Have left: B. Pasquiou (PhD), G. Bismut (PhD), M. Efremov, Q. Beaufils (PhD), J.C. Keller, T. Zanon,...
Transcript of Have left: B. Pasquiou (PhD), G. Bismut (PhD), M. Efremov, Q. Beaufils (PhD), J.C. Keller, T. Zanon,...
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)
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
N = 4.106
T=120 μK
How to make a Chromium BECHow to make a Chromium BEC
425 nm
427 nm
650 nm
7S3
5S,D
7P3
7P4
An atom: 52Cr An oven
A small MOT
A dipole trap
A crossed dipole trap
All optical evaporation
A BEC
Oven at 1425 °C
A Zeeman slower
750700650600550500
600
550
500
450
(1) (2)
Z
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
Cs BEC with tunable interactions(from Innsbruck))
Self-similar, (interaction-driven) Castin-Dum expansionPhys. Rev. Lett. 77, 5315 (1996)
TF radii after expansion related to interactions
Pfau,PRL 95, 150406 (2005)
Modification of BEC expansion due to dipole-dipole interactions
TF profile
Eberlein, PRL 92, 250401 (2004)
Striction of BEC(non local effect)
3( ) ( ') ( ') 'dd ddr V r r n r d r
(similar results in our group)
Frequency of collective excitations
2
2.
dH
dt
��������������
��������������
Consider small oscillations, then
2 2 21 1 12 2 22 2 22 2 23 3 3
3
3
3
H
with
In the Thomas-Fermi regime, collective excitations frequency independent of number of atoms and
interaction strength:Pure geometrical factor
(solely depends on trapping frequencies)
(Castin-Dum)
1.2
1.0
0.8
0.6
2015105
Asp
ect
rati
oCollective excitations of a dipolar BEC
Repeat the experiment for two directions of the magnetic field
(differential measurement)
Parametric excitations
( )t ms
Phys. Rev. Lett. 105, 040404 (2010)
A small, but qualitative, difference (geometry is not all)
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
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
Rev. Mod. Phys. 77, 187 (2005)
( )E k ck c is sound velocityc is also critical velocityLandau criterium for superfluidity
healing length
0( 2 )k k k cE E n g
Bogoliubov spectrum
1k
Moving lattice on BEC
Lattice beams with an angle.Momentum exchange
2 sin( / 2)Lk k
Anisotropic speed of sound
0.15
0.10
0.05
0.00
3000200010000
Frequency difference (Hz)
Fra
ctio
n of
exc
ited
atom
s
Width of resonance curve: finite size effects (inhomogeneous broadening)
Speed of sound depends on the relative angle between spins and excitation
20( 2 ( (3cos 1))k k k c d kE E n g g
224
( ) (3cos 1)3 k
dV k
k
k
B
A 20% effect, much larger than the (~2%) modification of the mean-field due to DDI
Anisotropic speed of sound
An effect of the momentum-sensitivity of DDI
(See also prediction of anisotropic superfluidity of 2D dipolar gases : Phys. Rev. Lett. 106, 065301 (2011))
c (mm/s) Theo Exp
Parallel 3.6 3.4
Perpendicular 3 2.8
Good agreement between theory and experiment;
Finite size effects at low q
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
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
Dipole-dipole interactions
22 203
11 3cos ( )
4dd J BV S gR
R
-101
-10
1
-2-3
2
3
without ddV
with ddV
-3-2
-1
01
2
3
-3 -2 -1 0 1 2 3
ddV
2
dd f BV g B
B=0: Rabi
In a finite magnetic field: Fermi golden rule (losses)
(x1000 compared to alkalis)
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
2
2
2
)1()(
R
llRVeff
f J Bg B
0l
2lcR
Interpartice distance
Ene
rgy
13,2 2,3
2
3,3
2( )in cR
Bmg
llR
BSC
2)1(
From the molecular physics point of view: a delocalized probe
PRA 81, 042716 (2010)
2-body physics
1/3cR n
c vdWR RB = 3 G
B = .3 mG
many-body physicsDistance r (nm)
g’ (
r)2
3
456
0.1
2
3
456
1
4 5 6 7 8 910
2 3 4 5 6 7 8 9100
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 !
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-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
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 !
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)
Conclusions (I)
1.2
1.0
0.8
0.6
2015105
Asp
ect
rati
o
0.15
0.10
0.05
0.00
3000200010000
Frequency difference (Hz)
Fra
ctio
n of
exc
ited
atom
s
Dipolar interactions modify collective excitations
Anisotropic speed of sound
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,
P. Pedri, M. Efremov, O. Gorceix