Have left: B. Pasquiou (PhD), G. Bismut (PhD), M. Efremov, Q. Beaufils (PhD), J.C. Keller, T. Zanon, R. Barbé, A. Pouderous (PhD), R. Chicireanu (PhD) Collaborator: Anne Crubellier (Laboratoire Aimé Cotton) A.de Paz (PhD), A. Chotia, A. Sharma, B. Laburthe-Tolra , E. Maréchal, L. Vernac, P. Pedri (Theory), O. Gorceix (Group leader) Dipolar chromium BECs Dipolar chromium BECs
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Have left: B. Pasquiou (PhD), G. Bismut (PhD), M. Efremov, Q. Beaufils (PhD),
J.C. Keller, T. Zanon, R. Barbé, A. Pouderous (PhD), R. Chicireanu (PhD)
Collaborator: Anne Crubellier (Laboratoire Aimé Cotton)
A.de Paz (PhD), A. Chotia, A. Sharma, B. Laburthe-Tolra, E. Maréchal, L. Vernac,
P. Pedri (Theory), O. Gorceix (Group leader)
Dipolar chromium BECsDipolar chromium BECs
Dipole-dipole interactions
22 203
11 3cos ( )
4dd J BV S gR
Anisotropic
Long range
Chromium (S=3): 6 electrons in outer shell have their spin aligned
Van-der-Waals plus dipole-dipole interactions
R
Hydrodynamics Magnetism
20
212m dd
ddVdW
m V
a V
Relative strength of dipole-dipole and Van-der-Waals interactions
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)Also coming up: heteronuclear molecules (e.g. K-Rb)
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-Thermodynamics: how magnetization depends on temperature-Spontaneous depolarization of the BEC due to spin-dependent interactions
2 Magnetism in opical lattices-Depolarized ground state at low magnetic field-Spin and magnetization dynamics
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
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
onSpontaneous magnetization due to BEC
BEC only in mS=-3(lowest energy state)
Cloud spontaneously polarizes !
900B G
Thermal population in
Zeeman excited states
Non-interacting multicomponent Bose thermodynamics: a BEC is ferromagnetic
Phys. Rev. Lett. 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
Phys. Rev. Lett. 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
Phys. Rev. Lett. 106, 255303 (2011)
Density dependent threshold
20 6 42
J B c
n a ag B
m
BEC Lattice
Critical field 0.26 mG 1.25 mG
1/e fitted 0.3 mG 1.45 mG
Load into deep 2D optical lattices to boost density.Field for depolarization depends on density
1.0
0.8
0.6
0.4
0.2
0.0543210
Magnetic field (mG)
BEC BEC in lattice
Fin
al m
=-3
fra
ctio
n
Phys. Rev. Lett. 106, 255303 (2011)
Note: Possible new physics in 1D: Polar phase is a singlet-paired phase Shlyapnikov-Tsvelik NJP, 13, 065012 (2011)
Dynamics analysis
Meanfield picture : Spin(or) precession
Ueda, PRL 96, 080405 (2006)
21/3 20( )4dd J BV r n S g n
Natural timescale for depolarization:
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
Mag
netiz
atio
n
25020015010050
Time (ms)
Bulk BEC In 2D lattice
PRL 106, 255303 (2011)
Produce BEC m=-3
Rapidly lower magnetic field
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
1 Spinor physics of a Bose gas with free magnetization-Thermodynamics: Spontaneous magnetization of the gas due to ferromagnetic nature of BEC-Spontaneous depolarization of the BEC due to spin-dependent interactions
2 Magnetism in 3D opical lattices-Depolarized ground state at low magnetic field-Spin and magnetization dynamics
Loading an optical lattice
2D
3D
Optical lattice = periodic (sinusoidal) potential due to AC Stark Shift of a standing wave
(from I. Bloch)
(in our case (1 , 1 , 2.6)* /2 periodicity)
We load in the Mott regime U=10kHz, J=100 Hz
U
J
In practice, 2 per site in the center (Mott plateau)
-3.0
-2.5
-2.0
-1.5
15105Magnetic field (kHz)
Mag
neti
zati
onSpontaneous demagnetization of atoms in a 3D lattice
20 6 44
J B cg B
n a a
m
3D lattice
Critical field
4kHz
Threshold seen
5kHz
6, 6S m 4, 4S m
-3-2
4" "6" "
Control the ground state by a light-induced effective Quadratic Zeeman effect
A polarized laserClose to a JJ transition
(100 mW 427.8 nm)
In practice, a component couples mS states
Typical groundstate at 60 kHz
Magnetic field (kHz)
1501209060300
-1
0
1
-2
-3
-3-2-10
-3 -2 -1 0 1 2 3
Ene
rgy
mS2
Note : The effective Zeeman effect is crucial for good state preparation
-1 0 1-2-3 2 3
Large spin-dependent (contact) interactions
in the BEC have a very large effect on the final
state
Adiabatic (reversible) change in magnetic state (unrelated to dipolar interactions)
tquadratic effect
-3
-2
BEC (no lattice)
3D lattice (1 atom per site)
Note: the spin state reached without a 3D lattice is completely different !
-3-2-10
-3
-2-101-3-2-1
Time (ms)
popu
lati
ons
0.6
0.5
0.4
0.3
0.2
20151050
m=-3 m=-2
Magnetization dynamics in lattice
vary timeLoad optic
al lat
tice
quadratic effect
Role of intersite dipolar relaxation ?
Magnetization dynamics resonance for two atoms per site
Magnetic field (kHz)
m=
3 fr
actio
n0.8
0.7
0.6
0.5
0.4
464442403836
-3-2
-10
12
3
Dipolar resonance when released energy matches band excitation
Towards coherent excitation of pairs into higher lattice orbitals ?
(Rabi oscillations)
Mott state locally coupled to excited band
Resonance sensitive to atom number
Measuring population in higher bands (1D)(band mapping procedure):
Population in different bandsdue to dipolar relaxation
m=3
m=2
-3-2
-10
12
3
0.12
0.10
0.08
0.06
0.04
0.02
0.00
16012080400
Magnetic field (kHz)
Frac
tion
of a
tom
s in
v=
1
1 BZ
st 2 BZ
nd2 BZ
nd
(a)x
z
y
y
PRL 106, 015301 (2011)
14x103
1210
8
64
20018016014012010080Magnetic field (kHz)
6040
Ato
m n
umbe
rStrong 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 (EdH effect)(problem of tunneling)
Magnetization changing dipolar collisions introduce the spinor physics with free magnetization
0D
40302010
B (mG)
Magnetism in optical lattices magnetization dynamics in optical lattices can be made resonant could be made coherent ? towards Einstein-de-Haas (rotation in lattice sites)
New spinor phases at extremely low magnetic fields
-3 -2 -1 0 1 2 3
(a)
(b)
(c)
(d)
Conclusions
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
Tensor light-shift allow to reach new quantum phases
A. de Paz, A. Chotia, A. Sharma, B. Pasquiou (PhD), G. Bismut (PhD), B. Laburthe, E. Maréchal, L. Vernac,