have left: b. pasquiou (phd), g. bismut (phd), a. chotia, m. efremov, q. beaufils, j. c. keller, t....
TRANSCRIPT
Have left: B. Pasquiou (PhD), G. Bismut (PhD), A. Chotia, M. Efremov , Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu
Collaborators: Anne Crubellier (Laboratoire Aimé Cotton), J. Huckans, M. Gajda
A. de Paz (PhD), A. Sharma, B. Laburthe-Tolra, E. Maréchal, L. Vernac,
P. Pedri (Theory), O. Gorceix (Group leader)
Dipolar chromium BECs, and magnetismDipolar chromium BECs, and magnetism
(magnetic) dipole-dipole interactions
22 203
11 3cos ( )
4dd J BV S gR
Anisotropic
Long range
Chromium : an artificially large spin (S=3):
R
Bd 6
24( ) ( )SV R a R
m
6
6( )
CV R
R
Van-der-Waals (contact) interactions
Short rangeIsotropic
20
212m dd
ddVdW
m V
a V
Relative strength of dipole-dipole and Van-der-Waals interactions
Anisotropic explosion pattern reveals dipolar
coupling.
Stuttgart: Tune contact interactions using Feshbach resonances (Nature. 448, 672 (2007))
1dd Spherical BEC collapses
0.16dd Cr:
R
1dd BEC stable despite attractive part of dipole-dipole interactions
Small (but interesting) effects observed – at the % level :- Striction – Stuttgart, PRL 95, 150406 (2005)- Collective excitations - Villetaneuse, PRL 105, 040404 (2010) - Anisotropic speed of sound, Villetaneuse, PRL 109, 155302 (2012)
Stuttgart: d-wave collapse, PRL 101, 080401 (2008)See also Er PRL, 108, 210401 (2012)See also Dy, PRL, 107, 190401 (2012) and Dy Fermi sea PRL, 108, 215301 (2012) … and heteronuclear molecules… )
1(137~
22
ddV
Polarized (« scalar ») BEC Hydrodynamics
Collective excitations, sound, superfluidity
22 203
11 3cos ( )
4dd J BV S gR
Anisotropic
Long-ranged
R
Hydrodynamics:non-local mean-field
Magnetism:Atoms are magnets
Chromium (S=3): involve dipole-dipole interactions
Multicomponent (« spinor ») BEC Magnetism
Phases, spin textures…
Interactions couple spin and orbital degrees of freedom
Key idea:
Study magnetism with large spins (S=3, S=6…)
This talk:
0 Introduction to spinor physics
1 Spinor physics of a Bose gas with free magnetization
2 (Quantum) magnetism in opical lattices
Exchange energyCoherent spin oscillation
Chapman, Sengstock…
10,0 1, 1 1,1
2
Quantum effects!KlemptStamper-Kurn
Domains, spin textures, spin waves, topological states
Stamper-Kurn, Chapman, Sengstock, Shin…
Quantum phase transitions
Stamper-Kurn, Lett,Gerbier
Introduction to spinor physics
Main ingredients for spinor physics
Spin-dependent contact interactions
Spin exchange
22 04 (a a
m
0,03
10,2
3
2
0,0
tottot
SS
mSmS
mm
Quadratic Zeeman effect
S=1,2,…
Main new features with Cr
S=3
7 Zeeman states4 scattering lengths
New structures
Purely linear Zeeman effect
Strong spin-dependent contact interactions
And
Dipole-dipole interactions
-101
Dipolar interactions introduce magnetization-changing collisions
Dipole-dipole interactions
22 203
11 3cos ( )
4dd J BV S gR
R
-101
-10
1
-2-3
2
3
without ddV
with ddV
Important to control magnetic field
Rotate the BEC ? Spontaneous creation of vortices ?
Einstein-de-Haas effect
2 BgmE BS
0 lS mm
Angular momentum conservation
Dipolar relaxation, rotation, and magnetic field
-3-2
-10
12
3
3,22,32
13,3
Ueda, PRL 96, 080405 (2006)Santos PRL 96, 190404 (2006)Gajda, PRL 99, 130401 (2007)B. Sun and L. You, PRL 99, 150402 (2007)
-3
-2
-1
0
1
2
3
B=1GParticle leaves the trap
B=10 mGEnergy gain matches band
excitation in a lattice
B=.1 mGEnergy gain equals to
chemical potential in BEC
S=3 Spinor physics with free magnetization
Technical challenges :
Good control of magnetic field needed (down to 100 G) Active feedback with fluxgate sensors
Low atom number – 10 000 atoms in 7 Zeeman states
1 Spinor physics of a Bose gas with free magnetization
2 (Quantum) magnetism in opical 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, 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
Below a critical magnetic field: the BEC ceases to be ferromagnetic !
Temperature ( K)
Mag
netiz
atio
n
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
1.20.80.40.0
1.0
0.8
0.6
0.4
0.2
0.0
0.50.40.30.20.1
Temperature ( K)C
onde
nsat
e fr
acti
on-Magnetization remains small even when the condensate fraction approaches 1!! Observation of a depolarized condensate !!
Necessarily an interaction effect
B=100 µG
B=900 µG
PRL 108, 045307 (2012)
Santos PRL 96, 190404 (2006)
-2
-1
-3-3-2-1 0
2 1
3
20 6 42
J B c
n a ag B
m
-2-1
01
23
-3
Large magnetic field : ferromagnetic Low magnetic field : polar/cyclic
Ho PRL. 96, 190405 (2006) -2
-3
4" "6" "
Cr spinor properties at low field
PRL 106, 255303 (2011)
2, 2
6 56, 4 4, 4
11 11
S S
tot tot
m m
S m S m
Good agreement between field below which we see
demagnetization and Bc
Open questions about equilibrium state
Santos and Pfau PRL 96, 190404 (2006)Diener and HoPRL. 96, 190405 (2006)
Phases set by contact interactions, magnetization dynamics set by
dipole-dipole interactions
- Operate near B=0. Investigate absolute many-body ground-state-We do not (cannot ?) reach those new ground state phases -Quench should induce vortices…-Role of thermal excitations ?
!! Depolarized BEC likely in metastable state !!
Demler et al., PRL 97, 180412 (2006)
-3 -2 -1 0 1 2 3
(a)
(b)
(c)
(d)
Polar Cyclic
11,0,0,0,0,0,1
2 11,0,0,0,0,1,0
2
Mag
neti
c fi
eld
Magnetic phase diagram
Measure Tc(B) and M(Tc,B) for different
magnetic fields BGet Tc(M)
Quasi-Boltzmann distribution
Bi-modal spin distribution
Phase diagram adapted from J. Phys. Soc. Jpn, 69, 12, 3864 (2000) See also PRA, 59, 1528 (1999)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-3.0-2.5-2.0-1.5-1.0-0.50.0
Magnetization
T/T
c
A
B
C
cB BcB B
0 Introduction to spinor physics
1 Spinor physics of a Bose gas with free magnetization
2 (Quantum) magnetism in opical lattices
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
Hubard model at half filling, Heisenberg model of magnetism (effective spin model)
Magnetization changing collisions
21 SS
1 2 1 2 1 2
1
2z zS S S S S S
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 band
Produce BEC m=-3detect m=-3
Rf sweep 1
Rf sweep 2
m=+3, wait time
Load optic
al lat
tice
14x103
1210
8
64
20018016014012010080Magnetic field (kHz)
6040
Ato
m n
umbe
rDirect manifestation of anisotropic interactions :
Strong anisotropy of dipolar resonances
Anisotropic lattice sites
22
5
3 ( )
2r
x iyV Sd
r
See also PRL 106, 015301 (2011)
At resonance
May produce vortices in each lattice site (Einstein-de-Haas
effect)(problem of tunneling)
1 2 1 2 1 2
1
2z zS S S S S S
1 2 1 2 1 2
1
4z zS S S S S S Magnetization
changing collisionsCan be suppressed in
optical lattices
21 SS
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)
Other differences from Heisenberg magnetism:
-Bosons…
-Not a spin ½ system: S=3
-Anisotropy
--1/r3 dependence
-Does not rely on Mott physics
- Can have more than one atom per site
Effective St
3 3 6,4,2,0...tS S S
=
6
4
6
4
46 ddV
2212121 31)(
4
1. zSSSSSS zz
Control the initial state by a tensor light-shift
A polarized laserClose to a JJ transition
(100 mW 427.8 nm)-1
0
1
-2
-3
-3 -2 -1 0 1 2 3
mS2
Quadratic effect allows state preparation
Adiabatic state preparation in 3D lattice
tquadratic effect
-2 -3
Initiate spin dynamics by removing quadratic effect
(2 atomes / site)
vary time
Load optic
al lat
tice
quadratic effect
2
6 4
4cB B n a a
m
0.9
0.8
0.7
0.6
0.5
0.50.40.30.20.10.0
-2.0
-1.5
temps (ms)
magnétization
Fra
ctio
n da
ns m
=-2
Short times : fast oscillations due to spin-dependent contact interactions
-3-2-1
( 250 µs)
(period 220 µs)Up to now unknown source of damping
(sudden melting of Mott insulator ?)
2, 2
6 56, 4 4, 4
11 11
S S
tot tot
m m
S m S m
PRELIMINARY
Long time-scale spin dynamics in lattice : intersite dipolar exchange
Sign for intersite dipolar interaction
(two orders of magnitude slower than on-site
dynamics)
21212
1SSSSMagnetization is constant
0.4
0.3
0.2
0.1
0.0
Pop
ula
tion
s
14121086420
Time (ms)
mS=-3 mS=-2 mS=-1 mS=0
PRELIMINARY
Oscillations arise from interactions between doubled-occupied sites
1.4
1.2
1.0
0.8
0.6
0.4
302520151050
Both doublons and singlons Only singlons Only singlons, shifted
Time (ms)
(m=
-3)/
(m=
-2)
Effect of doublons ?
Very slow spin dynamics for one particle per site:Intersite dipole-dipole coupling
PRELIMINARY
Our current understanding:
Spin oscillations due to inter-site dipolar exchange between doublons
1 2 1 2 1 2
1
4z zS S S S S S
(Very) long time-scale dynamics due to inter-site dipolar exchange between singlons
Exact diagonalization 2 pairs, 2 sitesFaster coupling because larger effecive spin
Timescale = 4 ms
1/e timescale = 25 ms
0.5
0.4
0.3
0.2
0.1
0.0
Fra
ctio
n
86420
Time (ms)
mS=-3 mS=-2 mS=-1 mS=0 mS=1
Theoretical estimate : 2 atoms, 2 sites : exchange timescale = 50 ms
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)
Conclusions1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-3.0-2.5-2.0-1.5-1.0-0.50.0
Magnetization
T/T
c
A
B
C
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=0
Magnetization dynamics is resonant Intersite dipolar spin-exchange