the input spectral amplitude at detuning data with the transmission amplitude transmission coefficient and then take the inverse Fourier transform and this will then give us the shape of the output piles so then let's look at what we see if we do this so if we launch now light through the fiber so here I sketch the transmitted power as a function of time the light blue shaded area is actually the bare pulse so it's a square pulse that we launch into the fiber the blue dots are the measured transmission and the red line is the theory prediction for the transmission through the ensemble and this was done with around 900 effectively 900 atoms coupled to the waveguide which corresponds here to an optical depth of 19 and here we introduced the detuning and this detuning is like 20 line widths so it's relatively far detuned here and you see the theory prediction matches our experimental prediction very nicely and in particular what we see here is multi-mode ravi oscillations or collective ravi oscillations you see that the transmitted power exhibits oscillations at a frequency which corresponds to the detuning of the pulse but if you look at it you also see that this is not just the damp sinusoidal as you might expect from say ravi oscillations of an ensemble where each atom has a slightly different ravi frequency but we see that here there's a kind of reduction of contrast but then a small revival of the contrast and actually we can understand that if we look at the microscopic picture so in the sense that we now look here at atom number 1 atom number 100 in our array and atom number 600 in the array and we look at the excited state probability of each of these atoms on a logarithmic scale here as a function of waiting time and then you see that the first atom, atom number 1 which only sees the incoming laser light will indeed perform just a damp sinusoidal ravi oscillation so this is how a damp sinusoidal ravi oscillation looks on a logarithmic scale but if we now look for example at atom number 600 then we see that it starts like the first atom but then after almost already after performing a full ravi cycle here it stops and then oscillates in like reverses the phase of the ravi oscillation oscillates again, here again reverses the phase of the ravi oscillation so here you see it oscillates in phase opposition to atom number 1 and the same happens also for atom number 100 which first oscillates in phase with atom number 1 but at some point also here you see oscillates in phase opposition so it changes the phase of the ravi oscillation with respect to the first atom Is it okay to ask a question? Yes please You talk about atom number 1 and 600 and so I mean you don't understand, you have a fiber Is it either gas? It's in a cloud, in a laser coin For the moment it is just a laser-cooled cloud of cesium atoms Later on it will indeed be trapped atoms It looks like you talk about they're sitting in a row and it doesn't matter how they fluctuate in and out and does the distance to the fiber better the cesium? Absolutely, so we do So here we assume indeed, so this is just the model prediction to understand what's going on and you're absolutely right, if the atom is further away from the fiber it will have a lower ravi frequency if it's closer to the fiber it will have a higher ravi frequency and here we assume a constant ravi frequency for the atoms so for all atoms but you can show that the prediction that you find for the ensemble also when including the variation of ravi frequency from atom to atom leads to the same result 900 atoms, how do you know? 900 is that a bit? So what I said here, this 900 atoms are actually effective atoms I used this word when I said 900 which means that you take the average coupling strength of the atoms to the guided mode and then you have an OD per atom and what we really measure is an OD of 20 here and we divide it by the OD, the average OD per atom so this is effectively 900 atoms but indeed it's just an average number if you like for the average coupling strength and the model I'm showing here to motivate why we see what we see is a simplified model here where I assume that all atoms have the same coupling strength which will be the situation in later experiments but this one here is indeed a 3D cloud of atoms interfaced with the 1D propagating waveguide mode okay, thank you for the question okay, so this is just to understand really what is going on here so in this model where we assume constant coupling strength we see that actually if we sketch it here it's kind of the same thing as we plot here so here I sketch the probability of finding atom number 100, 200 or 300 in the excited state as a function of time and we see these damped Rabi oscillations for the first atom which go on and are just damped but if you look here, you see that the phase of the Rabi oscillations of atom number 200 switches phase after a while and you see these lines where the atoms switch phase and later the atom the faster it switches phase of the Rabi oscillations and there's even a second phase switch of the Rabi oscillations and the reason is that the atom number say 500 is not only driven by the laser but also by the fields that are radiated by all preceding 499 atoms and the re-radiated light field has a high phase shift with respect to the incident light field this is what leads to absorption so actually what we see here is an effect of the atom 500 for example interacting both with the incoming laser light and with the re-radiated light by all preceding atoms and this leads to non-trivial dynamics and in particular this leads to super radiant decay if you look after the switch of the pulse at the decay rate of the different atoms then atom number 1 just decays as if it was on its own and atom number 100 already decays much faster and atom number 600 much much faster because its emission is stimulated also by the light that comes from the preceding atoms so this is a super radiant decay of atom number 600 now if we want to understand better this super radiant decay here then it's better to reduce the detuning a bit because then the energy stored in the atomic ensemble is higher and so the re-radiated light has a larger amplitude and we can now look at the decay rate of the pulse here after exiting our ensemble after switching off the drive pulse and we see that this looks kind of exponential here so we can just fit the slope at the beginning and then look at this slope and derive the decay rate as a function of for example optical depth so this was recorded again for an optical depth of 19 but we can vary the optical depth by varying the atom number and what we see is that the pulse decay rate indeed increases with increasing optical depth so there is super radiant decay of the ensemble into the waveguide modes however there is one important aspect that I would like to highlight here when you are dealing with super radians and try to look then you would think about super radians being a process that extracts the energy of our systems faster than say for the individual atoms the decay rate of the individual atoms but what we see here is just how fast the light switches off so the question is is that the same so do I when I see how fast the fluorescence from the atoms decays does that give me a good indication of how fast the energy disappears from the ensemble and interestingly if you now use the model that we have and compute because here we have a model Laguerre polynomial and this is what gives us here this switching off that after a certain waiting time the state of the atoms is fully sub radiant with respect to the with respect to the guided fiber mode so to explain it to you what I'm sketching here is the excitation amplitude which is in the case of resonant excitation a real is a real number so and it can be positive and negative and what you see is that while in the beginning I will have a state where all the atoms have positive amplitude after a while from this atom onwards due to these atoms being driven by the light emitted by the first 250 atoms here we have a sign change of the amplitude of the following atoms and if this area here is the same as this area here then there is destructive interference of the emission of light and this is what is predicted and happens here and then after waiting another time here of 30 nanoseconds then these atoms here again get this sign change because of the ravi oscillations stopping and turning the other way around so that I have now like positive, negative and again positive amplitude and again the interference of these amplitudes will add constructively and this corresponds again to a sub radiant state so when the filter goes on we have seen it's not visible here up to three like minimum of fluorescence emitted into the mode so maybe here is a good moment to ask for questions yes in your previous experiment if you change the time between the pulses this explanation that you get that it's a dynamical thing between the atoms that are in the ensemble will you see a change in this amplitude of this flash? as long, ok so what can happen if in this experiment I could change the time of the pulse of the time between the arrival of the pulses by simply making the fiber loop shorter and interestingly it's a question that we ask ourselves what happens in this case what you see will be a transition from waveguide quantum electrodynamics where you see just the single pass of the light through the ensemble and then how the light evolves to cavity quantum electrodynamics as soon as the pulses start to overlap it means that the modes of our resonator become so closely spaced that frequency components of the pulse excite several modes or in the time picture pulses start to overlap and we did experiments we are writing up the paper now where we changed the length of the fiber loop and could see a continuous transition from the dynamics I am presenting here to Rabi oscillations of an atomic ensemble in a cavity which however in the transition regime have these kinks and super flashes that come from waveguide quantum electrodynamics so actually you can we are able now to perform experiments which really unite two fields so to speak waveguide QED where the light passes once and cavity QED where you have periodic boundary conditions and if you make it longer like if you weight more nothing happens yeah you will not have these super flashes anymore oh yes the length as long as this condition is fulfilled the output will always look the same because all that happens is that my pulse propagates 20 more meters through the fiber loop nothing happens because of that as long as the atomic ensemble had had the time to decay and forgot about the pulse I can make the pulse propagate 40 meters or 400 meters okay there may be some losses because of propagation in the fiber but since this is here linear response theory it does not matter if the pulse reduces in amplitude a bit it is about the shape of the pulse the temporal shape of the pulse that dictates the response of the atoms and not the amplitude if I have a bit of losses it wouldn't change anything so the signal will look the same for a 100 meter long fiber skeptical yeah maybe I didn't understand well the effect of this stored energy inside the ensemble but I thought it was some kind of it has to be one long ensemble effective yeah effective super long ensemble effectively just increase the distance between some random atoms but purely in the ensemble yeah exactly it would be the same for example if you had one long ensemble of atoms with an od of 100 it doesn't matter if I change the line density of the atoms and like if I increase the inter-atom spacing by a factor of 2 I get the same result if I keep the optical depth the same yeah okay so I now I used up my 45 minutes that Thomas was calling out he's not here I mean I will skip the fourth part of the talk for sure but I could go on for another 5 minutes with the third part of the talk if you like I mean the fourth part is something that you probably know already anyways but this is what I now show is actually much is something that has not been discussed that I have never presented because all that I showed so far was in the weak excitation regime where I have at most one atom being excited at a time in the in the ensemble and then let us now see what happens if we increase the number of photons so the excitation happens from this single weak excitation regime to almost inverted ensembles so this was done again supervised by Philip and Jürgen and it was done by two PhD students chiefly Sebastian Pucher who's writing up his thesis now and Chris Liedl and there were two consecutive postdocs Shuai Jin and now there's Felix Tabin Newhans who joined so here we now work no longer just with a cloud of atoms but we indeed trap the atoms I won't go into the details just take my word for it that using a two color a two two detuned light fields propagating through the fiber we can trap the atoms in a periodic array of trapping minima and apart from thermal motion of the atom in this potential how the coupling strength is much better defined if the atoms at zero temperature the coupling strength would be the same for all atoms and now we do the same thing however our pulse we do the same thing in the sense we launch a pulse into the fiber but we now make the pulse much shorter than the atomic decay time much increase its power so that we are able to perform even up to optical pi pulses so that the atom becomes excited and then afterwards decays but the excitation takes less time than the decay of the atom so this means the pulses are 5 nanosecond long and in this case if we now look at the transmitted light as a function of time what we see I mean here I separate the time into while we launch the pulse so here the blue again the blue shaded area is the pulse without atoms so this is our reference signal and then the red data is when we have atoms coupled to the fiber and you see that when the pulse switches on then there is a transient regime where the atoms then start to establish a dipole moment and thus we get over time more and more absorption and then the pulse is switched off and we look at the fluorescence coming out of our ensemble this is magnified by a factor of 3 and we start here but then multiply by a factor of 3 for you to see it better and if the power is very low so this is a nanowatts here exactly the same as before so just this exponential decay of the fluorescence coming out of the ensemble at a rate which may be super radiantly increased so this is still linear response theory but now we are able to increase the power to the point where the prediction of linear response which is this dashed line starts to deviate both while the pulse is on and when we switch the pulse we look at the fluorescence so this is linear response theory as before and we see that our fluorescence signal is much less so this actually power here corresponds to about a pi half pulse and you see this because you see that here actually our absorption becomes lower because I start to actually excite the atoms and have some sizable like 50% probability of the atoms excited which means that we start to saturate the atoms and we see an onset of a ravi oscillation here and if we further increase the power here to 60 nanowatts or so then you see even a pi pulse so here the absorption of the atoms is almost gone again after this time here and we see that in this case we don't even see linear response theory anymore but we can nicely model our data so the black line is our model prediction but this model prediction now can no longer take the atoms as just Lorentz oscillators but we have to consider that the atoms are two level systems ok so our theoretical model is now extended in the sense that while between the atoms we always assume that there's a coherent field of approximation the atoms are described by density operators of a two level atom I don't go too much into the details of the theory just to say that here we of course when I couple a coherent state to a two level system after the two level system I don't have a coherent state anymore but we can pretend that it is the case by just taking the coherently radiated part coming from the atom and interfering it with the input light ok and this is what we do for this and this makes life much easier because then the computation in conjunction with this chiral coupling where the light only goes from left to right we can solve this equation plus the equation of motion for the atoms so the Lindblad master equation for each atom and then that time dependent quantities alpha k here and the coherence of atom number k and the excitation probability of atom number k and then we compute the transmitted power as being the incident power plus the this is the coherent part which is radiated but then so to speak by hand we also put the spontaneous emission which means that the power which we get at the end is not the same as the modulus squared of the coherent field according to this calculation because spontaneous emission is taken care of by putting it here and doing so we can really nicely model the dynamics of the system in particular if we here plot the number of absorbed photons per atom as a function of the pulse area so Rabi frequency times pulse time where we take the Rabi frequency of the first atom then you see that we can indeed almost get 80% probability of an atom being excited actually this is the solid line and the data is absorbed number of photons which can be inferred the difference of areas of the red and blue pulse here from that you can also compute really the excitation probability which is slightly lower because there is spontaneous emission also going on but still you reach like 75% after a pi pulse and then we can look at the fluorescence of the atom emitted by the atomic ensemble into the wave guide and again what we plot is the number of emitted photons into the wave guide as a function of pulse area and what I find interesting in this context here is that after a pi pulse where we have an inverted ensemble the emission into the wave guide is much less than after a pi half pulse it almost peaks after a pi half pulse it shows you that the directed emission into the wave guide comes from the coherent part which interferes constructively and emits into the wave guide and we can then also find the probability of an absorbed photon being emitted into the wave guide and you see that for weak excitation this reaches more than 60% but it falls down to the single atom beta factor at a pi pulse so the fraction of energy emitted into the wave guide is actually minimal for the ensemble being fully inverted so this is maybe counter intuitive or surprising but this is how it is because in that case the spontaneous emission does not give rise to collective emission which comes from constructively interfering radiating dipoles so maybe I switch to the conclusions in this case because I promise that I will skip the last slide now my computer is unhappy again yes so I hope that I could convince you that such coupled atoms are ideally suited for studying collective radiative effects from weak excitation to full inversion we saw experimentally coherent coupling between super and sub-radian states so we could show that the light that is emitted by the ensemble on its own switches on and off in a non-periodic fashion could see collective effects building up along the light's propagation direction and this is the part I skipped here for time reasons so these results I think can be used to better understand fundamentally the interaction of collective interaction of atomic ensembles with light but it could also lend itself to improve quantum memories or non-realized non-classical light sources or optical frequency standards based on collective super-radians and sub-radians this is something I skipped I told you that we are working on exploring the transition between waveguide QED and cavity quantum electrodynamics and what I said about the emission of a fully inverted ensemble into the waveguide being very weak is only true up to a certain threshold value of atoms turns out that when you have a high optical depth at some point when you have fully inverted ensemble the emission of a given atom induces stimulated emission of following atoms and we expect a super-radian burst of light so like a kind of stimulated bomb of photons coming out and actually our experiment should be able to access this regime and study such super-radian burst of light ok so with this I thank you for your attention and if you want to read up on the work then this is the references