Thank you, Robin, for the kind introduction.
Good morning, everybody.
It's a great pleasure to be here at this very interesting workshop.
Thank you very much for the invitation.
It's an even greater pleasure to present the latest results on the single atom-resolved
probing of strongly correlated systems.
The experiments I will be presenting were done at the Max Planck Institute for Quantum
Optics in Geising, and although I'm now at the University of Strathclyde in Glasgow.
Well, from the time the first computers were invented, physicists were intrigued by the
question whether computers can simulate any physical system perfectly.
But while we learned very quickly that it is very complicated and very difficult to
simulate especially strongly correlated systems, and we found that to simulate certain systems,
the computational power grows exponentially with the number of particles involved.
This turned out to be a severe restriction in understanding of particular physical systems,
and it was a real difficulty, and nobody found a way out of it how one can solve this problem
in principle.
But then in the 80s, Richard Feynman came up with the revolutionary idea of a quantum
computer that indeed a computer must use the laws of quantum mechanics to simulate other
quantum systems.
So the general idea of this quantum computer or quantum simulator is that you create a
well-controlled quantum system that can simulate the behavior of another quantum system.
And one particular example for this, this will be throughout many of the talks of the
workshops are atoms in optical lattices or ultra-cold atoms in general.
These atoms in optical lattices, I'll say a few more words later, like these optical
lattices are created by pairs of intersecting laser beams, and the ultra-cold atoms are
held in sort of egg-like, egg-box shaped potential wells basically, and the atoms can hop from
lattice site to lattice site with a tunnel coupling J and have an on-site interaction
pretty much as electrons can move in certain real materials in the potentials created by
ions.
And the beauty of these ultra-cold atom systems is that many of the experimental parameters
are tunable, and you can probe the system, as I will be reporting in this talk, with
a precision and even with single atom and single lattice site level that is virtually
impossible in real materials.
And that raises the hope that these quantum simulators can help us to answer unsolved
questions in quantum antibody systems, while one prime example is, I think, the 2D family
Hubbard model, which is conjectured to be the key model for high temperature superconductivity.
And we hope that these experiments will shed deeper insight and help us to understand these
and many other interesting phenomena in these strongly correlated systems.
Well, today I will be talking about, like in particular, on single site and single spin-resolved
imaging of strongly correlated systems in optical lattices.
And I'll first show you how we can apply these techniques to imaging strongly correlated
mod insulators, and then we go from the zero tunneling limit to finite tunneling, and I
will show you that we were able to see quantum correlated particle hole pairs, and then by
doing parameter crunches, sudden changes of the system, we were even able to see how correlations
spread across the system with a light cone-like spreading.
And then from the mere observation of these systems, we will be doing something more active,
which is what is flip individual spins in the mod insulator, and then we can not only
flip the spins, but also see the dynamics.
And in particular, I will present one of the latest results, which is the dynamics of a
mobile single spin impurity, which we could track with this quantum gas microscope I will
be showing to you in a second.
So as it is a mixed audience, not everybody is familiar with optical lattices.
I left one introductory slide on optical lattices.
So basically these optical lattices are created by laser beams, which in our case are readily
tuned to the atomic transition.
So the simplest optical lattice you can imagine is created by two counter-propagating laser
beams, in our case 1,064 nanometers, that creates an optical standing wave with a periodicity
of half this wavelength, and the atoms can basically be trapped in the intensity maxima
of this standing wave.
And here you can already see one of the difficulties when one wants to resolve individual lattices
as the spacing is 530 nanometers only, and that is compared to the wavelength, to the
fluorescence, to the resonance wavelength, in our case of rubidium atoms of 780 nanometers.
So one has to find a way how to discriminate these rather short distances, and you'll see
in a second how we can do it.
And this concept of optical lattices can easily be extended from one dimension to two dimensions.
So in 2D, if you have two pairs of intersecting laser beams, you'll end up with an array of
tubes.
These signify the intensity maxima, and in three dimensions you'll get, in this case,
a cubic lattice structure, like with a cubic arrangement of intensity maxima, and in the
following we will only be using a single layer out of such a three-dimensional optical lattice.
And we create this 3D lattice by, again, having three pairs of intersecting laser beams.
One comes from above and is reflected off this mirror, which is a mirror for the lattice
wavelength and transmits the fluorescence light of the atoms, and there are two other
pairs of laser beams in the horizontal plane that create the square lattice structure on
top of that.
And here you can already see the key ingredient of the experimental apparatus.
As I said, we want to resolve atoms on neighboring lattice sites.
For that purpose, we designed a very high-resolution optical imaging system with a numerical aperture
of 0.68, and we obtained at 700 nanometers a resolution of roughly 700 nanometers, which
is almost the same as the individual, as the spacing between two lattice sites.
And typically, all the experiments I will be presenting in the following, they start
with roughly 1,000 rubidium atoms in a single antinode of this vertical standing wave.
So basically, they are trapped in a plane, as I said, onto which we impose this lattice
structure from these horizontal lattice beams.
And the way we detect the atoms in the optical lattice is by fluorescence imaging.
So typically, all the experiments are done with rather shallow lattices measured in recoil
energies, typically 10, that's where there's still some finite tunneling between the different
lattice sites.
And then before we detect the atoms, we basically freeze all dynamics, and we make the lattice
suddenly very deep and increase the lattice depth to roughly 300 micro Kelvin.
And then we illuminate the atoms with a near-resonant laser field and optical molasses, and the
effect of this molasses is twofold.
On the one hand, the optical molasses continuously cools the atoms and holds them in place.
And on the other hand, the atoms continuously scatter photons from the optical molasses
and we emit them.
And with the imaging system, we have a position-resolved detection.
And typically, we collect by this 5,000 photons per atom in one second.
And this is a typical fluorescence image of a thermal cloud, and each white spot is an
individual atom.
So we can very clearly distinguish them, and the white spots designate the lattice sites.
And one particular feature of this fluorescence detection is that we have light-assisted
losses, light-assisted collisions.
You have to keep this in mind when you see all the pictures and data in the following
throughout my talk.
Please keep this in mind.
It's very important for the understanding.
So the idea is, or what happens is, whenever there are two atoms on a single lattice site
and they're illuminated by the optical molasses, they very quickly undergo a light-assisted
collision and leave the trap even before sufficient fluorescence photons are detected.
So that means when we have initially only one atom on the lattice site, nothing happens.
If we have initially two, we detect them as an empty site.
If we have initially three atoms per site, two of them leave the trap and we only detect
them as a single atom.
So basically what we are doing, we detect the parity of the atom number, or we measure
the occupation modulus, too.
So please remember this.
And so let's right away go jump into the physics.
So we want to study the strongly correlated systems.
We start with a mod insulator, and as we consider bosons on an optical light lattice, we use
the Bose-Hubbard model to describe this system.
So this Hamiltonian consists of these three terms.
On the one hand, there's the tunnel matrix element J that characterizes the strength
of coupling of tunneling from one side to another, and these a, a, d, a, and a are the
atomic creation and annihilation operators on site i and j.
And then another term is the on-site interaction as the atoms repel each other.
It costs energy to hold them onto a single lattice site, and that's characterized by
this on-site interaction u that's basically, and these n are the atomic number operators
that count the number of atoms on a lattice site.
And this third term characterizes the external harmonic confinement.
And in the following, we will be starting by considering just the atomic limit where
the tunneling is basically completely suppressed.
And then we are basically deep in the mod insulator regime.
So what describes the physics of this term is the ratio between J and U. So if the tunneling
is very large compared to the on-site interaction, we are in the superfluid regime.
And we can, for example, have a Bose-Einstein condensate in the lowest band of the lattice,
and that that's completely delocalized over the whole optical lattice.
And if, however, the interaction dominates over the tunneling, we're in the mod insulating
regime.
And we'll start with that.
So in the mod insulator, let me, so let me just introduce to you what you will see to
interpret the following pictures.
So as I said, the optical lattice is made out of laser beams and create this interference
pattern created by the laser beams.
But the laser beams have a finite size, and that leads to this external harmonic confinement.
And something very interesting happens if we now try to fill the lattice with atoms,
and the system tries to find the lowest energy state.
So if we fill the system with atoms, they first occupy the lowest line energy states.
And if we want to put more atoms into the system beyond this particular point, we could
either put another atom at the outer part of the system that would cost like this amount
of potential energy, or it is, in this case, more advantageous to put a second atom at
the center of the system and fill the inner part of the system with two atoms per lattice
side before more atoms come in at the outer part.
And this leads to the formation of these mod shells.
Many of you have come across, in this case, we have an inner shell of two atoms per side.
We are surrounded by a shell of one atoms per side.
And let's see whether we can see this with the microscope.
Here you can see two images of such mod insulators with different atom numbers.
So they look quite different from the picture of the thermal atoms you have seen before.
So we see that the atoms are very, very densely packed here with, as you will see in a second,
with one atom per lattice side.
And then here you see this ring structure with like some empty lattice sides here.
And initially there have been two lattice, two atoms per lattice side in the center.
As you remember, there are these light-assisted losses, so the doubly occupied sides are detected
as empty sides, and this is surrounded by a shell with one atom per lattice side.
And we can use a computer algorithm and the knowledge that uses the knowledge of the point
spread functions of the images of the individual atoms to deconvolute these images and get
basically a digital information out of this.
And we can do this deconvolution with very high fidelity, and we end up with just a distribution
of atom or no atom on the lattice side.
And what you can see here by, already by eye, is that we have a very, we have a very low
defect density.
We can map out individual defects, and the unit and the probability of finding one atom
at the very center of these shells is very high.
I should point out the beauty of this digitalization, basically this deconvolution going from the
real images to the digitized ones.
By this method we basically get rid of all technical noise from these images, and we
are only left by statistical uncertainties, basically governed by the number of atoms
in these images.
And you also notice that they are really nice, nice and round, so we can determine the center
of the images and then do asymptotal averages along these circles.
And we have a closer look at the atom number and the atom number variance as a function
of the radial distance from the center.
So here you can see, like what you already can see by eye, basically that the atom number
goes to one at the center of this n equals one shell, and then basically drops.
And more interesting is the atom number variance, so you can see that at the center of these,
of the mod insulator shell, the atom number variance drops to zero, indicating or directly
showing number squeezing and that the atom number variance goes to its maximum value
in between or at the border between the two shells and at the outer part of the system.
This behavior can be readily understood with a very simple model in the zero tunneling
approximation that is, and we can find an analytic expression for the probability of
finding n atoms at a radial distance r from the center that's this function, and it has,
and one can fit this model to the data, that's this red curve, and as free parameters to
this fit, we can in particular extract the temperature of the system.
And with this method, we can for the first time do in situ thermometry of these mod insulators
in optical lattices that was not possible before, and for this particular system we obtain,
for example, a temperature of 0.07 times U over KB that has to be compared with a melting
temperature at which the compressibility vanishes for the mod insulators that's at 0.2 U, so
with this we can prove that we are really deep in the mod insulating limit.
And what I should also point out is that this curve, this model fits all the data points
within the error bars, and that tells us that as far as we can see, the system is in
global thermal equilibrium, also let me stress again that these data points are from a single
shot only, so we can do thermometry on single samples.
And also, again, like this radial distance, I would like to draw your attention that this
is the distance in micrometer, so you can see here the changes of the variance of the
atom number on the scale basically of the lattice side, so this feature is only one
micrometer wide, and we can probe the statistics, the atom number statistics with this method
with a really unprecedented precision.
Now-
Can I ask one question?
Sure.
You say this is from a single shot, but the variance is not determined from a single shot.
Yes, it is from a single-
From the azimuthal behavior, is that how you do it?
Yes, so the question is, is this indeed a single shot?
Yes, and the variance is basically the variance of the atom number in a radial bin, so when
we do this azimuthal average, we have a number of atoms in this bin, and we can compute the
variance in this bin, and that's basically this value and the error bars, and the error
bars are just determined by the number of atoms we average over in this azimuthal average.
That's also why we have a larger spacing of the points for shorter distances, because
otherwise we wouldn't have, simply wouldn't have enough points, but this, indeed the data
you see here is particular from this picture, and no other picture, not averaged over several
other of these pictures, and we can do this for any of these pictures, and they look very
similar.
Okay, so what you have seen now was the mod insulator in the atomic limit where the tunneling
was completely suppressed, and now we should have a closer look at what happens when we
allowed tunneling, when we tune J over U, and in the following I will also restrict
myself to one-dimensional systems, so what you have already seen in the atomic limit
where we have no tunneling, basically the ground state of the system is rather boring,
so we have really no fluctuations and perfect unit occupancy one atom on every lattice side.
However, when we allow tunneling, quantum fluctuations appear, and these quantum fluctuations
lead to a virtual hopping of particles to another lattice side and back, and these quantum fluctuations,
they lead to these correlated particle hole pairs, I call them particle hole pairs, in
the following, they are actually like an empty side and a doubly occupied side, but throughout
the talk I call them particle hole pairs, and basically these quantum fluctuations appear
everywhere on every lattice side, so the sum runs over all lattice sides with a probability
amplitude J over U, so this sort of signifies the quantum state, and in contrast to these
quantum fluctuations, there are some fluctuations which however are spatially uncorrelated,
and when we increase the tunneling, more and more of these particle hole pairs proliferate
and they eventually extend in size and they lead to a deconfinement of these pairs at
the transition from a mod insulator to a superfluid, and the question is can we directly see these
quantum fluctuations, I should also say these quantum fluctuations, they are really fundamental,
so they would also appear at zero temperature, and that basically drives the transition from
the mod insulator to a superfluid, which as you know is a quantum phase transition that
would also occur at zero temperature, and the goal of this experiment is to answer the
question can we really nail down these quantum fluctuations and distinguish them from thermal
fluctuations, and the way we do it basically, so what we will have these quantum, these
particle hole pairs are doubly occupied side with an empty side, with an adjacent empty
side, and as you remember we have this parity projection, so a doubly occupied side will
also be detected as an empty side, so we would see these correlated particle hole pairs as
correlated holes, and we can assign to this occupation number a parity, so we have a parity
minus one for an even atom number and a parity plus one for an odd atom number, and the quantity
we use to characterize, to quantify these correlations are the nearest neighbor parity
correlations derived out of this parity, so that's the average value of the product of the
two adjacent on-site parities minus these on-site parities in which we subtract the
uncorrelated thermal fluctuations, and here you can already see for this particular value of J by
U, you can see in this sample by I, that we were able to catch a couple of these correlated holes,
and for more quantitative analysis we did many of these pictures and varied
the parameter J over U from the super deep in the mod insulator limit that's over here to the
superfluid, and we saw the red points, that's the parity correlations along the axis where we had
allowed tunneling, and the system, the lattice depth was rather deep along the other axis in
order to completely suppress tunneling, and as we would expect we don't see any of these parity
correlations at all, so in order to understand this data, so the first naive interpretation is like
first order perturbation theory, and one would expect for increasing J over U that these pair
correlations emerge as J over U squared, that's what we roughly see at the beginning for small
tunneling, that's the dash dotted line, but to describe the signal over the whole parameter
range we have to get our theory colleagues involved, so first we started the DMAG calculation with
Leonardo DiMazza from the MPQ did this for homogeneous system at zero temperature,
that's the dashed line which almost described the right shape of the curve but not the right
amplitude of the correlations and then a more involved calculation including the realistic
temperatures and the trap basically gave this solid line and that reproduces our data fairly well,
and with this curve basically we have shown that we indeed could see the quantum fluctuations
and just clearly distinguish them from any thermal fluctuations that were basically subtracted out
here, okay, and we could do something more rather than only observing the correlations
as like as they appear statically, we could also see the spreading of the correlations
in a quantum body system and for that we changed the setting a bit, so right now we try to excite
the system in a certain way, again we stay with the 1D systems and we do a parameter quench,
so we start with a system deep in the mod insulating regime for with u over j equals 40
and then within a time much smaller than the inverse tunneling rate, we ramp the system to
a point which is close to the critical point and the general philosophy of these quench experiments
is that we start with a system in an eigenstate and then as we rapidly change it the system is
no longer in an eigenstate with with for the new Hamiltonian and we have a time evolution under
this new Hamiltonian and the what we are looking at again we again have a look at these parity
correlations but right now we don't look at parity correlations only for neighboring atoms but we
we have we evaluate parity correlations for different pair distances as you can see here
with the index d and we see and in addition we have the parameter t so we see we want to see how
these parity correlations evolve over time and that's what you see here in the following
data set this is the the parity correlation for different pair distances one to six as a function
of the time and what you can clearly see that we have this maximum of the pair correlations
evolves through the system in time and we have a light cone like spreading of the correlations
and that's quite quite intriguing we found when we first saw that but then where we immediately
started to to ask our theory colleagues and Corinna Collard has greatly worked out many
theoretical models to understand this in detail so it can be like the data can be readily understood
with a time dependent demag calculation with rather simplistic assumptions of the system which
is infinitely infinite and homogeneous at zero temperature and even this this theory reproduces
our data fairly well this is the this the green curve and our theory colleagues even came up with
a more sophisticated model to understand what's what's happening after these parameter cringes
basically what what happens after the quench the system sort of is excited and fermionic
quasi particles emerge and they basically emerge everywhere from every single lattice site and
these fermionic quasi particles are correlated particle hole pairs and they emit it with
opposite momenta that's visualized here these red and blue balls are the quasi particles so the
the w-occupied sides and the holes so this is only approximate in reality the w-occupied
sides have a small mixture of a hole and vice versa but to first approximation this is
this is a valid picture and you must imagine that these particle hole pairs they are emitted
basically from every single lattice site simultaneously and and they are entangled
particle hole pairs so you have a hole emitted to the left plus and and w-occupied side emitted
to the right plus the inverse and these particle and holes propagate ballistically with different
velocities through the system and they follow a well-defined dispersion relation and that's
basically why you see this wave packet light like behavior so this dispersion relation also involves
like Bessel functions that's why you see this second maxima which you can almost recognize
from our data and there's also this dispersion relation also describes that this the amplitude
of this maximum of the correlation decreases and this spreading of correlations has got some rather
fundamental implications for quantum antibody systems and what if this interest started basically
already in the 1970 in 1972 where Leib and Robinson put up their famous theory and a theorem
stating that perturbation can propagates with a finite sort of speed of light if the evolution
is governed by local Hamiltonians and this theorem had wide-ranging implications for condensed matter
theory and quantum information and our experiment was basically the first observation the first
direct observation of this correlation spreading in a strongly correlated system okay so how much
time do i have five minutes okay so then we have to move a bit quick so i will start by showing
you a technique how we can address individual spins in the optical lattice and then we can
and then we will use this technique to deterministically prepare single spin impurities and
see how this single spin impurity propagates through the system okay the single spin addressing
basically we use everything's already in place so we have the high resolution imaging system
but instead of just using it for observing we shine in a laser beam from the back side of the
imaging system and focus it onto individual lattice sites and we can and with that we create
a diffraction limited spot size that we can move onto over the atoms in the optical lattices
by the help of this two-dimensional scanning mirror and the and we as a wavelengths for this
addressing beam we use a magic wavelength with a certain polarization that deforms that
deforms the lattice in a certain way so we consider the two
hyperfine state these two hyperfine states of rubidium and this magic wavelength only
acts on the atoms in the upper hyperfine state and the general idea of this addressing scheme
is that we shift one of the atoms we focus it onto a second single lattice site and shift
the the adverse atoms into resonance with an external microwave field that can drive the
transition from between the two spin states flip the spin and all the other atoms which are not
affected by this laser beam basically don't see the microwave and the spin remains in the
initial state okay let's do the experiment so we shine the laser beam onto a single site do a spin
flip and then do this repeatedly again and again for a couple of spins so in order and then in
order to reveal the spin flipped atoms we apply a laser pulse that removes all the atoms in the
upper hyperfine state and then we are left with the following you can see the modern initial
mod insulate and here we have in which we have removed a flipped 16 spin successively and then
we move them and well here you can see that it works quite beautifully and we also did a more
quantitative analysis where we characterize the fidelity here as a function of the pointing offset
between like of the addressing beam so zero pointing offset means we directly hit the lattice
site and 0.5 pointing offset means we hit in between two lattice sites so we can see that
if we do everything right we have a very high spin flip fidelity of 0.95 percent so we just count
the number of holes as a function of this offset and we see when we go away from the from the center
we see that this probability drops to a background that's given by the thermal holes of only
six percent and what's quite remarkable is that this curve has a width of 300 nanometers and
more interestingly an edge sharpness of 50 nanometers that has to be compared to the diameter
of this addressing beam of rather of roughly 600 nanometers and this proves that with this
technique light shift plus microwave we have realized this super resolution technique that
allowed us to reach a sub diffraction limited addressing resolution and we can also produce
just for the fun of it some nicer pictures in which we start with all the atoms in the upper
hyperfine state then flip a couple of spins and then remove the non-spin flipped atoms and then
we end up with the following so this is a deterministically prepared chain of 15 atoms
and as we are physicists we couldn't resist of preparing preparing of psi that's a psi out of
16 atoms okay now we that's very nice and we can use that to deterministically create a single spin
in the one-dimensional mod insulator and see how we how this propagates in order to do that
we slightly refined the technique instead of using a single laser beam to address only one
atom we sort of want to parallelize this technique and we now use instead of a single laser beam we
project a line onto the atoms and we use a digital mirror device to create a line-shaped laser field
that we basically project as for the single beam onto the individual atoms so we use a single line
and prepare a series of like use 1D systems and we create a series of 1D systems with one
flipped spin at the center so we can do other patterns skip this and this multi-site addressing
with this line shape beam works almost as well as the one of the scheme I've already shown you
let's let's go right away into the into the experiment so we basically start by flipping a
single spin and and this spin when we want to see how this propagates and we do this in parallel so
we flip a series of spin in again 1D systems or we consider again we are still in one-dimensional
systems so please please remember that and and then the the advantages of this line-shaped
beam is that we cannot only prepare these the initial state much faster flip all the spins
simultaneously but also we can pin the spin flipped atoms so we do this spin flips in a rather
deep lattice to completely suppress tunneling and then we ramp the lattice to a desired value as we
want to see the impurity the behavior of this impurity dynamics when we go across the super
fluid to mod insulator transition and this simultaneous addressing and we has the
advantage that we can pin the spin flipped atoms so we hold them in place and then can release them
and start the dynamics very deterministically and what what we expect to see it's like
is for the case of large interactions you much larger than j so we have usually a two component
Bose-Habart model that can be mapped into a Heisenberg model in this large interaction case
and basically we have this isotropic Heisenberg Hamiltonian many of you have already come across
I guess which involves this isotropic spin-spin coupling and one can rewrite this term basically
and using these spin these operators of the effective spin and the and this basically shows
that you can that the spins can hop from side j to side i or the other other way around and the
coupling parameter is the so-called j exchange coupling that's given by the single the free
particle tunneling j squared over u times times four and this is this super exchange coupling is
very similar to the Hamiltonian for the single particle tunneling so their j exchange is just
replaced by j and here you have the single particle tunneling as you have seen this term in the
Bose-Habart Hamiltonian only and this j exchange you should know that this is for the parameters
that is much smaller than j so all the dynamics what you expect to see for spin exchange dynamics
is much smaller and much slower than single particle tunneling and the way we detect the
system there basically two ways the problem is our detection is not spin resolved but you've seen
like for the single side addressing experiments that we can simply remove one spin component and
then image the rest so we do the same here so we have two ways of evaluating our data one which
we call is the positive image so we where we remove all all spins except for the impurity
and then just see where the impurity is after time and then there's the negative image where
we remove the impurity and we measure this spin impurity as an empty side and the one problem is
that as you have seen that we also have thermal holes in the system and when we do these negative
images we really don't know if we detect two holes which one was the spin impurity
so and we can solve this problem very elegantly basically when we do this experiment and evaluate
our data we will only use the samples with one empty side and then we know that this empty side
as the we can prepare the impurity with very high fidelity that it indeed has to be the impurity
and the system has no extra excitations and with this post selection basically we can artificially
select a zero temperature subset of the data and well let's have a look at the data for one
particular value that's deep in the mod insulating regime so we we show the probability of finding
the impurity at a certain position this is the position in lattice site so initially it is
prepared at the center and then you see after 60 after 40 60 and 80 milliseconds the probability
distribution so you can very clearly see that like it it has evolved in time and that the
probability distribution clearly shows distinct minima and maxima that's a clear sign for the
coherent evolution of this of this tunneling process and we can even understand the data with
an analytical function so this Heisenberg model can be solved analytically and this probability
is this Bessel function of the that involves the super exchange coupling as a free parameter and
that's a fit basically with the with this with this model so i think i have to come to an end
i thought i had five more minutes but okay so well let me let me just have so i will skip
skip this and this is the the summary of these of the spin impurity dynamics so we've we've probed
the dynamics of the spin impurity all across the super fluid to mod insulator transition and we
could find a very good agreement with the analytic solution of the Heisenberg model
deep inside the mod insulator limit and in the super fluid limit this this basically this
description breaks down breaks down and we had to again ask our theory colleagues in this case it
is Thierry Jamaki from Geneva who did TDMG simulations of the system that's this green curve
to describe and to understand the behavior and the super fluid regime and that matches our data
points fairly well and indeed we see that the dynamics in the bath of other spins is fairly
different from the dynamics of the of free particle tunneling which should and this propagation speed
basically should be two two times j times the lattice constant over h that's up here and the
all the velocities we've observed here are just much much lower okay i think i have to have to
come to an end so if we have seen many experiments and that we and we could use the quantum gas
microscope to probe strongly correlated systems c dynamical effects adverse individual spins with
single atom and single site resolution there there's a multitude of possibilities
that one can explore in the future so we one can continue with exploring the spin dynamics
correlated tunneling of adjacent atoms see how domain walls relax one in many groups are currently
striving towards single site detection of correlated fermionic quantum phases and also
my new setup in strathclyde is towards that goal so there's a setup for towards single site
imaging of potassium and turbidium in particular the fermionic potassium one can use the local
adverse ability to implement novel cooling schemes and also the possibility of generating
and projecting arbitrary light fields to deterministically remove regions with high entropy
there's the possibility which we also have explored and are still exploring in munich about
exciting atoms to ritberg states explore long rates interactions observe crystalline ordering
of the ritberg excitations and not talking about the huge possibilities this system offers for
quantum information processing as we have an array a huge array of individually addressable
quantum bits and there's a lot of things to do to explore these things to make a truly scalable
system for quantum information okay i think i have to stop and thank you for your attention