OK Well it's a pleasure to be able to
talk to this audience again I haven't

given a talk.

You probably ten years.

So.

I like to tell you about
the things we've been doing.

Most recently with the trickle gases and
particular with spinner V.C.S. and.

All right.

OK So let me start by just introducing
the topic with something you should.

Really be quite familiar with.

And a classical gas of atoms and and that

will be a prelude to the to the quantum
gases that we study in our laboratory.

So this is a slide which.

Outlines the difference a normal gas from
the perspective of an atomic physicist

is simply a box that contains a lot of.

Molecules that move back and
forth and collide with one another.

There are little balls as far as we
know at ordinary temperatures and

it's really at low temperatures that
an atomic physicist like myself gets

interested in this problem of what
happens to a gas that's moving about in

a container in which all the atoms collide
with one another but they're at such low

temperature that the the quantum
mechanical waif packet size which

is given by the thermal to very wavelength
becomes comparable to the to the to

the length scale of interactions between
atoms as what we call an ultra cold gas.

It's actually a pretty well defined
terminology although it sounds kind

of like a buzzword it's really when
this length scale becomes comparable

to the link scale of interactions and
if we go to even lower temperatures.

Such that the debris wavelength becomes
comparable to the distance between

particles and if you have a gas of
indistinguishable Bo's ons then they

form a Bose-Einstein condensate are very
low temperatures it's a kind of collective

forgetfulness the atoms don't really
know which state they're in and so.

They all pile up in
the ground state together.

And Sister give you
a perspective on this physics.

What happened it's really very it's a very
extreme range of temperatures where this

this kind of behavior occurs
not most of the time a gas to

schools down to low temperatures and
forms a solid but

the physics of a B.C. occurs at six orders
of magnitude lower temperature than

room temperature at which under ordinary
conditions it would form a solid but

we managed to keep the gas at very low
density so that it remains a gas and

this is only possible through
the remarkable techniques of laser and

evaporative cooling that allow you to
reach this temperature regime that's in

the Nano Kelvin range and
was the subject of two Nobel Prizes

the most recent was in two thousand and
one so Bose-Einstein condensates

of really come into their own since two
thousand and one that was about the time

that I joined Georgia Tech and
became involved in this field.

And so here's a graph which shows
you the rate of publication

in I pull this out of the inspected
abase from a few days ago

the number of articles that have the words
Bose-Einstein condensate in them.

So it's a subset of the field
of quantum gases but

you can see that right around ninety
five when the first B.C. was produced in

the laboratory the rate of
publications has grown immensely and

it's it seems that in the recent period
it really shows no signs of stopping.

So although people produce them and
said Wow.

It seems now they're really starting
to do things with the seas and

try to understand more and
more of their properties.

OK So one of gases of those
ons are interesting in.

For a number of reasons one is this really
the quantum mechanical limit to motion.

So if you have a gas and
it's cool down to the ground.

It.

The position uncertainty and
momentum uncertainty are really.

Related by the Heisenberg formula.

So this allows one to invent
envision atomic sensors

that are limited by quantum
mechanical effects.

So really all thermal motion is irrelevant
at these very low temperatures.

And so there's a real industry
of building really precise

devices in atomic physics and it's trying
to capitalize on this developments and

in laser cooling and evaporative cooling.

But there's another side to it which is
more what I'm going to focus on today.

But these are really novel and
unusual interacting quantum systems so

they're now because we can produce them
in the lab only now and there are unusual

because they have the properties of
interacting systems that are very

different from the typical kind of thing
you might encounter in contents matter.

So.

So it allows you to explore
things like phase transitions and

super fluidity in systems which
are really not condensed.

Phase they're really
something different and.

The other unique feature is
that we can find this in an X.

from the trap and that introduces its own
set of structures so for instance one can

create tailor made potentials or even
optical lattice as artificial crystals

in which to study the properties
of some gas of particles for

this talk I'm going to focus on
the properties that arise from spin.

So you take a gas of those ons and
it commences into the ground state and

you end up with a single quantum
mechanical way function.

Sometimes referred to as the order
parameter and that order parameter.

If you allow for spin can be a vector and
the relationship between these different

vector fields these two
a lot of rich structure.

OK So this this is a gas.

This is the order.

Amator for a spin one gas that's the gas
that I'll be talking about in this talk

and it has three spin projections
plus one zero and minus one and.

And.

So so I'll be telling you
about the properties of spin

one bows ons under
special circumstances so

these are the other unique features that
we can study nomic Librium dynamics.

So we can prepare the system
in some initial state and

watch as time evolution and that is
also something that's difficult to do in

commands matter systems where everything
relaxes to the ground state very quickly.

These are isolated gases in traps
inside an ultra high vacuum chamber and

they are for the most part removed
from external part of ations So

that presents some unique possibilities
for studying On Equilibrium physics.

OK.

OK so I told you about interactions so
these are interacting many body systems

the interactions come from
two particle collisions.

If you have two.

Two particles that collide with one
another at very low temperatures.

Then you can't think of it in this
way you really have to think of it in

terms of scattering lengths so
to body scattering lengths and for

the case of the spin one B. C.
there are two lengths that matter.

That they're determined by atomic
properties they're called eight two and

a zero.

And the interaction Hamiltonian for the
entire gas can be written in this form.

So those say this is an interaction
the energy density is

proportional to the square of the density
of the particles and there are two terms

in the Hamiltonian there's a cs ear And a
C two the C. zero does not depend on spin.

And it's simply a geometric mean
of a weighted sum of these two

of these two scattering lengths the term.

See too does depend on spin and it's
related to spin exchanges the difference

between these two scattering
lines which are almost the same.

For most of these quantum gases and

therefore the ratio of C two
to see zero is very small.

So there's a spin dependence to the
interaction Hamiltonian that's very weak

and therefore the timescales for
spin dependent process are very slow but

nonetheless they play
a very significant role.

OK So there are two flavors of
this two scattering like either

the C two coefficient if that which is the
difference between them can be positive or

negative and
if it's negative then the system wants to.

Magnetically Order wants to produce
the ground state has and that's spent and

if C two is positive then it wants
to set the net's been to be zero.

And we distinguish these by calling
one affair a magnet the other and

a firm magnet.

So in the fair magnetic case you have
magnetic ordering in this fluid.

And in the attic are magnetic case
you have pneumatic ordering so this

at this very magnetic state is
what's What seen in rubidium B C.

There have been some pioneering work
at Georgia Tech and at Berkeley in my

Chapman's group and dance temperance group
in Berkeley on the rubidium spinner B.

C. and the sodium work which I'll be
telling you about comes from Margaret.

To give you a sense of the scale if I
take the the seed to coefficient and

multiply by that by the particle
density I get an energy and

this is an energy that you're probably
not used to thinking about is really tiny

it's an energy scale
that's in that of Calvin.

And if you ever wondered how to
convert from than a Kelvin to Hertz

you just multiply by twenty one.

OK All right.

So we're expanding mental
physicists were always trying to

find some new product that might be.

There that might solve a lot of the the
problem so I got very excited when I saw

this this company that claims to
have things like ideal hookey and

springs and magnetic monopoles and
we work with magnets so

I got very excited but then I thought
well this must be just a hoax but

then I saw that they they
go to the trouble of.

Specifying the magnetic field accuracy to
one of our squared to point one percent.

So I said this is really a spec
that that an experimental

physicist would like to have but
unfortunately I looked at the cost and

said is shipping five thousand dollars so

I said that's not going to fly with with
Georgia Tech's sole source purchasing.

So anyway.

A real B.C. experiment is
a little bit more complicated.

And so we start out with a hot gas.

What's that.

For it's a bit more than five thousand but
not for

an individual piece of Fortunately
we buy it in pieces or.

When we travel.

So we start out with the hot gas and
cool the atoms using laser light.

And then we have to then transfer
them into a magnetic trap.

This is simply a pair of quails around
current in opposite direction and

the atoms are spin polarized and
they're attracted to the center

of this make in homogeneous
magnetic field and there.

Once they are trapped there.

We can further cool them without using
laser light but simply by evaporating.

The hot atoms away and the sample cools
to a lower and lower temperature.

It's what's known as force evaporative
cooling so these techniques were developed

in the in the ninety's and
led to the formation of B.C.

So now it's a fairly robust technology and
the one additional step is we

transfer the atoms from the condensate in
this magnetic trap into an optical trap.

That's a trap.

That's formed simply by a single
focused laser beam in space that.

Intensity maximum attracts
the atoms to the center.

Forming an elong.

Ated jam a tree in this single focus.

So for that we use infrared laser
light at about one micron So

this whole process takes
about twenty five seconds.

From start to finish so if you want to
do an experiment with multiple runs it

really takes a long time for
us to do to collect data.

So how do we detect
the atoms once we formed it.

We shut off the trap at some time and
we can allow the atoms to expand for

some period of time up to
thirty milliseconds or so and

then we shine a near resonant laser
light in the form of a pulse and

the atoms cast a shadow
that image onto the C.C.D.

camera and then we can take that shadow
image and turn it into something.

Pretty That's false color that
shows the the face transition and

action so as you cool the gas down
to lower and lower temperatures.

It goes from having a Maxwell Boltzmann
distribution to see to having a bi modal

distribution to being slowly comprised of
a condensate with almost nothing else.

The condensate can be distinguished
by it's an isotropic expansion

in this particular image.

OK So sodium B.Z. is a Georgia Tech.

We've had them for a few years now but
the most recent version of our apparatus

looks like this and the most recent
versions of the personnel look like that.

We trap about five million
atoms in the optical trap.

In our B. C..

After which we can
prepare them in any spin

state we like by just using
radio frequency magnetic fields.

We apply a D.C. bias magnetic field
of one hundred milligram dose.

That's on the scale of the Earth's
magnetic field if you're not used to

thinking of magnetic fields and

we have to reduce the ambient think very
feels in the lab to below ten milligram So

that's a pretty challenging thing at these
guys have gotten very good at doing.

So.

After we produce the condensate we can
do this time of flight imaging but

we can add a twist to it.

We can apply a magnetic field
gradient during the expansion and

separation and the cloud separates
into three different spin states

three spin components in the optical trap.

So these three spin projections
correspond to the spin

projection minus one zero one plus one.

And actually the spatial structures
that you see here are real and

I'll tell you more about
them as time goes on.

OK.

So to understand spin or physics takes
several slides worth of introductory

material so I am only about eighty
percent there before we get to our data.

So one of the most
important features is and

this distinguishes again gets back to
distinguishing between atomic gases and

condensed matter systems and atomic gases
have this thing called Spin conservation.

So the entire system has to
conserve spin angular momentum and

that means that if I have
a collision between two atoms that

the sum of the two spin projections has to
be preserved in a particular collision so

if I have two atoms in the spin
zero states they can either

stay in the spend zero state after the
collision or one of them can be promoted

to the spin state minus one while
the other one is demoted to the state.

Plus one and that way.

M. one plus M.
two is preserved in the collision.

That's simply conservation
of angular momentum and

if you apply that to the entire system
that means that the total number of spin

up minus in down atoms
is a conserve quantity.

So there's no.

There's no thermal baths
to which you can get rid

of magnetization it remains conserved.

If you start out in a state with some
magnetization at the end of the experiment

magnetization will be the same.

So there's another feature
of this energy diet.

This is what's called a bright
Robbi diagram from the.

From atomic physics it's
simply includes a linear and

quadratic magnetic field shifts
the quadratic shift appears because

it's the linear shift appears because
of the magnetic moment of the electron.

The quadratic energy shift appears because
of the high profile structure of the atom

and there's a very small shift
at very low fields and so

during this in this collision
the linear shift cancels Exactly.

And what's left is only
the quadratic energy shift

which in our experiment ends up
being a number of about three Hertz.

So it's a tiny energy remember that
from the previous graph I said one

hundred thirty Hertz to six Nanak Alpha.

So this is an energy much
less than an a Calvin but

it still plays a role in this problem
because of spin conservation.

So that's what's so unique about
spinner V.C.S. So if I include this

this quadratic energy shift in
the problem then I can write down and

a spin dependent part of the Hamiltonian
now so this is just the spin

part from the previous Hamiltonian
that I had a couple slides ago.

So there's the interaction term here and
now I can add a quadratic is a man energy.

And this parameter in front is
proportional to the square of the Ambien

magnetic field or
the applied magnetic field.

OK so if.

So since I have a Hamiltonian with two
different terms I can have different

quantum phases and
I can have transitions between the phases.

So for the MT for magnetic case if Q.

is positive then the ground
state is a polar B. C..

Means that all the atoms would prefer
to be in the spin zero state because

they can't overcome that small
three Hertz of energy barrier.

So the ground state is a pure
equal zero but if Q were negative.

Then one has an entry for
the grants it is an empty for

a magnetic phase which is
a mixture between these two spins.

So for this talk I'll be telling
you about how we navigate bitter.

In these two these two phases.

OK So
we do that using microwave translations.

So if I look at the ground state of
the US of an alkali atom like sodium.

It has a three as a half ground state we
detect the atoms by shining light between

the three S. and three P. levels and we
detect the atoms using optical absorption.

But if I look at this ground state.

High profile structure.

I see two levels.

There is an F. equals two an F. equals one
of these are high profile quantum numbers

and it's the spin or physics as in
the slower high profile manifold with

a few calls one where there you see
the three spin projections but at F.

and a finite magnetic field these energies
are all split from one another by seven

hundred kilo hurts her Gauss which is half
the bore magnet on and with a micro if.

Magnetic field we can drive
the transition between the zero.

Spin projection in the ethical one and the
zero percent projection unethical to this

is known as the clock transitions
the basis of of atomic clocks not

in sodium but in cesium and is very
precisely determined even in sodium.

So if we drive this transition.

It's very long lived so you can see
coherent Robbi oscillations on this

zero to zero transition using my career
feels this is important because it

allows us to calibrate
the strength of the Michael.

Mike Rayfield.

And one can also tune the micro
field around and explore this

spectrum of these different transitions
and that's also pretty important.

It allows us to see.

To really know with what we're doing and
to be able to calibrate our Make that it

feels very carefully so going to drive
transitions between the zero and

zero state zero minus one or minus one
to zero minus one in minus two and

the splitting here allows us to
calibrate the magnetic field.

So using microwaves we can control the
populations between these different levels

and there's a third and we can use that
as a diagnostic but there's a third and

very important part and that is we can.

Tune the microwave frequencies so
it's very far from resonance and

then we don't drive any populations at
all but we induce an AC start shift.

So if you have.

A field is too far from resonance
it shifts the energy levels and

shifts them in a way that's what Radek.

And so the net effect is to create
a quadratic energy so if shifts so

that parameter Q. that I wrote down in
the Hamiltonian can be the sum of both

a static term.

There's a static.

Sorry of term due to the static field
that is the quadratic energy shift is

proportional to the square of B.
and that's always positive for

the spin one case but
this second term as arises from the A C.

field due to the microwaves and the AC
start shift is proportional to the square

of the Rabi frequency divided by the D.

tuning and so by changing the addition
you can change the sign of this term.

So you change the energy level shifts
here you can induce a phase transition

in the entire system.

So that's what we're going
to look at if I plot the.

Population in the fraction of atoms
now that are detected in the zero

States as a function of
the frequency of these microwaves

you can see that at some frequencies it
drops from one We start out with this.

All the atoms and
spin zero drops from one and Over here it.

It does the same but but it does so in

two very important ways One is that
as the fraction of atoms in the zero

state goes down the fraction of atoms
in the plus and minus one are going up.

And that's because of spin exchange
collisions that populate the plus and

minus one states equally.

So these are the spin
dependent interactions.

And can can also see
that the whole spectrum

here is detuned with respect to the clock
transition and should be symmetric.

That is one should have in principle
equal XA Taishan on the red.

Side of signs of the clock transition
as one does on the blue side of

the clock transition.

Whereas this data is clearly asymmetric So
for instance a very broad region over here

where where the the population
varies over here it's all flat.

And so this is a sign that there is

this is this is this is the stark
stark effect induced and I mean yes.

Yeah OK so that's an interesting question.

So.

So he says that the green in the blue
should add up to one minus this and

in many cases they do the cases where
they don't are where we're OK so

I haven't told you everything about this
graph it's actually pretty complicated but

but there are multiple resonances
in here the residence is that

you saw in the previous graph very
close to the resonances the a stark

effect is is not the only player
you have to consider the X. direct

acceptation to these to the excited level
and the atoms in that level can decay and

they can decay in a spin state dependent
way so in fact the the the physics of

the spin exchange is disrupted in
the presence of this resonances But

if you're far away from the residences for
instance over here.

It's from Merrily dominated by this
a stark effect so this when we saw spectra

that looked like this we began to realise
that that the spin exchange processes were

we're acting in in a way that was
dependent upon the quadratic energy shift.

OK so now if I park my

microwave frequency here detune
from any of these residences by.

By a large amount and I simply look at
the time evolution of that I mean it

was zero population so I turn on
the microbes at some point in time and

look at the fractional population in
the zero state as a function of time.

So in this case I've actually turned
the microwave amplitude to zero.

So there's no microwaves at all.

You're simply looking at the time
evolution of a pure I'm equal zero state

as it is and
it decays slowly into a plus minus

one pair over a timescale
of about two seconds.

So in this case.

Q. this parameter Q.
is positive and but very close to zero.

So on this axis the scale for

comparison here is that spin
dependent interaction energy.

Which was one hundred thirty Hertz.

So here Q. is very close to zero and so
we call this the maddest able States of

its It lives but only for
it only for a couple of seconds.

So if I shift Q. now so
that it's likely negative.

Then that instability happens faster the
gas only lives for about half a second in

the suspend zero state before it collapses
into a superposition of plus minus one.

And if I shift Q.
even a little bit further then

this chemical zero state
becomes extremely unstable.

So if the case within a time
of thirty milliseconds or so.

So we can really tune
the this instability rate.

So if I define the crossover time or
one of a crossover time as the instability

rate then we can see that
that instability rate goes.

Goes up in a very dramatic way as you
very this quadratic energy shift.

So we start out with something positive.

You got a quadratic energy shift negative
the instability rate grows very rapidly.

So this is a signature we've crossed
through this phase transition

from positive Q. to negative Q.
where we have a crossing between this and

this polar phase and
MT for a magnetic face but

it's not a face transition in the way
that you might be familiar with it.

That's mediated by finite temperature so
when you cool

something down below a certain temperature
you can have a face transition.

This is a face transition that's
essentially happening at zero temperature

or very close to zero temperature and
it's really media did.

By quantum fluctuations that change
the ground state from one form to another

now in our experiment we're not
actually staying in the ground state.

We're initiating it.

This continuous change in the Hamiltonian
and so the system then evolves.

But as it evolves from one state to
another it's it's really changing it's

the change in character of the of
the ground state is what's

driving the dynamics.

It's really looking at
the dynamical evolution of.

As you go through this phase transition.

Yes.

Well for one thing this instability of
rate increases by two orders of magnitude

over a tiny range of parameters.

Well OK yes so maybe it wasn't
obvious from the previous graph.

But.

But this whole ranges here
is only about ten percent of

of the characteristic energy in a problem.

OK so it's really crossing
through some tiny range where

where tunes where it goes from.

From an instability rate which
is less than one percent and

two one which is one hundred
almost hundred per second.

Something is dramatically changed as
you go through this at this point.

OK so.

So what's what's happening to
our to the spinner condensate.

So one way we can visualize
this is in terms of and

the magical water parameters so.

So there's no spin.

I told you before the spin is conserved so
there's no net spin.

We start out with all the atoms
in a spin zero state.

And the way to describe
that is in terms of.

For one way to look at that is
in terms of this probability.

The probability surfaces so
a fair magnetic state would be

represented as as a as a ball that's
displaced from the X.Y. plane.

Whereas an empty for a magnetic state
a state of with spins zero projection

might think it's a kind of boring
object because it has spin zero.

But in fact it has a lot of structure so
really looks more like a donut.

In spin space with with
a node on the axis and

what's interesting is that that axis can
be rotated in space through some angle

in which case the spin zero develops
into something that has an equal.

Contribution from plus and
minus one so the general state has

equal aptitudes in plus or minus one
that's what makes it pneumatic and

it has all three spin projection so
what we're really observing is the we're

Taishan of this pneumatic director away
from the Z. axis where you have this.

This is written as anti far make it is
really polar polar and if our magnetic.

Rotation of this pneumatic
director away from this polar axis

to point along some some arbitrary
direction in atomic and molecular physics

is very familiar it's called Spin
alignment without orientation but but

it's something quite unique to this and
affirming that it casts.

OK So in two thousand and
ten there was a paper by Sharma where

they showed that one can map this and
magnetic want to see

system of spins into it into a exactly
into a quantum rotor Hamiltonian.

So you take them anybody Hamiltonian it
includes a spin dependent interactions and

this quadratic Zaman energy and it turns
out that that many body problem for

for the case of a spatially.

Single mode system can be mapped to
rectally into a single particle Hamilton.

Any and for
a single quantum rotor that has.

That has a macroscopic anchor momentum and
it's not that surprising to think about it

when you whenever you have a director that
can freely rotate in space that has its

length constrained that looks like
a diatomic molecule rotating in space and.

This this single particle Hamiltonian
can be can be very easily understood

at least qualitatively.

So the the kinetic energy part
is is the rotational kinetic

energy of the rotor and the potential
energy part is the quadratic energy shift.

So the court Radek energy shift tends to
try to align the rotor with the Z. axis.

Whereas It's kinetic energy causes it
to be the localized So when we tune Q.

we're really starting out with a wave
packet that's localized in this potential.

And as Q. is reduced.

And finally made negative you start
out with a wave packet that's

sitting at the origin that then
is unstable against against

motion as dispersion and
through the entire.

Through throughout the entire sphere.

So what we're seeing is an instantaneous
collapse of this wave packet and

that's roughly consistent
with what we observe.

If we look at this time evolution of
the spin zero state the atom start out and

spin all the spin zero but then they
evolve rapidly into something that in

which the spin zero fraction is finite and
this roughly corresponds to the dispersion

of the wave packet over
the entire city here.

So although it's not clear that
our system yet obeys this quantum

wrote a Hamiltonian there's still some
intuition to be really derived from it.

OK so.

In this quantum rotor Hamiltonian this
there's another feature that as you very

this potential energy the the energy
levels here in this rotor.

Potential are getting so.

Closer and closer together and if you
think about that in a spatially extended

system that means that there's an energy
gap that's going to zero as you

approach the space transition
until finally the the energy

levels become negative the energy
of execution becomes negative and

that describes an instability in
which you have imaginary frequencies.

So we can look at our data and
try to understand it in

terms of an energy gap which goes to zero
at the transition point of the center G.

gap now depends on
the way vector of exits.

So these are spin waves and
these spin waves have an energy for

a homogeneous system
that has this formula.

And so this form the energy
depends upon the quadratic.

Energy shift the interaction energy as
well as the momentum of the of the spin.

Spin waves.

And as you tune Q.
to zero this energy gap goes to zero and

finally becomes imaginary
at the transition point.

So this curve here.

The dotted curve describes this.

Imaginary frequency instability for
the cake with zero mode and it disagrees

with our data pretty pronouncedly at low
or drydock energy shifts particularly.

So it's not that I want to
turn to now we don't have

a homogeneous system so that formula only
applies in a homogeneous system we really

have something in which the density is
highest at the center of the trap and

goes to zero at the edges where
the density is the highest

the rate of the spin exchange
collisions the highest and so

we expect that the instability will
be nucleated in a spatially dependent

way to start out with something
that's all in the spin zero state and

its nucleus and instability and we can see
that by looking at the spatial structure.

Now it turns out that for

the imaging method that we
use there's no spatial ings.

Mation really in the vertical direction.

Apart from the from the stronger
like spin separation but

if I look at one of these blobs for
instance the vertical direction has

contains no spacial information but
the axial direction is primarily along

the direction long axis of the trap and
because of the technical aspects

of the expansion the spatial information
along that direction is preserved.

So in fact you get a spatial map
along one dimension of this cloud

is another feature and
that is because the trap is so

along gated the spin structures
primarily are one dimensional.

So what you see is is that the instability
is nucleated in terms of plus or

minus one pairs that
are form primarily near the.

The center.

And they form a small domain and
that domain grows with time and

if you plot the width of this domain it.

It grows until it expands until finally it
reaches the size of the entire condensate.

And once it's done that
it can't grow anymore.

So it remains flat roughly.

However there are some
finer details here that.

That one could and I do in time

that one could in principle resolve but in
this experiment we were unable to because

because there were residual density
fluctuations in the condensate that

prevented us from really being
able to see what was going on.

So for instance if we didn't
initiate the instability we still

saw small features like this so.

So we worked a little bit
harder on trying to since then

on trying to trying to to
observe these spin domains and

it turns out that the spin
domain characteristic length is

something known as the spin healing length
so it's the energy scale in quantum

mechanics associated with that's
been dependent interaction.

And that number turns out to be about
a micron for our experiment for sodium.

Spinner condensates so.

It's clear that the structures that we're
seeing here are much much bigger than

one micron one micron is about the scale
of the width of a domain wall.

So in principle one can have domains that
are as small as that or close to that but

they're really not being resolved in
this experiment at the moment so.

So we we really wanted to see these
domains so we came up with a new method of

trying to image them and I'll tell you
about that in the last part of the talk.

So if we use the same
microwave pulse now we

add a second frequency that's very close
to resonance to simply for detection.

So we can drive.

The transition between these two high
profile levels and we can detect the atoms

only in the upper hyper fine level so
the light that we use does not

probe the atoms in the lower level it only
probes the atoms in the upper level and

if we drive the transition from
the zero state to the zero state and

we don't detect the plus or minus one.

We only image the the atoms
in the spin state zero So

way to do spin selective imaging in situ.

OK And so we apply a pulse and
then of microwave pulse and

then we obviously detect the atoms
on this F. equals to two F.

equals three excited level in
the three P three halves manifold.

So if we do that then then we can take
images of the condensate at different

times but these are now going to be almost
in situ images I say almost in situ

because we we actually expect
we'll put it on pause for

a second we allow the atoms to expand
slightly in the vertical direction just to

overcome the spatial optical resolution
but you can see that started on its own.

Still getting used to her.

Point movies.

OK so.

So let's look at this this
is a gas at time zero.

So is this a long dated optical trap it
has a density profile that's very very

elongated and one dimensional and
if you allow it to evolve with time.

It's five milliseconds per frame you see
that the density profile becomes totally

unstable and after a short period of time
evolves into something that has very very

fine structures contained within it.

So this is now past the point

where the chemicals plus minus one phase
has expanded to the size of the entire B.

C. and now we're getting detailed
information about what's going on.

Locally inside the gas.

So I think this is a very
promising technique.

It's something that in principle can
be applied to to gases that have

more than just one spatial dimension

where one can look at these kinds of
structures in two D. for instance.

OK So with that I'll conclude.

And so.

Currently we're looking at the spatial
dynamics and trying to understand how to

characterize them as as a function of time
and also as a function of the amount of

energy that's available through
the quadratic term so dimensionality as

I said is another very interesting future
direction that one may be able to.

To create a trap that has that
has two dimensional extent.

So currently the width of the trap in
this direction is smaller comparable to

the healing length of the spin healing
right so there's too much energetic cost

to creating to creating spin
domains in this direction so

they primarily form in this direction but
if we relax the trapping geometry we could

create something that's
more spatially extended and

could try to look at two D. the two D. is
actually particularly interesting because.

At the moment we've only looked at
the at the the populations in these

different levels.

But if you explore
the coherence between them.

There is the relative phase
between plus and minus one.

There are predictions for top logical
defects that are supposed to form and

can be initiated by this kind of crunch so
this isn't can reorganize itself by by

creating domains by it reorganizes
self by creating domains.

But it can also do so by creating top
a logical defects and these typological

defects or are known to occur in other
models of Quantum Point just so for

instance the kibbles erect mechanism
predicts the rate at which top

logical defects are supposed to form and
it would be a part may be possible for

us to measure that this is cable direct
mechanism was developed in the context of

cosmology many years
ago to try to predict.

The top logical defect formation after X.

after the inflationary
period of the universe.

So with that I'll just conclude by
acknowledging a verbal commands and

underneath it was counted post-op
who worked on these experiments and

months of first year graduate
second year of registered.

And with that I'll conclude Thank you.

Let me just say we have graduate student.

We're always looking for
new graduate students to join our group.

So we have some positions and.

We're definitely interested to.

To to expand our our group at this moment.

Thank you thank you.

Thank you.

Yes.

So you can create a laser that
has an elliptical profile.

And it can.

You're going to expand the size of
the system in the other dimension.

So the reason it has to be so

tightly focused is primarily to
balance the atoms against gravity.

Because at these low temperatures
if the numbers don't go anywhere.

They just sit and fall.

So you have to provide
a force that balances the.

Condensate against gravity.

So that force can be applied
in the form of a sheet.

Something that's two dimensional but
realizing something that's really three

dimensional This is a challenge
because of this particular issue.

If.

You know

this that that topic has quite a history.

There were some extra proposals to put
cold atom experiments in space where

the fundamental limitation
of atoms falling.

So for instance Tommy Clarke experiments
are limited by the observation time.

At least in part because of the falling of
atoms due to gravity and so the proposal

was to put the atoms in space so that
you could extend the observation time.

And then NASA decided to go to Mars.

So that whole funding programs.

Got eliminated that.

It's a nice idea but very expensive.

Yes.

So that's a I didn't I didn't
know if I quite emphasize that.

So the plus and minus one are not
separated from one another.

There.

Retracted to one another.

That's what makes it an anti fan magnet.

But they're repelled from the zero.

So it's a little different from this from
the typical And if our magnet unfair

magnet that you see in incremental matter
systems which are which are spin a half.

This is a spin zero So there's this extra
guy that's the spin zeroes component and

he interacts with the other two.

So.

That's what gives rise to this pneumatic
behavior but it also means that the plus

and minus one are attracted to one
another by their palette from the zero.

So on these graphs.

It means that wherever you
don't see a spin zero.

There's plus and minus one filling it
up so the overall density profile.

If you follow it from here to
here doesn't change at all.

So there's no change in
the density profile it's

simply the spin state reorganization and
anything.