have left: b. pasquiou (phd), g. bismut (phd), m. efremov, q. beaufils, j. c. keller, t. zanon, r....
TRANSCRIPT
Have left: B. Pasquiou (PhD), G. Bismut (PhD), 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. Chotia, A. Sharma, B. Laburthe-Tolra, E. Maréchal, L. Vernac,
P. Pedri (Theory), O. Gorceix (Group leader)
Magnetization dynamics of a dipolar BEC in a 3DMagnetization dynamics of a dipolar BEC in a 3Doptical latticeoptical lattice
Dipole-dipole interactions
22 203
11 3cos ( )
4dd J BV S gR
Anisotropic
Long range
Chromium (S=3): Van-der-Waals plus dipole-dipole interactions
R
20
212m dd
ddVdW
m V
a V
Relative strength of dipole-dipole and Van-der-Waals interactions
0.16dd Cr:
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) … and heteronuclear molecules…
Anisotropic explosion pattern reveals dipolar coupling.
Stuttgart: Tune contact interactions using Feshbach resonances (Nature. 448, 672 (2007))
1dd BEC collapses
0.16dd Cr:
R
1dd BEC stable despite attractive part of dipole-dipole interactions
1.2
1.0
0.8
0.6
2015105
Asp
ect
rati
oVilletaneuse, PRL 105, 040404 (2010)
Stuttgart, PRL 95, 150406 (2005)
Collective excitations
Striction
Anisotropic speed of sound
0.15
0.10
0.05
0.00
3000200010000
Frequency difference (Hz)
Fra
ctio
n of
exc
ited
atom
s
Bragg spectroscopyVilletaneusearXiv: 1205.6305 (2012)
Hydrodynamic properties of a BEC with weak dipole-dipole interactions
Interesting but weak effects in a scalar Cr BEC
Saddle shape
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…
Focus on : Magnetization dynamics in a 3D optical lattice :
- 3 regimes :
- B is of the order of the lattice band excitations. Observation of dipolar resonances and of band excitations mediated by dipole interactions.Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution.
- B is below the first excitation band : Observation of intersite dynamics, with constant magnetization.
-B is very low : spontaneous depolarization.
Observation of spin changing collisions resonances and band excitations:
- BEC atom number N=10^4 atoms. - Loaded adiabatically in a 3 D anisotropic optical lattice.
k1
k3
OX
k2
Lattice in horizontal plane
Typical frequencies:
x = 2kHz y = 2kHz
z = 2kHz
BEC In m=-3
Rf sweep
20 ms T
V0 ≈ 25 ErTime sequence :
m=+3
+B amplitude and direction is setStern Gerlach analysis
2
1
Mott distributionWith our parameters
2
3,22,3 3,3
)1(
2,2)2(
-3
-2-1
01
2
3
Two dipolar relaxation channels for two atoms in m=+3, sharing a same lattice site
Here, z is fixed by the B field orientation.
8000
6000
4000
2000
6040200
time
Ato
ms
rem
ain
ing
in m
=-
3
If B is higher than the lattice depth (25 Er), dipolar relaxation leads to losses. This case allows to measure the number of site with single occupancy.
B is higher than the trap depth
B is lower than the trap depth
Mott distribution
2
1
Simple measure of site with two atoms or more
If B is lower than the lattice depth : magnetization dynamics with no loss.
Dynamics very sensitive to the magnetic field orientation and value.
Bg BSL
Observation of resonances due to dipolar relaxation (fixed time T=12 ms)
Anisotropic lattice sites
Bg BSL
-Two particles in a harmonic anisotropic potential with frequencies x, y andz.- Consider the relative orbital motion-Initial relative orbital motion |nX=0, nY=0, nZ=0>-Coupling to final relative orbital motion of the atomic pair |nx,ny,nz>
Initial
Final0,0,03,3
0,2,02,2
For channel 2 :
B along OX
Predication of the resonances position:
22 )( izyV
2,23,3 L2
Width of the resonances enlarged by the tunneling
Lower energy resonance around 50 kHz :- Tunneling very small (100 Hz)- Focus on this lowest energy resonance.
Red curve :
Lowest energy resonance at L=Y
Typical frequencies:
x = 2kHz y = 2kHz
z = 2kHz
With (nY+nZ) even
Lower energy resonance. Probe of the atom number distribution.
Black curve : two atoms / site. Contact interaction : shift and splitting of the resonance.
Shift due to contact interactions
Molecular Basis :
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
Note: Lineshape of dipolar resonances probes number of atoms per site
3 and more atoms per sites loaded in lattice for faster loading
B(kHz)
Frac
tion
in m
=+
3
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
Few-body physics !The 3-atom state which is reached has entangled
spin and orbital degrees of freedom
Probe of atom squeezing in Mott state
0,0,23,3,20,0,03,3,3 spin orbit
Focus on : Magnetization dynamics in a 3D optical lattice :
- 3 regimes :
- B is of the order of the lattice depth. Observation of dipolar resonances and of band excitations mediated by dipole interactions.Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution.
- B is below the first excitation band : Observation of intersite dynamics, with constant magnetization.
-B is very low : spontaneous depolarization.
From now on : stay away from dipolar magnetization dynamics resonances,Spin dynamics at constant magnetization (<15mG)
New tool : Control the initial state by a tensor light-shift
A polarized laserClose to a JJ transition
(100 mW 427.8 nm)
In practice, a component couples mS statesMagnetic field (kHz)
1501209060300
-1
0
1
-2
-3
-3 -2 -1 0 1 2 3E
nerg
y
mS2
Quadratic light shift effect allows state preparation
3Sm
Adiabatic state preparation in 3D lattice
tquadratic effect
-2 -3
12, 2 3, 1 1, 3
2
2, 2
6 56, 4 4, 4
11 11
S S
tot tot
m m
S m S m
2
6 4
4cB B n a a
m
Initiate spin dynamics by removing quadratic effect
(2 atomes / site)
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
On-site spin oscillations
-3-2-1
( 250 µs)
vary timeLoad
optical
lattic
e
quadratic effect
(due to contact oscillations)
(period 220 µs)
Up to now unknown source of damping
Time (ms)
popu
lati
ons
0.6
0.5
0.4
0.3
0.2
20151050
m=-3 m=-2
Long time-scale spin dynamics in lattice
vary timeLoad
optical
lattic
e
quadratic effect
Sign for intersite dipolar interaction ?
(two orders of magnitude slower than on-site
dynamics)
21212
1SSSS
1.4
1.2
1.0
0.8
0.6
0.4
20151050
pop(
m=
-3)/
pop(
m=
-2)
time (ms)
Coherent spin oscillations at lower lattice depth
The very long time scale excludes on-site oscillations
where spin-exchange collisions dominate
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
2.0
1.5
1.0
0.5
0.0
Osc
illa
tion
am
plit
ude
16141210864201D lattice depth (Er)
1.5
1.0
0.5
0.0
Width
ofdiffractio
npea
k
Probing spin oscillations from superfluid to Mott
Intersite coherent spin oscillation seems to need phase coherence
between sites
Superfluid more robustProbes magnetism from superfluid to
insulator
(Probes coherence length)
(probes coherent spin oscillations)
Focus on : Magnetization dynamics in a 3D optical lattice :
- 3 regimes :
- B is of the order of the lattice depth. Observation of dipolar resonances and of band excitations mediated by dipole interactions.Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution.
- B is below the first excitation band : Observation of intersite dynamics, with constant magnetization.
-B is very low : spontaneous depolarization.
-3.0
-2.5
-2.0
-1.5
15105Magnetic field (kHz)
Mag
neti
zati
on
At extremely low magnetic field (<1.5 mG):Spontaneous 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" "
PRL 106, 255303 (2011) ( in bulk BEC)
Summary - Magnetism in lattice1.2
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
Away from resonances: spin oscillationsSpin-exchange : intrasite and inter site dynamics
Not robust in Mott regime
1.4
1.2
1.0
0.8
0.6
0.4
20151050
pop(
m=
-3)/
pop(
m=
-2)
time (ms)
Resonant magnetization dynamicsFew body vs many body physics
Spontaneous depolarization at low magnetic fieldTowards low-field phase diagram
-3.0
-2.5
-2.0
-1.5
15105Magnetic field (kHz)
Mag
neti
zati
on
A.de Paz, A. Chotia, A. Sharma B. Pasquiou, G. Bismut, B. Laburthe-Tolra, E. Maréchal, L. Vernac,
P. Pedri, M. Efremov, O. Gorceix
Thanks for your attention!.
A.de Paz, A. Chotia, A. Sharma B. Pasquiou, G. Bismut, B. Laburthe-Tolra, E. Maréchal, L. Vernac,
P. Pedri, M. Efremov, O. Gorceix