 So, welcome everybody for this, today's CCQ colloquium which will be given by Roy Ossiri from the Weisman CCQ as you can see here and Roy is actually one of the official collaborators of the CCQ actually, long time ago, made an application and we really hope that this is not a one time event where we meet in person so I think that we expect to have a lot of collaboration also in the future and as you can see from the topic here of today's talk it's about all the coal atom ion interaction and it's actually telling I think everything about your background in science because Roy started doing a quantum gas experiments in the Earth Davidson group as a PhD student and finished that in about 2003 years I think I remember and then he moved on to say that okay now I really have to do something real serious physics and then I lost an electron yes we have to take off and then he moved to the violence group in NIST and worked there as a postdoc for four years or something like this after which I mean he was really I think more or less hijacked back to Weisman Institute in various positions which in 2019 then he became a full professor and at the same time more or less also got the duty of being the vice director for communication and development at Weisman Institute as such so it's a big task to take over but I mean I'm sure that your Roy has done very well in this job as well because he has contributed extremely much to the field both in neutral atom and ion physics and so I think it's kind of natural for you to kind of make these two things together and see what you can get out of it and that's what we're going to hear about today so welcome again Roy well thank you very much it's a pleasure being here it's a second time I get to visit our house and last time was a December visit so I'm very happy to see the other side of the coin and thanks for organizing such a beautiful weather on my on my visit so it's it's really beautiful right so what I thought I'll be telling you about today are ultra cold atom ion interactions that's a project that we started in my group in 2009 I believe so quite a few years ago what you see here this little dot here is the fluorescence from a single strontium plus ion and it's overlapped with a simultaneous absorption imaging picture which is taken of dipole trapped cloud of rubidium atoms that surrounds it so we take single ions and we immerse them in a cloud of ultra cold atoms now why would you call something ultra cold it's always then dangerous to give superlatives to situations because what happens next if we cool further what are we going to call it super duper ultra so but usually when people refer to ultra cold interactions they refer to a situation where at least in the in the case of two two body interactions when you think of many body interactions of course there's other energy scales that come in when you think of the two body problem then cooling further would not change the essence of the interaction that happens usually when you cool such that the the Broly wavelength in the center of mass frame is already larger than any you know typical size of potential interaction between these two particles and then you're dominated by a single parameter that you know that governs the behavior of the collision the s-wave scattering scattering of the problem so it's like scattering a laser from a target which is much smaller than the laser wavelength so this is the tail that I'll I'll describe here which is ultra cold or at least towards ultra cold interactions between between atoms and ions so I started off by saying that this is something that we started working on in in 2009 which means it's already a third generation of graduate students that have been working on this on this difficult I should say experiment and before I forget I want to recognize all the names of the heroes the hard-working heroes who are brave enough to embark on this on this project yeah I don't know if you recognize Dave Meir who is one of the first PhD students and this on this experiment recently also returned to the Weitzman Institute to perform quantum logic spectroscopy of molecules yeah okay so trapped ions versus neutral atoms so I think that you know both these systems have been laser cooled many many years ago trapped ions were cooled at the end the laser cooled at the end of the 1970s few years later neutral atoms were laser cooled as well and these two systems are cool to the to the you know to the quantum regime but have been used to rather different different ends if you like trapped ions are extremely well coherently quantum controlled systems you know you can actually interact with them one by one people have used them to build extremely precise atomic clocks they're a very highly leading platform for quantum computing they're heavily used in precision measurements their interaction though is rather trivial you know the interaction between these ions is the Coulomb interaction it's long range in a sense it's classical so for example the spin statistics of the ions doesn't matter at all and that's because their wave functions don't overlap so the question of whether using fermions or bosons as a trapped ion platform doesn't come into play at all at all we think of their interaction in full classical terms the only quantum thing in their interaction is then the phonons you know the phonons within the normal modes is what we think about as as quantum quantum in quantum terms but the interaction between the ions is is fully classical neutral atoms is actually the you know quite the opposite people so you know right from the onset the interactions between neutral atoms was the quantum thing that people have been have been looking at without that those interactions I think atomic systems would be rather boring but you know you know a few years or a decade after people were able to laser-cooled cold atoms then people have been able to cool them further to quantum degeneracy to look at both BC as well as Fermi degenerate gas again in both these examples without interactions that would be a tremendously boring system but you know interactions drive Fermi degenerate gases into super fluidity and BC has a rich excitation spectrum and using these systems now people have looked or not now 20 years already and on the superfluid moth insulator transition so people have been emulated condensed matter systems in the last decade or so people have been looking on dipolar gases where the interactions become longer and longer range in fact with dipolar gases you can't get to that ultra cold or if like to the S wave regime where there's only one partial wave dominating the interactions so these are rather different systems and and since about 2009 people have started mixing trapped ions and and an ultra cold gases and you might ask yourself why would that be interesting why go in that direction and I think the one of the honest answers is because we can and it hasn't been studied before and it's a new playground so we let's play and that's always I think you know when I say that and people say no you're a scientist you need a very good reason to do something you should know I think that's a very good reason I think if there is a new playground that we can play in and we can drive it into unexplored territories even if we don't know exactly what we'll find it's a very good reason to do it another good reason to study these is that their chemistry hasn't been explored in the in in the cold or ultra cold regime and their chemistry is very interesting and even important that's the chemistry that dominates interstate interstellar molecular formation and the reason for that is that ion-ion interaction you know is repulsive so that's not going to lead to any chemistry neutral neutral interactions are very short range and that's why they're not going to lead to very efficient chemistry in interstellar medium but ion neutral is long range and therefore that's the main driving force behind generating interstellar molecular formation and if you want to understand that chemistry that's a very good system to do that another motivation is that ions can serve as a highly localized we already said that ions are extremely good local probes they're very good sensors they can be coherently controlled with extreme accuracy in this case ions can be extremely highly localized but then extremely controlled and precise probes of ultra cold gases and that's that would be a useful tool if you like a local microscope of an ultra cold gas and then you know there's the the entire spectrum of reasons of studying ultra cold many body matter in general which is emulation of condensed matter systems and you know i know georg here has been working and thinking georg there i'm sorry he has been thinking of ideas along these lines of using these ions as charged polarons with long range interactions looking at mediated interactions such as the ruderman kittel kasula yoshida rkk y and condensed matter between these between these impurities condo crystals and there are many many more examples of spin impurities or other impurities in condensed matter systems with rich rich many body behavior so we have a motivation and since 2009 there have been more and more labs working on these mixed systems and this is this is here a list i hope i apologize if it's not completely full but it shows many many groups one of the things that you'll see here is a it's all in the northern hemisphere but that means nothing really the other thing you'll notice is that it's a very plural very democratic world so unlike the world of neutral atoms or ions at least 10 years ago or so where you would see rubidium and rubidium and rubidium and maybe a little bit potassium here the you know there's at least it's a buy it's a two-body problem you need to choose one of both and there are many many choices and different choices show different physics so it's it's a very you know there are many many options to to choose from and the reason i put some of them in black and some of them in red is that you know you could try and mix atoms in a mott and overlap them with an ion trap and that's that's good and it's it's even easier technically but it's not going to be able to drive you into the ultra cold regime because in a mott the temperatures are are much much higher we'll see soon that they're way too high in order to study these these interactions and secondly because the the atoms are never in the ground state they're always excited on s on an s to p transition all the experiments in red are experiments in which the atoms are not just laser cooled in a mott but then trapped in dipole potentials evaporated cool to lower temperatures these are all experiments that are trying to drive this atom ion systems into the into the into the ultra cold regime so a few um a few introductory remarks on on ion neutral interactions actually that problem was initially you know thought of um classically actually uh at the beginning of the 20th century by poland jevon and poland jevon has shown that uh when you look at the interaction between an ion and a neutral atom if the collision between these two happens above a certain critical impact parameter then all that happens is that the atom is slightly deflected in the interaction potential and not much momentum is being transferred i by the way i forgot to say that the interaction between a charged particle and a neutral atom which has a polarizability goes like minus one over r to the fourth the reason is very simple uh this is a dipole it's it's interaction between the field of a charged particle and a dipole but because the dipole moment is proportional to the field it's induced by the field the interaction goes like minus the polarizability times the field square because the field of a charged particle goes like one over r squared this interaction goes like minus one over r to the fourth so it's much softer than the van der Waals minus one over r to the sixth interaction at long at long range if the collision happens below this critical impact parameter then in the center of mass you get a spiraling in of of the relative coordinate until a very short range collision occurs and then the two separate pretty much pretty much isotropically these are collisions where momentum transfer is very very um it's very efficient these are also the collisions that govern chemistry or any inelastic collision rates because most of these inelastic or collisions or chemical reactions need short range interaction uh to take place one interesting feature about the longevity rate is that the longevity cross section is proportional to one over the square root of their energy or one over the velocity and because the rate goes like the density times the cross section times the velocity the cross section times the velocity is independent of energy altogether it's one over the velocity times the velocity so classically the longevity rate is energy independent that's a unique feature of the minus one over r to the fourth potential now how do you connect this classical picture to quantum mechanics well in quantum mechanics the way you calculate the cross section is by summing over all the partial waves up to the last partial wave that my energy allows for okay so a sum from l equals zero to l max there's some pre-factor here of four pi over k square where k is the momentum of that collision and then you somewhere each partial wave with a contribution of two l plus one times sine square of phi where phi is the phase that the wave function in the center of mass frame accumulates over the molecular potential okay back and forth now if i have many many partial waves that's going towards the classical regime each partial wave contributes a random phase okay because the phase you acquire is many many two pi it's a very deep interaction potential and then this sine square the sum over this sine square samples the interval between zero and one arbitrarily and that's some averages to one half and actually if you take that sum actually within a factor of two which doesn't matter where that comes from you recover you recover the classical langevan cross section so that's the connection between the classical and the quantum langevan description now as we said if we cool sufficiently low instead of having many partial waves contributing to the collision i'm going to have a single partial wave that my energy would allow for that would be the s wave the zero angular momentum state that would happen when the collision energy would be below the centrifugal barrier of the p wave of the partial wave with a single quanta of angular momentum okay now in neutral atoms if you ask yourself where does that happen you have you have to you have to look at the at the energy barrier of the p wave and that happens well it happens at that at uh at um well we can get to that lens scale soon uh it happens this centrifugal barrier for the van der waas minus one over r to the six potential happens in neutral atoms typically at a distance of a few nanometers okay that's that's the reason that the scattering length for rubidium is about 100 100 bore it's about five nanometers okay and the energy you need in order to be below that centrifugal barrier is typically hundreds of micro kelvin what does it mean it means that all you need is a magneto optical trap with a little bit of scissor fool schooling and boom you're in the you're in the s wave regime okay you're already in the quantum regime the minus one over the fourth potential is actually much softer and because it's much softer the lens scale at which the this centrifugal barriers shows up is much much longer larger it's for us for rubidium strontium plus which is the mixture we use it happens at about quarter of a micron what does it mean it means that you need to cool to energies of tens of nano kelvin in order to drive your yourself into the into the s wave s wave regime you need to be much much much colder another observation which would become later on in the talk is that this lens scale is much much longer than the lens scale over which chemistry happens okay the the area where the molecular potentials are significant okay centrifugal forces act very far away from the from the center of origin this is a very different situation than the situation you have in neutral atoms where five nanometers are slightly larger but not very very large you know they're a hundred bore they're not 10 000 bore okay so how how do we know that we have uh you know we're in the quantum regime usually we see that the cross section remember i told you that the langevin cross section is energy independent that's clearly not the case when you hit the quantum regime so for example one of the first things that you you're a you should be able to see is a phenomena that happens when the collision energy matches a quasi bound state which is bound by the centrifugal barrier of one of the partial waves okay this is a little bit like a a fabry-perot resonator for matter waves when that happens we get a a resonance enhancement of the collision the collision cross section so for example we can measure that by a resonant enhancement of all sorts of inelastic inelastic collisions these resonances are example of of these examples are called shape resonances but there are the resonances that people observe like fechbach resonances and so on so when we go to the quantum regime we see a significant effect of wave dynamics on the collision between the ion and and the atoms well i'll show you later how we tune it we tune it by putting the atoms in an optical lattice and then changing the frequency difference between the two optical lattice beams and then controlling the velocity with which the atoms are being transported across the trapped ion so yeah i told you that we have elastic collisions we also have inelastic collisions so one other particular aspect of these systems and that's common to most systems not all systems for strontium plus and rubidium if we look at the at the entrance channel to the collision it's not and this is this channel here rubidium in the s ground state and strontium plus in the s ground state this is not the molecular ground state the reason it's not the molecular ground state is because both these guys are alkalis they have one free electron and they're very reactive they're chemically crazy okay and then if i take the electron from rubidium and transfer it to strontium i'm going to get rubidium plus which is a noble atom it has only closed shells so a lower energy configuration and i'm going to get a paired electron pair in the ground state of strontium which again is energetically favorable so if i look at the at this option it's actually way below it's optically there's an ir photon that separates the ground state of strontium rubidium plus from the ground state of strontium plus and rubidium so we're not colliding at the ground state of this of these molecular potentials and that's why this is a movie that i can show you if we put eight ions in within this cloud you see that slowly ions disappear from the crystal but their fluorescence disappears they're still there because you can see that the ions hop around around empty spaces so you can fit a one over e curve to that decay of fluorescence the reason fluorescence decays is because strontium plus which are susceptible to scattering photons from that resonant laser beam become rubidium plus and then they're not they're not scattering photons any longer and we measure that about 10 to the about 10 every 10 to the 4 lange van collisions radiatively a photon is emitted from this singlet entrance channel to the ground state singlet and the electron hops from strontium plus strontium plus rubidium so a few words about our experimental system this is our machine it's composed out of two vacuum chamber in the lower chamber we have an rf pole trap we trap single or a few trap strontium plus ions we collect atoms in the upper chamber in a magneto optical trap we move them into an optical dipole trap in which we evaporatively cool them and then we transfer them into a one dimensional vertical optical lattice and then by changing the frequency between these two vertical beams we transport the atoms 25 centimeters from the upper chamber to the lower chamber when we either leave them in the lattice or move them to a cross dipole trap and overlap them overlap them with a with a trap with a trapped ion it takes about uh 0.3 seconds or so a few times a second we can transport them down to the so using this system uh we actually did all sorts of experiments we looked at non-equilibrium dynamics spin dynamic excitation exchange the phasing of optical clock transitions and so on what i'd like to concentrate today in telling you about is mainly non-equilibrium dynamics and spin dynamics and maybe end with some quantum logic detection of collisions between these two species good so the first thing we looked at is what happens when the atoms the cloud of atoms collides elastically with a single trapped ion so usually uh you would think of this problem as you know the ion would thermalize with a bath of neutral atoms around it so if i start with the ion let's say uh actually i started with milli Kelvin temperatures after Doppler cooling but i overlap it with a cloud of atoms at micro Kelvin temperatures what i expect is the ion to thermalize with the atoms at micro Kelvin micro Kelvin temperatures this naive picture however does not hold and the reason it doesn't hold is because we don't trap ions in static potentials and the reason we don't trap ions in static potential is is Laplace equations which requires that the second order derivative of the electric electric electric potential would be equal zero that means that if we in two dimensions we have a trapping potential in the third dimension we're going to have an anti trapping potential with the sum of quadratures of both traps so it's not a stable configuration so you can see here that if we uh you know if we increase the voltage on on these two electrodes and we have trapping fields we'll have uh field lines going in the opposite direction providing anti trapping so the reason the way we trap ions is by using non-static fields we oscillate electric fields very very quickly much quicker than the ion can respond so we generate a quadruple uh field configuration and we oscillate it back and forth and when we do that this is again of the movie you can see that if the field lines oscillate faster than the ion can respond the ion would be repelled from the large amplitude RF regions into low amplitude RF regions and this provides a staple trapping mechanism as long as the harmonic frequency of oscillation within these quadruple potentials is much much smaller than the RF frequency and we refer to this parameter as the Q parameter the Matthew Q parameter because it shows in a Matthew equation which is behind this mechanism and as long as Q is much much smaller than one we get stable confinement so if we look at the solution this is a classical solution of ion motion in the trap we see that it it does have uh an amplitude of oscillation at some secular frequency this is the effective harmonic potential that traps the ion but on top of that we have an additional term of oscillation at the RF frequency and this is driven motion okay so how would that motion look like if I have some thermal motion in the trap whenever the ion is in the RF null it's not going to see any driven motion you see the driven motion is proportional to this pre-factor so if this pre-factor is zero I don't have any zero motion but as the ion is moves away from the trap center we see more and more driven motion superimposed on it okay we call this micromotion so what are the consequences of having micromotion uh on the thermalization or lack of of ion being immersed in a cloud of atoms it means that the ion can collide with the atoms not just due to its thermal motion but also due to its driven motion and this mechanism continuously pumps energy into the temperature distribution of the ion so what I'm missing one yeah I'm missing my slide here but I'll I'll skip it anyways and in fact uh theoretical work by the group of Vlad and Vuletich uh already in in 2012 has shown that even if you don't have any intrinsic micromotion meaning you actually have a zero line of zero RF of zero RF amplitude in the trap you won't be able to thermalize the ion with the atoms naively you could think okay this this mechanism might be true I have driven motion colliding uh pumping energy into the secular motion of the ion but I do have a region where the RF amplitude is zero so if my ion is cold enough it's not going to experience any driven motion and therefore collisions with the atoms should thermalize it so that should be a stable solution to my equations this theory work has suggested that that's not the case and the reason is that the minus one over r to the fourth potential is sufficiently long range such that when the atom and ion become the atom comes closer to the ion it pulls the ion away from the trap center into finite micromotion regions and then energy will be transferred from the driven motion into the into the thermal motion of the ion and that would prevent the ion from thermalizing with the atoms the associated energy scale is written here and two things that you can notice right away is that one the energy scale depends on the mass ratio between the atom and the ion if you choose an ion which is much much heavier than the atoms if mi is much larger than ma then this energy scale would become smaller in other words if momentum transfer in a collision between the atom and the ion is inefficient then this mechanism would be shut off to a large extent secondly if you're using very weak traps omega here is the harmonic frequency of the trap for using weak traps and slowly go towards the you know the free atom a free ion case again this this energy transfer is going to be is going to be small so we set out to measure this this effect the way we did this experiment is we cool the ion to the ground state of the trap in all three dimensions then we overlapped it with a cloud of ultra cold rubidium atoms at micro kelvin temperatures and what we've seen is that we started with the ion at a temperature of well actually well below one half a milli kelvin but as the number of landgevan collisions increased we actually saw that the ion heats up it didn't only heat up it acquired an energy distribution which was non-thermal it actually acquired an energy distribution which was quadratic okay and we could see the power law of the distribution going down from being very large which reproduces max world waltzman distribution into being about four okay at steady state and four means that if i look at the probability distribution of energies i have a probability distribution that looks like e squared over e to the fourth power which goes like one over e squared one over e squared is a distribution which doesn't even have an average all its moments diverges it's a distribution which is completely dominated dominated by by extreme events by the way the reason the distribution we measure here is so radical is because we choose to work with strontium plus and rubidium which have almost exactly the same mass okay if you would choose to work with an atom which is much lighter than the ion you would get a distribution that resembles a thermal distribution to a greater extent since then people have investigated theoretically this power law distribution extensively and you know a few things to say about this power law distribution one is you know why would you get something which is not a get not a normal distribution to begin with normal distributions really come about when you build a random variable out of a sum of many many uncorrelated random variables and then you have the central limit theorem that tells you that what you're going to get is is a Gaussian distribution that what happens when we think of thermalization you know in the normal sense you have many many collisions but the energy transferred in each of the collisions is uncorrelated to the energy that was transferred in a previous collision here that's not the case because if we did transfer energy in one collision the amplitude of secular motion of the ion in the chap would be larger meaning it'll it'll explore higher RF regions which means that the energy it can get in the next collision can be larger and proportional to the energy it got in the previous collision this is a multiplicative random process and that's the engine between these power law distributions it's a little bit like an all-in casino right I have I bet all my money if I win I bet all my money if I win I bet all my money of course I can lose all my money but all I need is about a streak of 10 successful wins and I'm going to be stinking rich right so and and I'm going to I'm going to have the amount of money I'll have I'll win is going to be way above the most frequent result parallel distributions are actually very abundant in in nature you see them actually in stock markets in ecology in many many correlated correlated systems these parallel distributions have diverging moments to those of you who are old enough in the crowd to remember velocity selective coherent population trapping back in the 1990s or so or 80s people were speaking about the the resulting velocity distributions which are dominated by levy flights this is a very similar mathematics right so these are the energy distributions that depend on the atom ion mass ratio and this mechanism is really a strong preventer in our ability to take these systems and drive them into the ultra cold regime you remember that I've told you that the ultra cold regime is a tens of nano kelvin nevertheless this mechanism prevents it keeps us at the milli kelvin scale so a factor about 10 to the 4 in terms of energy above the ultra cold regime so in the next of the talk what I'd like to describe is two directions in which despite this mechanism people have been able to go into the ultra cold regime the first solution people find is to actually use you know what what I told you a few minutes ago use a highly mass imbalanced mixture of ions and atoms so this is an example from the gerizma group in amsterdam where they they are using uterbium plus ions you know 180 almost atomic or 170 atomic mass units a chubby atom and they collide it with lithium with which has nine atomic mass units a very slim ion and then the momentum transfer in this collision is very inefficient therefore the energy scale associated with coupling driven motion the secular motion is much smaller the other added value is that the reduced mass of this mixture in the center of mass is much lower it's actually dominated by the like lithium and therefore if you look at the energy to enter the s wave scattering regime it's not in the tens of nano kelvin range it's actually a 10 micro kelvin so you win on both ends it's much easier to take your system into the s wave scattering regime and by using this mixture indeed the gerizma group were able to show how a spin exchange cross section deviates from being energy independent you remember i told you that classically the longevity cross the longevity rates are energy independent in this case the longevity rate was energy dependent in a very clear signature of of quantum dynamics another example is an experiment that was done by the schatz group in freiburg again using barium a heavy ion together with lithium lithium is the is this the favorite of this of this approach and here they were able to show that by scanning the magnetic field they see deep resonances these resonances actually belong to s wave scattering and p wave scattering so it's not a single partial wave but nevertheless we see quantum resonances in the cross section between ions and atoms again using a highly imbalanced field in the rest of the talk so i keep saying the rest of the talk but the rest of the talk keeps getting shorter so don't worry about it i want to speak about how we in our group have seen quantum phenomena even though we are stuck we use same mass so a completely mass balanced mixture we're limited by this heating mechanism so that means that we're stuck at at least a hundred micro kelvin or so of energy the s wave scattering temperature is is you know a hundred nano kelvin or so so we were very far away from the s wave scattering regime nevertheless we do see quantum signatures in our in our scattering cross section the dynamics we're looking at is that of spin dynamics so we take the ion it's a spin one half system we immerse it in a class of rubidium atoms also a spin system actually it's a spin one or spin stout system depending on the hyperfine state we choose and then we look at the dynamics of that ion impurity when it's immersed in in that rubidium cloud so here is the experiment we did we took the ion and we initialize that either in the plus one half or the minus one half state these are the two states so this is the probability of being in the in the spin downstate in the minus one half state we initialize this probability either at the 100 percent or the zero percent and we compare two situations one situation in which we initialize rubidium at the stretch state of the f equal one manifold so the spin of rubidium has a preferred direction or we initialize the rubidium spin at the m equals zero state where the rubidium spin does not have a preferred direction and we see that if rubidium spin has a preferred direction the spin of the ion aligns itself collisionally with the spin of rubidium after about 10 10 or so collisions at the 90 percent level okay so the ion spin is being collisionally pumped to align itself with it with a spin of the atomic cloud whereas if the spin of rubidium doesn't have a preferred direction we very quickly or after a similar number of collisions we find the ion spin depolarizes completely has a 50 probability to be in the upstate and downstate from that rate we can actually extract the spin exchange cross section it's about 10 per lunge van collision or probability which means that after about nine lunge van collisions the atom and ion exchange their spin but there's also some coupling of spin to orbit the angular momentum that's the reason this doesn't happen at the 100 percent level and that happens after about 50 lunge van collisions now this is actually kind of cool because when you have that and you can control the spin of the ion through the interaction with the atoms you can actually control through the spin polarization of the atomic cloud you can control the rate with which chemical reactions occur so for example remember that charge exchange reaction I've shown you in that little movie of the eight ions losing fluorescence slowly that happens because of radiative decay from the entrance channel of the collision to the ground state of that of that molecule now the ground state of a molecule is a singlet state that's the ground state of the strontium atom now the excited state can be either a singlet or a triplet state but radiation the emitted photon can only couple a singlet state to a singlet state it can't couple a triplet state to a singlet state and therefore we expect that the overlap with a singlet state would determine the rate at which charge exchange occurs and that's exactly what we measure here we measure that the charge exchange when rate when we when we initialize at one zero or at one minus one determines the rate of that chemical reaction so this is an example of spin controlled atom ion chemistry now how do I think of these spin exchange collisions or or or or reactions so spin exchange takes up down and transfers it into down up now I can think of the down up as the odd superposition of the singlet in the triplet states and I can write the up down as the even superposition of the singlet in the triplet states now the reason that up down becomes down up is because as the ion and atom collide they collide on a superposition of the singlet in triplet states now during the collision they acquire a phase shift between these two states and that phase shift turns up down into down up okay it's a phase which is accumulated between the triplet and the singlet state again if I would like to calculate at least semi-classically the cross-section for such an interaction to occur I have a pre-factor of a matrix element square connecting my input to my output state with some spin time spin the product of two spin operators but then again I take the 4 pi over k pre-factor sum over all the partial waves until the maximum partial waves I my energy allows for 2l plus 1 pre-factor then sine of a phase but this time instead of just the phase over the potential that I collide it's a phase difference between the singlet and the triplet phase difference between these two that would give me my spin exchange cross-section and again if I have many many partial waves semi-classically that would this would average the sine square factor would average to one half and I will get my semi-classical spin exchange cross-section the probability or this matrix element is about 10 percent that's actually consistent for our states that's consistent with what we measured if you remember about 10 per lunge of on collision the thing is we don't know we don't know the the singlet to triplet potential difference a priori we don't know what the phase difference here is but if it averages to one half it doesn't matter so when we looked at the at the results of our of our of our experiment and we did that with with Timur Cherboul and Masato Murita from Reno University and these are molecular structure and scattering theoreticians just to make sure we understand we asked them to vary the difference between the singlet and the triplet in their calculations and what we found to our astonishment is that when we looked at the at the cross section for spin exchange it actually oscillated very very coherently extremely coherently you get a sine function that goes all the way to zero a hundred percent contrast which is completely not what you expect to get if the sine of this term averages to one half and we have at our energies about 20 partial waves involved so how come do we see such a coherent behavior so we looked at these at the potentials that we have and now you know through some relatively naive wave function integration calculated the phase that we get on the triplet and the phase that we get at the singlet so what you see here in in red and blue data points is the sine square of these two faces and you see that for both the singlet and the triplet we actually sample randomly the interval between zero and one okay there's no there's no particular phase this is what you expect when you're not in the s-wave regime however when we looked at the phase difference between them the phase difference between them was completely locked it did not change at all it was completely independent from the partial wave we're using and it took a little bit of time until we understood this s-wave like behavior with many partial waves what we see here is quantum interference we see an s-wave like behavior however completely outside the s-wave regime you know a temperature which is 10 to the 4 times larger than the the ultra cold threshold the reason for that is that spin exchange is is controlled by short-range physics it's controlled by the the difference between the the singlet and the triplet that happens at about 10 or 20 bore very very short distances okay at these distances different partial waves look exactly the same and the reason for that is that the centrifugal forces act very very far away if you remember because of the minus one over r to the fourth potential centrifugal forces act at a quarter of a micron away from the center of the origin so it's true that the phase you accumulate by on different partial waves for example on the triplet state is completely random but that random factor occurs at distances very very far away hundreds of nanometers from the origin chemistry occurs at at regions where all partial waves behave the same centrifugal forces don't act at these distances and this is the reason you get this beautiful interference even though you have several partial waves it's a separation of lens scales type phenomena so you know using this formalism we could also show that with 20 partial waves we actually expect to see to see shape resonances when we scan the energy of the ions across of the atoms or the energy of the collision if you like so we'll be able to see shape resonances even though we have many many partial waves so again this is our machine in order to be able to to measure these these collisions what we did is we now left the ions in the in the optical lattice we changed the frequency between the two lattice beams to scan the velocity of the of the atoms as they pass across the ion we made sure that the atoms density is very low such that we have about one collision per pass with this type of machine we're also able to measure the elastic collision cross-section so very shortly we do that by injecting very strong micromotion into the into the ion and then a single collision heats the ion so much so we can actually measure it so the probability here of heating the ion as a function of the micromotion saturates at the Langevin collision probability per pass so we know what the Langevin probability is and now we want to try and measure these these quantum interference effect now we can't really change the energy difference between the singlet and the triplet states right that would be really great if we had a knob that would change the difference between the singlet and the triplet and then we would measure the cross-section follow a sine function we can't do that what we can do though is change the isotope of strontium ions that we use if we measure the spin exchange probability over an isotope chain the different isotopes would have a slightly different singlet to triplet gap if we're in the classical regime again this doesn't matter we expect to see the same cross-section if we're in the quantum regime we expect to see a variation between the different isotopes so we need to measure over a different isotopic chain problem is we don't have control over all isotopes of strontium plus so in order to be able to measure we actually borrowed an idea that was used in the quantum lot in in the spectroscopy world that's the idea of quantum logic spectroscopy in quantum logic spectroscopy you take one probe ion that's an ion that you have full control over you can elitionalize it you can measure it you can do anything you want in terms of coherent control to that ion and you take an either ion that you can't really control it but you can't interrogate it using light you can perform spectroscopy on it and then by the mechanical action of spectroscopy on that ion you measure the transfer of momentum if you like to the logic ion and this way interrogate the likelihood of spectroscopy with that uh with that spectroscopy ion okay and there are several variations on these ideas and today these ideas are really advancing very fast they're used in the most precise optical atomic clocks they're used in order to to perform spectroscopy on molecular ions it's very difficult to coherently control molecular ions or laser cool them it's used in order to perform spectroscopy of highly charged ions so it's a very very powerful and and popular tool in our system we follow the same ideas we have two ions one is a logic ion strontium 88 plus we can initialize it we can detect it we can control it fully and the other ion is a chemistry ion okay we can't control that ion at all and then we pass the atoms across this ion crystal any collision of the atoms with a chemistry ion would show up in the momentum that was transferred especially if this collision is is an inelastic collision and it's exothermal so if energy was released in this collision we will be able to measure the effect of this energy release on the on the logic ion we use this method in order to measure the spin exchange probability over four different isotopes of strontium plus strontium 88 strontium 86 strontium 84 and strontium 87 and we've seen that while the cross spin exchange cross section for all the even isotopes of strontium was similar the odd isotope had a significantly different cross section now again together with with theory colleagues of ours max valesky valevsky matthew fray and michael tomse from warsaw university who calculated the spin exchange cross section for these different species what they've seen is that if you calculate the cross section for spin exchange versus the reduced mass you see oscillations you don't know a priori what the phase of the oscillations is it's actually fixed by the singlet to triplet energy gap but what they have seen is that while we don't know what the phase of these oscillations you know the period of the oscillations rather accurately in the period of that oscillation is exactly two atomic mass units and because it's two atomic mass units you actually expect all even isotopes to have the same cross section and the odd isotope to have a cross section which is at anti-phase and that means that if this picture is correct and this is again preliminary data and calculations we will be able to extract the s-wave scattering length and all the quantum scattering parameters from a measurement that is done using 20 partial waves so this is as far as i know a first experimental observation of s-wave behavior far ups outside the s-wave regime so another example i'm not going to dwell on that is we've looked you know on top of spin exchange we look at charge exchange reactions we in our logic spectroscopy experiment we used again strontium 88 as a logic ion rubidium 87 plus which is a noble gas you can't control it with lasers as a as a chemistry ion we measured charge exchange reactions and we've seen the charge exchange reaction is about an order of magnitude below the langivine cross section which again is an indication of of strong quantum suppression i'm going to skip the last part of the talk due to time shortage and i'll just sum up and say that you know the maybe i'll summarize in words you know the community of atom ion experiments has started you know a little over 10 years ago with a clear intention of going into the quantum regime going into the quantum regime with these systems is much more difficult it's much more difficult because the quantum regime is it's much lower energies and because the presence of rf fields in the trap is is a strong impedance you know in this route it pumps energy into the system more and more nevertheless people have been able to get initial glimpses of quantum scattering in these systems one avenue is to really try to go to very large imbalance atom ion mass ratios and go to the s-wave regime another method which we followed takes advantage of that situation so the reason that we have very low s-wave scattering energies is because of the long-range nature of the potential it's because you needed the Broly wavelength which is on the order of a quarter of a micron the upside of that situation is that many physical reactions occur at chemical distances which are way shorter than that lens scale and that's why with these systems even though you have a much higher temperature and you're not at all in the s-wave scattering regime you still observe s-wave like behavior that's the other i'll end by saying three things one is that we do in our group many other things so this is one area of research that we have in our group we also work on quantum computing and simulations we have activity in quantum metrology and optical atomic clocks also directed to physics searches similar to things that Michael and his group were doing and we also have an experiment this is in collaboration with near Davidson group studying mediated interactions in Bose Fermi mixtures so there are many areas of common interest between what we do at the Weizmann Institute and what you do here and hence the the formal collaboration between your center and Amos which is our center of atomic molecular and optical sciences i would also like to thank my group and there's a recent group picture at the Weizmann Institute and i'll end by showing this this is the beach of Nitsanim which is about 20 minutes drive away from the Weizmann Institute and the reason i'm showing it is that if any of you is interested in in spending time in warmer weather then we have available phd and postdoc positions and let me know if you're interested i'll have you come and visit and get a direct impression of our activities thank you very much and if you have questions i'll be happy to answer