Transcript Diapositive 1 - Paris 13 University

Dipolar chromium BECs
A. de Paz (PhD), A. Chotia, A. Sharma,
B. Laburthe-Tolra, E. Maréchal, L. Vernac,
P. Pedri (Theory),
O. Gorceix (Group leader)
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)
Chromium (S=3): 6 electrons in outer shell have their spin aligned
Van-der-Waals plus dipole-dipole interactions
Dipole-dipole interactions
Vdd 
0 2
1
2
S  g J  B  1  3cos 2 ( )  3
4
R

R
Hydrodynamics
Magnetism
Long range
Anisotropic
Relative strength of dipole-dipole and Van-der-Waals interactions
0 m2 m Vdd
 dd 

2
12 a VVdW
 dd  1
BEC collapses
Stuttgart: Tune contact interactions using Feshbach resonances (Nature. 448, 672 (2007))

R
 dd  1
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)
Anisotropic
explosion pattern
reveals dipolar
coupling.
BEC stable despite attractive part of dipole-dipole interactions
Cr:
 dd  0.16
How to make a Chromium BEC
 An atom:
7P
52Cr
 An oven
 A Zeeman slower
4
 A small MOT
Oven at 1425 °C
7P
3
650 nm
425 nm
5S,D
N = 4.106
T=120 μK
427 nm
7S
3
(1)
600
(2)
550
Z
500
450
500
600
650
700
750
 A dipole trap
 All optical evaporation
 A BEC
550
 A crossed dipole trap
1 – Hydrodynamic properties of a weakly dipolar BEC
- Collective excitations
- Bragg spectroscopy
2 – Magnetic properties of a dipolar BEC
- Thermodynamics
- Phase transition to a spinor BEC
- Magnetism in a 3D lattice
Interaction-driven expansion of a BEC
A lie:
Imaging BEC after time-of-fligth
is a measure of in-situ
momentum distribution
Self-similar, (interaction-driven)
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
In the Thomas-Fermi regime, collective excitations
frequency independent of number of atoms and
interaction strength:
Pure geometrical factor
(solely depends on trapping frequencies)
12 

22 
332 
Collective excitations of a dipolar BEC
Parametric excitations
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)
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)
20


  dd
Note : dipolar shift very sensitive to trap geometry : a consequence of the
anisotropy of dipolar interactions
Bragg spectroscopy
Probe dispersion law
Quasi-particles, phonons
E (k )  ck
k  1
c is sound velocity
c is also critical velocity
Landau criterium for superfluidity
Moving lattice on BEC


healing length

d
Rev. Mod. Phys. 77, 187 (2005)
Bogoliubov spectrum
 k  Ek ( Ek  2n0 gc )
Lattice beams with an angle.
Momentum exchange
k  2 kL sin( / 2)
Fraction of excited atoms
Anisotropic speed of sound
0.15
0.10
0.05
0.00
0
1000
2000
3000
Frequency difference (Hz)
Width of resonance curve: finite size effects (inhomogeneous broadening)
Speed of sound depends on the relative angle between spins and excitation
Anisotropic speed of sound
A 20% effect, much larger than the (~2%) modification of the mean-field due to DDI
An effect of the momentum-sensitivity of DDI
4 d 2
V (k ) 
(3cos 2  k  1)
3
B
 k  Ek ( Ek  2n0 ( g c  g d (3cos 2  k  1))
k
Good agreement between
theory and experiment;
k
Finite size effects at low q
c (mm/s)
Theo
Exp
Parallel
3.6
3.4
Perpendicular
3
2.8
(See also prediction of anisotropic
superfluidity of 2D dipolar gases : Phys.
Rev. Lett. 106, 065301 (2011))
Hydrodynamic properties of a BEC
with weak dipole-dipole interactions
Striction
Stuttgart, PRL 95, 150406 (2005)
Collective excitations
Villetaneuse,
PRL 105, 040404 (2010)
Aspect ratio
1.2
1.0
0.8
0.6
Anisotropic speed of sound
Fraction of excited atoms
5
10
15
20
0.15
0.10
Bragg spectroscopy
Villetaneuse
arXiv: 1205.6305 (2012)
0.05
0.00
0
1000
2000
3000
Frequency difference (Hz)
Interesting but weak effects in a scalar Cr BEC
1 – Hydrodynamic properties of a weakly dipolar BEC
- Collective excitations
- Bragg spectroscopy
2 – Magnetic properties of a dipolar BEC
- Thermodynamics
- Phase transition to a spinor BEC
- Magnetism in a 3D lattice
Dipolar interactions introduce magnetization-changing collisions
without Vdd
Dipole-dipole interactions
0 2
1
2
2
Vdd 
S  g J  B  1  3cos ( )  3
4
R

R
1
0
-1
3
2
1
0
-1
-2
-3
with Vdd
B=0: Rabi
-3 -2 -1 0
1
2
3
  Vdd
In a finite magnetic field: Fermi golden rule (losses)
3
2
1
0
  Vdd    f  g  B B 
2
-1
-2
-3
(x1000 compared to alkalis)
Dipolar relaxation, rotation, and magnetic field
Angular momentum
conservation
mS  ml  0
3,3 
1
 3,2  2,3
2

  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
B=1G
 Particle leaves the trap
3
2
1
B=10 mG
 Energy gain matches band
excitation in a lattice
0
-1
-2
-3
B=.1 mG
 Energy gain equals to
chemical potential in BEC
From the molecular physics point of view: a delocalized probe
l (l  1) 2
Veff ( R) 
2R 2
Energy
l 0
l (l  1) 2
RC 
mg S  B B
3,3
 f  g J B B
Rc
1
 3, 2  2,3
2
l 2
Rc  RvdW
2
1
6
5
4
2
g’ (r)
2-body physics
   in ( Rc )
PRA 81, 042716 (2010)
Interpartice distance
B=3G

3
2
0.1
B = .3 mG
1/3
Rc  n
many-body physics
6
5
4
3
4
5
6
7 8 9
2
3
10
Distance r (nm)
4
5
6
7
8 9
100
S=3 Spinor physics with free magnetization
New features with Cr:
Alkalis :
- S=1 and S=2 only
- Constant magnetization
(exchange interactions)
 Linear Zeeman effect irrelevant
- S=3 spinor (7 Zeeman states, four
scattering lengths, a6, a4, a2, a0)
- No hyperfine structure
- Free magnetization
Magnetic field matters !
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
S=3 Spinor physics with free magnetization
Alkalis :
- S=1 and S=2 only
- Constant magnetization
(exchange interactions)
 Linear Zeeman effect irrelevant
New features with Cr:
- S=3 spinor (7 Zeeman states, four
scattering lengths, a6, a4, a2, a0)
- No hyperfine structure
- Free magnetization
Magnetic field matters !
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
At low magnetic field: spin thermally activated g B B  kBT
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
We measure spin-temperature
by fitting the mS population
(separated by Stern-Gerlach
technique)
Spin Temperature ( K)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.2
0.4
0.6
0.8
1.0
Time of flight Temperature ( K)
1.2
T>Tc
T<Tc
Condensate fraction
Spontaneous magnetization due to BEC
1.0
B  900G
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.0
1.2
Temperature (K)
Thermal
population in
Zeeman excited
states
-0.5
-3 -2 -1 0 1 2 3
a bi-modal spin
distribution
BEC only in mS=-3
(lowest energy state)
Magnetization
-3 -2 -1 0 1 2 3
-1.0
-1.5
-2.0
-2.5
Cloud spontaneously
polarizes !
-3.0
0.0
0.2
0.4
0.6
0.8
Temperature (K)
Non-interacting multicomponent Bose thermodynamics:
a BEC is ferromagnetic
Phys. Rev. Lett. 108, 045307 (2012)
Below a critical magnetic field: the BEC ceases to be ferromagnetic !
0.0
1.0
B=100 µG
-0.5
Magnetization
-1.0
B=900 µG
-1.5
-2.0
Condensate fraction
0.8
0.6
0.4
0.2
-2.5
0.0
-3.0
0.0
0.4
0.8
1.2
Temperature (K)
-Magnetization remains small even when the
condensate fraction approaches 1
!! Observation of a depolarized condensate !!
0.1
0.2
0.3
0.4
0.5
Temperature (K)
Necessarily an interaction effect
Phys. Rev. Lett. 108, 045307 (2012)
Cr spinor properties at low field
-1
3
2
1
0
-1
-2 
-3
3
-2
0
-2
1
2
-1
-3
-3
Large magnetic field : ferromagnetic
g J B Bc 
2 n0  a6  a4 
2
Low magnetic field : polar/cyclic
" 6 "
m
-3
" 4 "
-2
Santos PRL 96,
190404 (2006)
Ho PRL. 96,
190405 (2006)
Phys. Rev. Lett. 106, 255303 (2011)
Density dependent threshold
Final m=-3 fraction
1.0
g J B Bc 
0.8
0.6
0.4
BEC
BEC in lattice
2 2 n0  a6  a4 
m
BEC
Lattice
Critical field
0.26 mG
1.25 mG
1/e fitted
0.3 mG
1.45 mG
0.2
Phys. Rev. Lett. 106, 255303 (2011)
0.0
0
1
2
3
4
Magnetic field (mG)
5
Load into deep 2D optical lattices to boost density.
Field for depolarization depends on density
Note: Possible new physics in 1D: Polar phase is a singlet-paired
phase Shlyapnikov-Tsvelik NJP, 13, 065012 (2011)
Dynamics analysis
0.0
Magnetization
-0.5
-1.0
-1.5
-2.0
Bulk BEC
In 2D lattice
Rapidly lower magnetic field
-2.5
PRL 106, 255303 (2011)
-3.0
50
100
150
200
250
Time (ms)
Meanfield picture :
Spin(or) precession
Natural timescale for depolarization:
Vdd (r  n
1/3
0 2
2
)
S  g J B  n
4
Ueda, PRL 96,
080405 (2006)
Magnetic field
Open questions about equilibrium state
Santos and Pfau
PRL 96, 190404 (2006)
Diener and Ho
PRL. 96, 190405 (2006)
Phases set by contact interactions,
magnetization dynamics set by
dipole-dipole interactions
Demler et al.,
PRL 97, 180412 (2006)
- 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 ?
(a)
Polar
Cyclic
(b)
1
1, 0, 0, 0, 0, 0,1
2
1
1, 0, 0, 0, 0,1, 0 
2
(c)
(d)
-3
-2
-1
0
1
2
3
!! Depolarized BEC likely in metastable state !!
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
Optical lattice = periodic (sinusoidal) potential due to AC Stark Shift of a standing wave
2D
3D
(from I. Bloch)
We load in the Mott regime U=10kHz, J=100 Hz
J
U
(in our case (1 , 1 , 2.6)* /2 periodicity)
In practice, 2 per site in
the center (Mott plateau)
Spontaneous demagnetization of atoms in a 3D lattice
Magnetization
-1.5
3D lattice
-2.0
-2.5
Critical
field
4kHz
Threshold
seen
5kHz
g J  B Bc 
-3.0
5
10
Magnetic field (kHz)
15
4
2
n0  a6  a4 
m
" 6 "
" 4 "
-2
-3
S  6, m  6
S  4, m  4
Control the ground state by a light-induced effective Quadratic Zeeman effect
1
-1
0
1
2
3
Energy
-3 -2
A s polarized laser
Close to a JJ transition
(100 mW 427.8 nm)
a mS
0
-1
2
In practice, a  component couples mS states
-2
0
60
30
Note : The effective Zeeman effect is
crucial for good state preparation
90
120
150
-3
Magnetic field (kHz)
Typical groundstate
at 60 kHz
-3 -2 -1 0
1
2
3
0
-1
-2
-3
Adiabatic (reversible) change in magnetic state (unrelated to dipolar interactions)
t
-3
-2
3D lattice (1 atom
per site)
0
-1
-2
-3
Note: the spin state reached without a 3D lattice is completely different !
1 0 -1 -2 -3
BEC (no lattice)
Large spin-dependent
(contact) interactions
in the BEC have a very
large effect on the final
state
-1
-2
-3
Magnetization dynamics in lattice
vary time
0.6
m=-3
m=-2
populations
0.5
Role of intersite dipolar
relaxation ?
0.4
0.3
0.2
0
5
10
15
Time (ms)
20
Magnetization dynamics resonance for two atoms per site
0.8
3
m=3 fraction
0.7
2
0
1
-1
-2
0.6
-3
0.5
Dipolar resonance when released
energy matches band excitation
0.4
36
38
40
42
44
46
Magnetic field (kHz)
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):
3
2
0
1
-1
-2
-3
m=3
z
m=2
y
x
(a)
nd
st
2
1
BZ BZ
nd
2
BZ
y
Fraction of atoms in v=1
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Population in different bands
due to dipolar relaxation
0
PRL 106, 015301 (2011)
40
80
120
Magnetic field (kHz)
160
Atom number
Strong anisotropy of dipolar resonances
3
14x10
12
10
8
6
4
40
60
80
100
120
140
Magnetic field (kHz)
160
180
200
Anisotropic
lattice sites
At resonance
Vr 
3 2 ( x  iy )
Sd
2
r5
2
May produce vortices in each
lattice site (EdH effect)
(problem of tunneling)
See also PRL 106, 015301 (2011)
Conclusions (I)
Dipolar interactions modify collective excitations
Aspect ratio
1.2
1.0
0.8
0.6
Anisotropic speed of sound
10
Fraction of excited atoms
5
15
0.15
0.10
0.05
0.00
0
1000
2000
Frequency difference (Hz)
3000
20
0.0
Conclusions
-1.0
Magnetization
Magnetization changing dipolar collisions
introduce the spinor physics with free
magnetization
-0.5
-1.5
-2.0
-2.5
-3.0
0.0
(a)
0.4
0.8
1.2
Temperature (K)
(b)
(c)
New spinor phases at extremely low
magnetic fields
(d)
-3
-2
-1
0
1
2
3
Tensor light-shift allow to reach new
quantum phases
0D
10
20
30
B (mG)
40
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)
A. de Paz, A. Chotia, A. Sharma,
B. Pasquiou (PhD), G. Bismut (PhD),
B. Laburthe, E. Maréchal, L. Vernac,
P. Pedri, M. Efremov, O. Gorceix