Have left: A. Chotia, A. Sharma, B. Pasquiou , G. Bismut, M. Efremov, Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu

Collaborators: Anne Crubellier, Mariusz Gajda, Johnny Huckans,

Perola Milman, Rejish Nath

B. Naylor (PhD), A. de Paz (PhD), A. Chotia, A. Sharma, O. Gorceix, B. Laburthe-Tolra, E. Maréchal, L. Vernac,

P. Pedri (Theory), L. Santos (Theory, Hannover)

Magnetism with a dipolar condensate: spin dynamics and thermodynamicsMagnetism with a dipolar condensate: spin dynamics and thermodynamics

This talk

1 Thermodynamics of a Bose gas with free magnetization

Purification of a BEC by spin-filtering

2 Exotic quantum magnetism in optical lattices

Intersite spin-spin many-body interactions from Mott to superfluid

Nov 2007 : Chromium BEC

April 2014 : Chromium Fermi sea

104 atoms

103 atoms

Experimental system

F=9/2

S=3

(from only 3.104 atoms in dipole trap !)Phys. Rev. A 91, 011603(R) (2015)

A “hot” topic : Cold atoms revisit (quantum) magnetism

Non-interacting spin-less bosonsSengstock: classical frustration

Interacting spin-less bosons(effective spin encoded in orbital degrees of freedom)Greiner: Anti-ferromagnetic (pseudo-)spin chainsI. Bloch,… Spin ½ interacting Fermions or Bosons

Super-exchange interactionEsslinger: short range anti-correlationsI. Bloch, T. Porto, W. Ketterle, R. Hulet…

Spinor gases:Large spin bosons (or fermions)

Stamper-Kurn, Lett, Klempt, Chapman, Sengstock, Shin, Gerbier, ……

Ion traps: spin lattice models with effective long-range interactions C. Monroe

Dipolar gases: long range spin-spin interactions

J. Ye, this work…

This seminar: magnetism with large spin cold atoms

Stern-Gerlach separation:(magnetic field gradient)

0Sm

1Sm

1Sm

-2-1

0123

-3

Optical dipole traps equally trap all Zeeman state of a same atom

2( )S S BE m m g B B Linear (+ Quadratic)Zeeman effect

Spinor physics due to contact interactions:scattering length depends on molecular channel

2

6 4

4cB B n a a

m

-3

-2-1

( 250 µs) (period 220 µs)

2, 2

6 56, 4 4, 4

11 11

S S

tot tot

m m

S m S m

Magnetism… at constant magnetizationlinear Zeeman effect does not matter

0.4

0.3

0.2

0.1

0.0

Fra

ctio

nnal

pop

ulat

ion

0.80.60.40.2time (ms)

-2-3

-1

0

Spin oscillations (exchange)

Spin-changing collisions have no analog in spin ½ systems

24( ) ( )SV R a R

m

6

6( )

CV R

R

Van-der-Waals (contact) interactions

Domains, spin textures, spin waves, topological statesStamper-Kurn, Chapman, Sengstock, Shin…

Quantum phase transitions

Stamper-Kurn, Lett,Gerbier

Spinor physics driven by interplay between spin-dependent contact interactions and quadratic Zeeman effect

Chapman, Sengstock,Bloch, Lett, Klempt…

NB: high spin fermions coming up! third energy scale set by Fermi energy

22 04 (a a

m

10-1

-101

SU(N) physics, spinor physics (Sengstock, Fallani, Bloch, Ye…)

Dipole-dipole interactions

22 203

11 3cos ( )

4dd J BV S gR

Anisotropic

Long range

24( ) ( )SV R a R

m

6

6( )

CV R

R

Van-der-Waals (contact) interactions

Short range

Isotropic

Two types of interactions

R

(only few experiments worldwide with non-negligible dipolar interactions - Stuttgart, Innsbruck, Stanford, Boulder)

Chromium: unusually large dipolar interactions(large electronic spin)

Two new features introduced by dipolar interactions:

Free Magnetization

Non-local coupling between spins

-3 -2 -1 0 1 2 3

ddV

3

1

RVdd

1st main feature : Spinor physics with free magnetization

-101Without

dipolar interactions

-10

1With anisotropic

ddV

-3 -2 -1 0 1 2 3

(a)

(b)

(c)

(d)

PRL 106, 255303 (2011)

20 6 42

J B c

n a ag B

m

Example: spontaneous demagnetization of a dipolar BEC

Occurs when the change in magnetic field energy is smaller than the spin-

dependent contact interaction

Need a very good control of B

(100 µG)BgmE BS

Fluxgate sensors

Rotate BEC ? Vortex ?

Einstein-de-Haas effectQuantum Hall regime with fermions?

Spin-orbit coupling (conservation of total angular

momentum)

1st main feature : Spinor physics with free magnetization

Ueda, PRL 96, 080405 (2006)Santos PRL 96, 190404 (2006)Gajda, PRL 99, 130401 (2007)B. Sun and L. You, PRL 99, 150402 (2007)Buchler, PRL 110, 145303 (2013)

Carr, New J. Phys. 17 025001 (2015)Peter Zoller arXiv:1410.3388 (2014)H.P. Buchler, arXiv:1410.5667 (2014)

Flat bands, topological insulatorsXYZ magnetism

FrustrationBgmE BS

0Eengineer

Magnetization changing processes write an x+iy

intersite phase

2nd main feature of dipolar interactions: Long range-coupling between atoms

Implications for lattice magnetism, spin domains…

0 Introduction to spinor physics

1 Thermodynamics and cooling of a Bose gas with free magnetization

2 Exotic quantum magnetism in optical lattices

Spin temperature equilibriates with mechanical degrees of freedom

Time of flight Temperature ( K)

Spi

n T

empe

ratu

re (

K)

1.4

1.2

1.0

0.8

0.6

0.4

0.2

1.21.00.80.60.40.2

We measure spin-temperature by fitting the mS population(separated by Stern-Gerlach

technique)

At low magnetic field: spin thermally activated

-10

1

-2-3

2

3

B Bg B k T

-3 -2 -1 0 1 2 3

Related to Demagnetization Cooling expts, T. Pfau, Nature Physics 2, 765 (2006)

1.0

0.8

0.6

0.4

0.2

0.01.21.00.80.60.40.2

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

1.21.00.80.60.40.20.0

Temperature ( K)

Temperature ( K)

Mag

neti

zati

onC

onde

nsat

e fr

acti

on

Spontaneous magnetization due to BEC

BEC only in mS=-3(lowest energy state)

Cloud spontaneously polarizes !

900B G

Thermal population in

Zeeman excited states

A non-interacting BEC is ferromagneticNew magnetism, differs from solid-state

PRL 108, 045307 (2012)

T>Tc T<Tc

a bi-modal spin distribution

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

180 160 140 120 100 80 60

ms=-3 ms=-1

Opt

ical

dep

th

ms=-2-3-2-1 0

2 1

3

Only thermal gas depolarizes…

get rid of it ?

(Bragg excitations or field gradient)

Purify the BEC

A new cooling method using the spin degrees of freedom?

A BEC component only in the ms=-3 state

BEC

Thermal

ms=-3 ms=-3, -2, -1, …

(i) Thermal cloud depolarizes

(ii) Kill spin-excited states

0.8

0.6

0.4

0.2

1.21.00.80.60.40.20.0

final condensate fraction

12x103

10

8

6

4

2

0

Ato

m N

umbe

r

1.00.80.60.40.2

BEC atom number Thermal atom number

A competition between two mechanisms

BEC

Thermal

ms=-3ms=-3, -2, -1, …

(i) Thermal cloud depolarizes

(ii) BEC melts to re- saturate ms=-3 thermal gas

(and cools it)

(iii) Kill spin-excited states

Losses in thermal cloud

due to depolarization

BEC melts (a little)

?WhoWins

?B

EC

fra

ctio

n

B-field

1.2

1.0

0.8

0.6

0.4

1.00.90.80.70.60.50.40.3

c f

T

T

c i

T

T

A competition between two mechanisms

At high T/Tc, BEC melts

(too few atoms in the BEC to cool the

thermal gas back to saturation)

At low T/Tc, spin filtering of excited

thermal atoms efficiently cools the gas

Theoretical model: rate equation based on the thermodynamics of Bosons with free magentization.

Interactions are included within Bogoliubov approximation

B=1,5mG

1.0

0.8

0.6

0.4

0.2

0.0

1.20.80.40.0

Summary of the experimental results as a function of B

7,50 2,5 5

Magnetic field (mG)

Fin

al c

onde

nsat

fra

ctio

n

(large field, no effect)

0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6

0 .2

0 .4

0 .6

0 .8

c f

T

T

c i

T

T

Theoretical limits for cooling

There does not seem to be any limit other than practical

In principle, cooling is efficient as long as depolarization is efficient

Process can be repeated

As T→0, less and less atoms are in the thermal cloud, therefore less and less spilling

However, all the entropy lies in the thermal cloud

Therefore, the gain in entropy is high at each spilling provided T~B

Initial entropy per atom

Ent

ropy

com

pres

sion 1.2

1.0

0.8

0.6

0.4

0.2

0.0

3.02.52.01.51.00.5

Proposal: Extension to ultra-low temperatures for non-dipolar gases

In our scheme, limitation around 25 nK, limited by(difficult to control below 100 µG)

BgTk BJB

Proposal: use Na or Rb at zero magnetization.

Spin dynamics occurs at constant magnetization-101

GkHz

Bg BJ

/8.2

2/70 GHzq

F=1, mF=-1, 0, 1

We estimate that temperatures in the pK regime may be reached

Nota: the spin degrees of freedom may also be used to measure temperature then

Related to collision-assisted Zeeman cooling, J. Roberts, EPJD, 68, 1, 14 (2014)

0 Introduction to spinor physics

1 Thermodynamics and cooling of a Bose gas with free magnetization

2 Exotic quantum magnetism in optical lattices

A 52Cr BEC in a 3D optical lattice

Optical lattice: Perdiodic potential made by a standing wave

3D lattice Strong correlations, Mott transition…

Our lattice architecture: (Horizontal 3-beam lattice) x (Vertical retro-reflected lattice)

Rectangular lattice of anisotropic sites

Study quantum magnetism with dipolar gases ?

3

212120 ).)(.(3.

4 R

uSuSSSgV RR

BJdd

222

111

212121

2

.24

32

1

SrSrzS

SrSrzS

SSSSSS

z

z

zz

Dipole-dipole interactions between real spins

Magnetization changing collisions

21 SS

1 2 1 2 1 2

1

2z zS S S S S S Heisenberg model of magnetism (effective spin model)Tentative model for strongly correlated materials, and

emergent phenomena such as high-Tc superconductivity

Condensed-matter: effective spin-spin interactions arise due to exchange interactions

2t

U

t

Control of magnetization-changing collisions:Magnetization dynamics resonance for a Mott state with two atoms per site (~15 mG)

Magnetic field (kHz)

m=

3 fr

actio

n

0.8

0.7

0.6

0.5

0.4

464442403836

-3-2

-10

12

3

Dipolar resonance when released energy matches band excitation

Mott state locally coupled to excited bandNon-linear spin-orbit coupling

Phys. Rev. A 87, 051609 (2013)

Magnetization changing collisions

21 SS

See also Gajda: Phys. Rev. A 88, 013608 (2013)

1 2 1 2 1 2

1

2z zS S S S S S

Magnetization changing collisions

Can be suppressed in optical lattices

21 SS

Ressembles but differs from Heisenberg magnetism:

From now on : stay away from dipolar magnetization dynamics resonances,Spin dynamics at constant magnetization (<15mG)

Related research with polar molecules:

1 2 1 2 1 2

1

2z zS S S S S S A. Micheli et al., Nature Phys. 2, 341 (2006).A.V. Gorshkov et al., PRL, 107, 115301 (2011), See also D. Peter et al., PRL. 109, 025303 (2012)

2212121 31)(

4

1. zSSSSSS zz

See Jin/Ye group Nature (2013)

Initiate spin dynamics by removing quadratic effect

vary time

Load optic

al lat

tice

quadratic effect

Adiabatic state preparation in 3D lattice

quadratic effect

-2-3

-2-1

01

23

-3

Explore spin dynamics in two configurations

(i) Mott state with a core of two atomes per site

(ii) Empty doublons: singly occupied sites, unit filling

Spin dynamics after emptying doubly-occupied sites:A proof of inter-site dipole-dipole interaction

Experiment: spin dynamics after the atoms are promoted to ms=-2

Theory: exact diagonalization of the t-J model on a 3*3 plaquette (P. Pedri, L. Santos)

Magnetization is constant

Phys. Rev. Lett., 111, 185305 (2013)

1.0

0.8

0.6

0.4

0.2

0.0

20151050

Time (ms)

Pop

(m

=-3

)/s

Pop

(m=

-2)

s

Timescale for spin dynamics = 20 msTunneling time = 100 ms

Super-exchange > 10s

!! Many-body dynamics !!(each atom coupled to many neighbours)

Mean-field theories fail

-1.0

-0.5

0.0

0.5

1.0

10008006004002000

-1.0

-0.5

0.0

0.5

1.0

10008006004002000

-3 -1-2 -2

Spin dynamics in doubly-occupied sites:Faster dynamics due to larger effective dipole (3+3=6 ?)

Magnetization is constantPhys. Rev. Lett., 111, 185305 (2013)

A toy many-body model for the dynamics at large lattice depth

2212121 31)(

4

1. zSSSSSS zz

2,2,3,2,...2,1,2,...2,222,....,2,2,

,ji

jiV

jijiV

,

2,2

(i) (j)

Exact diagonalization is excluded with two atoms per site (too many configurations for even a few sites)

Toy models for singlons

Toy models for doublons: replace S=3 by S=4 or S=6

Measured frequency: 300 HzCalculated frequency: S=4: 220 Hz

S=6: 320 Hz

Toy models seems to qualitatively reproduce oscillation; see related analysis in Porto, arXiv:1411.7036 (2015)

Observed spin dynamics, from superfluid to Mott

2.5

2.0

1.5

1.0

1.4

1.0

0.6

14121086420

Time (ms)

p /p3 2

3 ER

25 ER 1.2

0.8

0.4

0.0

0.60.40.20.0

Superfluid

Mott

-3 -1-2 -2

-3-1-2

-2

J Vdd

Vc

J

Large lattice depth: dynamics dominated by dipolar interactions

Lower lattice depth: super-exchange may occur and compete

An exotic magnetism driven by the competition between three types of exchange

DipolarSpin-dependent contact interactions

Super-exchange

Amplitude of exponential behaviour

Amplitude of oscillatory behaviour

Empirical description, from superfluid to Mott

Spin dynamics mostly exponential at low lattice depth

Dynamics shows oscillation at larger lattice depth

Slow cross-over between two regimes?

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Spi

n dy

nam

ics

am

plitu

de

2520151050

Lattice depth (Er)

4

6

8100

2

4

6

81000

2

4

Fre

qu

en

cy (

Hz)

302520151050

Lattice depth (Er)

Observed, and calculated frequencies

Two-body spin dynamics in isolated lattice sites

Many-body spin dynamics due to intersite couplings

naam

46

2

4

),(

2,2

jijiV

GP- mean-field simulation

-1.0

-0.5

0.0

0.5

1.0

6004002000

-3

-1

-2

-2-1.0

-0.5

0.0

0.5

1.0

10008006004002000

superexchange

Summary: a slow cross-over between two behaviors

In the Mott regime:

Two well separated oscillating frequencies corresponding to:

-On site contact-driven spin-exchange interactions

-Many-body intersite dipole-dipole interactions

At low lattice depth:

- GP-simulations predict long-lived oscillations (not seen on the experiment)Temperature effect ?

-Drift in spin dynamics qualitatively reproduced by simulation

-The dynamics depends on an interplay between contact and dipolar interactions

3.0

2.5

2.0

1.5

1.0

0.5

151050

7 Er

Time (ms)

p /p3 2

In the intermediate regime: -oscillations survive. - Two frequencies get closer

No theoretical model yet

-3 -1-2 -2

-3-1-2

-2

J Vdd

Vc

J

More probes to caracterize both regimes (1)

Hamiltonian should create entanglement (collaboration Perola Milman; Paris 7 University)

We are looking for an entanglement witness based on measurements of global spin variables.

(e.g. for any mixture of separable states)

Idea: adapt this criterion to our observations, measure spin fluctuations

Entanglement may only arrise at high lattice depth(otherwise BEC-like state)

When does entanglement appear/disappear?

SSSS zyx

2212121 31)(

4

1. zSSSSSS zz

2,2,3,2,...2,1,2,...2,222,....,2,2,

,ji

jiV

(i) (j)

More probes to caracterize both regimes (2)Mean-field vs « many-body » dynamics

22 203

11 3cos ( )

4dd J BV S gR

0 ddVd

At the mean-field level, dipolar interactions cancel out for an homogeneous system

Spin dynamics is a border effect(low lattice depth)

True many-body Hamiltonian predicts non-vanishing spin dynamics

2212121 31)(

4

1. zSSSSSS zz

2,2,3,2,...2,1,2,...2,222,....,2,2,

,ji

jiV

jijiV

,

2,2

(i) (j)

Deep lattices: spin dynamics occurs in the core

Measure locally could differentiate between regimes

What have we learned (1)?

Bulk Magnetism: spinor physics with free magnetization

New spinor phases at extremely low magnetic fields-3 -2 -1 0 1 2 3

(a)

(b)

(c)

(d)

1.2

1.0

0.8

0.6

0.4

1.00.90.80.70.60.50.40.3

c f

T

T

c i

T

T

New cooling mechanism to reach very low entropies (in bulk):Use spin to store and remove entropy

Should be applicable to non-dipolar speciespK regime possible

What have we learned (2)?

Lattice Magnetism:

1.2

1.0

0.8

0.6

0.4

0.2

0.0

4442403836

0.6

0.4

0.2

0.0

2 atoms per site 3 atoms per site

0.4

0.3

0.2

0.1

0.0

Pop

ula

tion

s

14121086420

Time (ms)

mS=-3 mS=-2 mS=-1 mS=0Magnetization dynamics is resonant

Intersite dipolar spin-exchange

Exotic quantum magnetism, from Mott to superfluid

Different types of exchange contribute

Consequences for magnetic ordering ?4

6

8100

2

4

6

81000

2

4

Fre

qu

en

cy (

Hz)

302520151050

Lattice depth (Er)

What have we learned ? (3)

Truly new phenomena arrise due to dipolar interactions when the spin degrees of freedom are released.

- Free magnetization. Spin orbit coupling. Also an interesting challenge from the theoretical point of view.

- Effective Hamiltonians relevant for quantum magnetism. Some of the physics is specific to high spin atoms (no analog with electrons or with

heteronuclear molecules)

- Large spin atoms in optical lattices: a yet almost unexplored playground for many-body physics (even without dipolar interactions)

Carr, New J. Phys. 17 025001 (2015)Peter Zoller arXiv:1410.3388 (2014)H.P. Buchler, arXiv:1410.5667 (2014)

See M. Wall et al., arXiv 1305.1236

Bruno Naylor

A. de Paz (PhD), A. Sharma, A. Chotia, B. Naylor (PhD) E. Maréchal, L. Vernac,O. Gorceix, B. LaburtheP. Pedri (Theory), L. Santos (Theory, Hannover)

Thank youThank you

Aurélie De Paz Amodsen

Chotia

Arijit Sharma

Post-doctoral position available

This is not the whole picture: the (small but interesting) effect of demagnetization cooling

Our theoretical results predict that depolarization may induce an increase of the BEC atom number!!

How is it compatible with the fact that the entropy must increase?

thBc

B fkT

TkNS 6.36.3/

3

Entropy of a saturated cloud: Entropy of a non-saturated cloud: is… larger

The entropy can therefore be stored in the non-saturated gas, and the BEC atom

number increase, without filtering!

For a fully saturated gas, the entropy is given by the condensate fraction: you cannot increase the condensate fraction and entropy at the same

time !

NB: this effect is associated to demagnetization cooling

T. Pfau, Nature Physics 2, 765 (2006)

Tk

BgBgTk

B

BJBJB

exp3

3.5

3.0

2.5

2.0

1.5

1.0

0.5

1.21.00.80.60.40.20.0

thBc

B fkT

TkNS 6.36.3/

3

How to characterize the cooling efficiency: use entropy per particle

As T→0, less and less atoms are in the thermal cloud

Therefore less and less spilling

However, all the entropy lies in the thermal cloud

Therefore, the gain in entropy is high at each spilling provided T~B

Initial entropy per atom

Ent

ropy

com

pres

sion 1.2

1.0

0.8

0.6

0.4

0.2

0.0

3.02.52.01.51.00.5 7,50 2,5 5

Magnetic field (mG)

Ent

ropy

(gi

ven

by B

EC

fra

ctio

n)

1 2 1 2 1 2

1

2z zS S S S S S

Complex Many-body physics

Many open questions…

Our approach : Study magnetism with strongly magnetic atoms : dipole-dipole interactions between real spins

R

Simple two-body Hamiltonian

3

212120 ).)(.(3.

4 R

uSuSSSgV RR

BJdd

222

111

212121

2

.24

32

1

SrSrzS

SrSrzS

SSSSSS

z

z

zz

Possibilities for quantum simulation – possibilities for exotic quantum magnetism

Quantum magnetism, some paradigms, from solid-state physics

High-Tc superconductivity Antiferromagnetism Hubbard model

Frustrated magnetism

??

Spin liquids

1 2 1 2 1 2

1

2z zS S S S S S

Heisenberg model of magnetism (real spins, effective spin-spin interaction)

Condensed-matter: effective spin-spin interactions arise due to exchange interactions

2t

U

t

Ising ExchangeOur experiment:

real spin-spin interactions due to dipole-dipole interactions

This is not the whole picture: the (small but interesting) effect of demagnetization cooling

ms=-3 ms=-3, -2, -1, …

At finite magnetic field, depolarization implies a

conversion of kinetic energy in magnetic energy

T. Pfau, Nature Physics 2, 765 (2006)

Tk

BgBgTk

B

BJBJB

exp3

At finite magnetic field, depolarization

may induce an increase of the BEC

atom number!!

Bg BJ

How is it compatible with the

fact that the entropy must increase?

thBc

B fkT

TkNS 6.36.3/

3

Entropy of a saturated cloud:

Entropy of a non-saturated cloud: is… larger

The entropy can therefore be stored in the non-saturated gas, and the BEC atom number

increase, without filtering!

For a fully saturated gas, the entropy is given by the condensate fraction: you cannot increase the

condensate fraction and entropy at the same time !