Transcript Diapositive 1 - Laboratoire de Physique des Lasers

Laboratoire de Physique des Lasers
Université Paris Nord
Villetaneuse - France
Elastic and inelastic dipolar effects in chromium BECs
B. Laburthe-Tolra
G. Bismut (PhD), B. Pasquiou (PhD)
B. Laburthe, E. Maréchal, L. Vernac,
P. Pedri (Theory),
O. Gorceix (Group leader)
Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu
Collaborator: Anne Crubellier (Laboratoire Aimé Cotton)
Invited professors: W. de Souza Melo (Brasil), D. Ciampini (Italy), T. Porto (USA)
Internships (since 2008): M. Trebitsch, M. Champion, J. P. Alvarez, M. Pigeard, E. Andrieux, M. Bussonier,
F. Hartmann, R. Jeanneret, B. Bourget
Types of interactions in BECs
Van-der Waals, short range and isotropic.
Pure s-wave collisions at low temperature.
Effective potential aS d(R), with aS scattering lenght,
tunable thanks to Feshbach resonances
Multicomponent BECs:
More than one state, more than one scattering length.
Exchange interactions decide which spin configuration reaches the lowest energy
Quantum phase transitions
Ferromagnetic / Polar/ Cyclic phases
Dipole-dipole interactions
(magnetic atoms, Cr, Er, Dy, dipolar molecules, Rydberg atoms)
Alkalis: Van-der-Waals interactions (effective d potential)
Chromium (S=3): Van-der-Waals plus dipole-dipole
Dipole-dipole interactions
Vdd 
0 2
1
2
S  g J  B  1  3cos 2 ( )  3
4
R
Long range
Anisotropic
« Elastic »:
Non local anisotropic
mean-field
« Inelastic »:

R
Coupling between spin
and rotation
Elastic
Relative strength of dipole-dipole and Van-der-Waals interactions
0 m2 m Vdd
 dd 

2
12 a VVdW
 dd  1
Cr:
 dd  0.16
BEC collapses
Stuttgart: Tune contact interactions using Feshbach resonances (Pfau, Nature. 448, 672 (2007))

Stuttgart: d-wave collapse, PRL 101, 080401 (2008)
R
 dd  1
Anisotropic
explosion pattern
reveals dipolar
coupling.
(Breakdown of self
similarity)
BEC stable despite attractive part of dipole-dipole interactions
Parabolic ansatz still good. Striction of BEC. (Eberlein, PRL 92, 250401 (2004))
Interaction-driven expansion of a BEC
A lie:
Imaging BEC after time-of-fligth
is a measure of in-situ
momentum distribution
Self-similar, Castin-Dum expansion
Phys. Rev. Lett. 77, 5315 (1996)
Cs BEC with tunable interactions
(from Innsbruck))
TF radii after expansion related to interactions
Modification of BEC expansion due to dipole-dipole interactions
TF profile
 dd (r )   Vdd (r  r ')n(r ')d 3r '
Striction of BEC
(non local effect)
Eberlein, PRL 92, 250401 (2004)
Pfau,PRL 95, 150406 (2005)
(similar results in
our group)
Frequency of collective excitations
(Castin-Dum)
Consider small oscillations, then
d2
 H .
2
dt
with
 312

H   22
 32

12
322
32
12 

22 
332 
Interpretation
Sound velocity
mvS2    gn
In the Thomas-Fermi regime, collective
excitations frequency independent of number
of atoms and interaction strength:
Pure geometrical factor
(solely depends on trapping frequencies)
vS
E  
R
TF radius
1
m 2 R 2    gn
2
Collective excitations of a dipolar BEC
Due to the anisotropy of dipole-dipole interactions, the
dipolar mean-field depends on the relative orientation of the
magnetic field and the axis of the trap
Repeat the experiment for two directions of the magnetic
field (differential measurement)
Parametric excitations
Phys. Rev. Lett. 105, 040404 (2010)
Aspect ratio
1.2
1.0
0.8
0.6
5
t (ms )
10
15
A small, but qualitative, difference (geometry is not all)


  dd
20
A consequence of anisotropy :
trap geometry dependence of the frequency shift
Shift of the
quadrupole
mode
frequency
(%)
Shift of the
aspect ratio
(%)
Sign of dipolar meanfield depends on trap
geometry
(oblate / elongated)
•Related to the trap
anisotropy
Phys. Rev. Lett. 105, 040404 (2010)
Good agreement with
Thomas-Fermi predictions
Eberlein, PRL 92, 250401 (2004)
Non local anisotropic meanfield
-Static and dynamic properties of BECs
Small effects in Cr…
Need Feshbach resonances or larger dipoles.
With… ? Cr ? Er ? Dy ? Dipolar molecules ?
Then…, Tc, solitons, vortices, Mott physics,
new phases (checkboard), 1D or 2D physics,
breakdown of integrability in 1D…
Interest for quantum computation ?
Inelastic
Spin degree of freedom coupled to orbital degree of freedom
- Spinor physics and magnetization dynamics
Dipole-dipole interactions
Vdd 
0 2
1
2
S  g J  B  1  3cos 2 ( )  3
4
R
Anisotropic

R
Introduction to dipolar relaxation
Angular momentum
conservation
mS  ml  0
1
 3,2  2,3
2
3,3 

  2
E  mS g B B
3
2
0
1
-1
-2
-3
Rotate the BEC ?
Spontaneous creation of vortices ?
Einstein-de-Haas effect
Ueda, PRL 96, 080405 (2006)
Santos PRL 96, 190404 (2006)
Gajda, PRL 99, 130401 (2007)
B. Sun and L. You, PRL 99, 150402 (2007)
Important to control
magnetic field
Energy scales
Molecular binding enery : 10 MHz
Trap depth : 1 MHz
Band excitation in lattice : 100 kHz
Chemical potential : 4 kHz
Vortex : 100 Hz
Magnetic field = 3 G
300 mG
30 mG
1 mG
.01 mG
A journey in dipolar physics through 7 decades of magnetic field intensities
Magnetic field (G)
1000
(T. Pfau’s Feshbach resonance – pure dipolar fluid)
100
10
Suppression of dipolar relaxation due to inter-atomic repulsion
1
0.1
Spin relaxation and band excitation in optical lattices
0.01
0.001
0.0001
Magnetization dynamics of spinor condensates
4 Gauss
3
2
0
-1
1
E  mS g B B  11MHz
-2
-3
…spin-flipped atoms gain so much energy they leave the trap
Dipolar relaxation in a Cr BEC
BEC m=+3, vary time
detect BEC m=-3
-13
Inelastic loss parameter 10 cm s
3 -1
100
7
6
5
4
Fermi golden rule
  Vdd   f 
3
2
2
 f  g J B B
10
7
6
5
4
3
2
1
2
0.01
4
6 8
0.1
2
4
6 8
2
1
4
6 8
10
Magnetic field (G)
PRA 81, 042716 (2010)
See also Shlyapnikov PRL 73, 3247 (1994)
Never observed up to now
Interpretation
l (l  1) 2
Veff ( R ) 
2 R 2
Energy
l 0
3,3
 f  g J B B
Rc
l2
1
 3, 2  2,3
2
Interpartice distance
In
Out
Rc = Condon radius
   in ( Rc )
2
Rc  aS
Determination of scattering lengths S=6 and S=4
Zero coupling

New estimates of Cr scattering lengths
Collaboration Anne Crubellier
PRA 81,
042716 (2010)
a6 = 103 ± 4 a0.
a6 = 102.5 ± 0.4 a0
Feshbach resonance in d-wave PRA 79, 032706 (2009)
Dipolar relaxation: a localized phenomenon
1
6
5
4
3
g’ (r)
Interatomic potentials
l (l  1) 2
RC 
mg S  B B
2
2
0.1
6
5
4
3
4
5
6
7 8 9
2
3
4
5
6
7
8 9
10
Interparticle distance
Distance r (nm)
g 2 (r )
1  a / r 
2
r  RVdW
L. H. Y. Phys. Rev. 106, 1135 (1957)
A probe of correlations :
here, a mere two-body effect, yet unacounted for in a
mean-field « product-ansatz » BEC model
100
40 mGauss
3
2
1
…spin-flipped atoms go from one band to another
Dipolar relaxation in optical lattices
Optical lattices:
periodic potential made by AC-stark
shift of a standing wave
3,3 
1
 3,2  2,3
2

  2
E  mS g B B
• Lattices provide very tightly confined geometries
Energy to nucleate a « mini-vortex » in a lattice site
Ev  2 L
gB B  L
m=3
(~120 kHz)
m=2
A gain of two orders of magnitude on the magnetic field requirements
to observe rotation due to spin-flip (Einstein-de Haas effect) !
Reduction of dipolar relaxation in optical lattices
Load the BEC in a 1D or 2D Lattice
BEC m=+3, vary time
detect m=-3
  Vdd   f 
2
One expects a reduction of
dipolar relaxation, as a result
of the reduction of the density
of states in the lattice
3D
-19
3 -1
Rate parameter (10 m s )
10
PRA 81,
042716 (2010)
1
2D
0.1
1D
0.01
789
0.01
2
3
4 5 6 789
0.1
Magnetic field (G)
Phys. Rev. Lett.
106, 015301 (2011)
What we measure in 1D (band mapping procedure):
3
2
0
(b)
1
-1
-2
-3
Non equilibrium
velocity ditribution
along tubes
Integrability
z
z
(a)
m=3
y
nd
st
2
1
BZ BZ
nd
2
BZ
y
x
m=2
Population in different bands
due to dipolar relaxation
Heating due to collisional deexcitation from excited band
What we measure in 1D:
(a)
(b)
0.10
Temperature (K)
Fraction of atoms in v=1
0.12
0.08
0.06
0.04
3
2
1
0.02
0.00
0
40
80
120
160
Magnetic field (kHz)
20
60
100
140
Magnetic field (kHz)
(almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices
B. Pasquiou et al., Phys. Rev. Lett. 106, 015301 (2011)
Theoretical model:
Fermi-Golden rule, taking into account:
-The width of the excited band (tunneling)
-All excited states along the tubes
m=3
m=2
Calculated : 2. 10-19 m3 s-1
Measured : 5. 10-20 m3 s-1
Qualitatively ok. Correlations (and more) ignored
z
(almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices:
a consequence of angular momentum conservation
mS  ml  0
mS  1
g  B B  E  E (l  2) 
a
2
ma
2
L
 L
Below threshold:
Above threshold :
a (spin-excited) metastable 1D
quantum gas ;
should produce vortices in each
lattice site (EdH effect)
(problem of tunneling)
Interest for spinor physics, spin
excitations in 1D…
Towards coherent excitation of
pairs into higher lattice orbitals ?
L
.4 mGauss
3
2
1
0
-1
-2 
-3
3
0
-2
1
2
-1
-3
Similar to M. Fattori et al., Nature Phys. 2, 765 (2006) at
large fields and in the thermal regime
…spin-flipped atoms loses energy
S=3 Spinor physics with free magnetization
- Up to now, spinor physics with S=1 and S=2 only
- Up to now, all spinor physics at constant magnetization
(exchange interactions, no dipole-dipole interactions)
- They investigate the ground state for a given magnetization
-> Linear Zeeman effect irrelavant
New features with Cr
-First S=3 spinor
- Dipole-dipole interactions free total magnetization
- Can investigate the true ground state of the system
(need very small magnetic fields)
1
0
-1
3
2
1
0
-1
-2
-3
S=3 Spinor physics with free magnetization
3
2
1
0
-1
-2 
-3
7 Zeeman states; all trapped
four scattering lengths, a6, a4, a2, a0
3
-2
-1
-3
g J  B Bc 
2
2
n0  a6  a4 
m
(at Bc, it costs no energy to go from
m=-3 to m=-2 : difference in
interaction energy compensates for
the loss in Zeeman energy)
ferromagnetic
i.e. polarized in
lowest energy
single particle
state
Magnetic field
0
1
2
Santos PRL 96,
190404 (2006)
Ho PRL. 96,
190405 (2006)
a0/a6
Phases set by contact interactions
(a6, a4, a2, a0)
– differ by total magnetization
Population
At VERY low magnetic fields,
spontaneous depolarization of 3D and 1D quantum gases
vary time
Rapidly lower magnetic field
Magnetic field control below
.5 mG (dynamic lock)
(.1mG stability)
(no magnetic shield…)
Stern Gerlach experiments
Mean-field effect
Final m=-3 fraction
1.0
g J  B Bc 
2
2
n0  a6  a4 
m
0.8
BEC
Lattice
Critical field
0.26 mG
1.25 mG
1/e fitted
0.4 mG
1.45 mG
0.6
0.4
BEC
BEC in lattice
0.2
0.0
0
1
2
3
4
Magnetic field (mG)
5
Field for depolarization depends on density
Remaining atoms in m=-3
Dynamics analysis
Magnetic field due to dipoles
1.0
0.8
0.6
0.4
Ueda, PRL 96, 080405 (2006)
Kudo Phys. Rev. A 82, 053614 (2010)
0.2
0.0
2
3
4
5
6
7 8 9
2
3
4
5
100
Time (ms)
Meanfield picture : Spin(or) precession (Majorana flips)
When mean field beats magnetic field
Natural timescale for depolarization:
Vdd (r  n 1/3 ) 
0 2
2
S  g J B  n
4
(a few ms)
A quench through a zero temperature (quantum) phase transition
Santos and Pfau
PRL 96, 190404 (2006)
Diener and Ho
PRL. 96, 190405 (2006)
33
2
2
1
1
3
0
-1
-2 
-3
0
-2
-3
-1
1
2
- Operate near B=0. Investigate absolute
many-body ground-state
- We do not (cannot ?) reach those new
ground state phases !!
- Thermal excitations probably dominate
Phases set by contact interactions,
magnetization dynamics set by
dipole-dipole interactions
« quantum magnetism »
Thermal effect: (Partial) Loss of BEC when demagnetization
Spin degree of freedom is released ; lower Tc
Population
Condensate fraction
0.8
350
300
250
-33
-22
-11
200
15
0
0.6
0.4
0.2
0
-1
-2 3
-
100
16
140
0
02 8
02 6
02 4
02 2
02 0
01 8
0.0
0
50
100
150
Time (ms)
As gas depolarises, temperature is constant,
but condensate fraction goes down !
200
250
300
Thermal effect: (Partial) Loss of BEC when demagnetization
Spin degree of freedom is released ; lower Tc
Condensate fraction
1.0
0.8
B=0
0.6
B=20 mG
0.4
Tc 
0.2
1
T
1/3 c
(2S  1)
PRA, 59, 1528 (1999)
J. Phys. Soc. Jpn, 69, 12, 3864 (2000)
0.0
0.1
0.2
0.3
0.4
0.5
Temperature
lower Tc: a signature of decoherence
Dipolar interaction open the way to spinor thermodynamics
with free magnetization
Conclusion
Collective excitations – effect of non-local mean-field
Dipolar relaxation in BEC – new measurement of Cr scattering lengths
correlations
Dipolar relaxation in reduced dimensions
- towards Einstein-de-Haas
rotation in lattice sites
Spontaneous demagnetization in a quantum gas
- New phase transition
– first steps towards spinor ground state
(Spinor thermodynamics with free magnetization
– application to thermometry)
(d-wave Feshbach resonance)
(BECs in strong rf fields)
(rf-assisted relaxation)
(rf association)
(MOT of fermionic 53Cr)