Diapositive 1

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Dipolar chromium BECs

• 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)
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Chromium (S3) 6 electrons in outer shell have
their spin aligned Van-der-Waals plus
dipole-dipole interactions
Dipole-dipole interactions
Long range
Anisotropic
Hydrodynamics
Magnetism
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Relative strength of dipole-dipole and
Van-der-Waals interactions
Stuttgart Tune contact interactions using
Feshbach resonances (Nature. 448, 672 (2007))
Anisotropic explosion pattern reveals dipolar
coupling.
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)
Cr
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How to make a Chromium BEC

• An atom 52Cr

• An oven

• A Zeeman slower

• A small MOT

Oven at 1425 C
N 4.106 T120 µK

• A dipole trap

• All optical evaporation

• A BEC

• A crossed dipole trap

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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
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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)
TF radii after expansion related to
interactions
Cs BEC with tunable interactions (from Innsbruck))
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Modification of BEC expansion due to
dipole-dipole interactions
TF profile
Striction of BEC (non local effect)
Eberlein, PRL 92, 250401 (2004)
(similar results in our group)
Pfau,PRL 95, 150406 (2005)
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Frequency of collective excitations
(Castin-Dum)
Consider small oscillations, then
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)
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Collective excitations of a dipolar BEC
Parametric excitations
Repeat the experiment for two directions of the
magnetic field (differential measurement)
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
Phys. Rev. Lett. 105, 040404 (2010)
A small, but qualitative, difference (geometry is
not all)
Note dipolar shift very sensitive to trap
geometry a consequence of the anisotropy of
dipolar interactions
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Bragg spectroscopy
Probe dispersion law Quasi-particles, phonons
c is sound velocity c is also critical
velocity Landau criterium for superfluidity
Moving lattice on BEC
w
wd
q
healing length
Rev. Mod. Phys. 77, 187 (2005)
Lattice beams with an angle. Momentum exchange
Bogoliubov spectrum
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Anisotropic speed of sound
Width of resonance curve finite size effects
(inhomogeneous broadening) Speed of sound
depends on the relative angle between spins and
excitation
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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
Good agreement between theory and
experiment 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))
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Hydrodynamic properties of a BEC with weak
dipole-dipole interactions
Striction
Stuttgart, PRL 95, 150406 (2005)
Collective excitations
Villetaneuse, PRL 105, 040404 (2010)
Anisotropic speed of sound
Bragg spectroscopy Villetaneuse arXiv 1205.6305
(2012)
Interesting but weak effects in a scalar Cr BEC
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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
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Dipolar interactions introduce magnetization-chang
ing collisions
1
0
Dipole-dipole interactions
-1
3
2
1
0
-1
-2
-3
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B0 Rabi
-3 -2 -1 0 1 2 3
In a finite magnetic field Fermi golden rule
(losses)
(x1000 compared to alkalis)
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Dipolar relaxation, rotation, and magnetic field
Angular momentum conservation
Important to control magnetic field
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)
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• B1G
• Particle leaves the trap

• B10 mG
• Energy gain matches band excitation in a lattice

• B.1 mG
• Energy gain equals to chemical potential in BEC

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From the molecular physics point of view a
delocalized probe

PRA 81, 042716 (2010)
B 3 G
2-body physics
B .3 mG
many-body physics
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S3 Spinor physics with free magnetization

• New features with Cr
• S3 spinor (7 Zeeman states, four scattering
  lengths, a6, a4, a2, a0)
• No hyperfine structure
• Free magnetization
• Magnetic field matters !

• Alkalis
• - S1 and S2 only
• - Constant magnetization
• (exchange interactions)
• Linear Zeeman effect irrelevant

Technical challenges Good control of magnetic
field needed (down to 100 mG) Active feedback
with fluxgate sensors Low atom number 10 000
atoms in 7 Zeeman states
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S3 Spinor physics with free magnetization

• New features with Cr
• S3 spinor (7 Zeeman states, four scattering
  lengths, a6, a4, a2, a0)
• No hyperfine structure
• Free magnetization
• Magnetic field matters !

• Alkalis
• - S1 and S2 only
• - Constant magnetization
• (exchange interactions)
• Linear Zeeman effect irrelevant

• 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

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Spin temperature equilibriates with mechanical
degrees of freedom
At low magnetic field spin thermally activated
-3 -2 -1 0 1 2 3
We measure spin-temperature by fitting the mS
population (separated by Stern-Gerlach technique)
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Spontaneous magnetization due to BEC
TgtTc
TltTc
-3 -2 -1 0 1 2 3
-3 -2 -1 0 1 2 3
Thermal population in Zeeman excited states
a bi-modal spin distribution
BEC only in mS-3 (lowest energy state)
Cloud spontaneously polarizes !
Non-interacting multicomponent Bose
thermodynamics a BEC is ferromagnetic
Phys. Rev. Lett. 108, 045307 (2012)
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Below a critical magnetic field the BEC ceases
to be ferromagnetic !
B100 µG
B900 µG

• Magnetization remains small even when the
  condensate fraction approaches 1
• !! Observation of a depolarized condensate !!

Necessarily an interaction effect
Phys. Rev. Lett. 108, 045307 (2012)
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Cr spinor properties at low field
-1
3
3
2
2
1
1
-2
0
0
-1
-1
-2
-2
-3
-3
-3
Large magnetic field ferromagnetic
Low magnetic field polar/cyclic
Santos PRL 96, 190404 (2006)
Ho PRL. 96, 190405 (2006)
-2
-3
Phys. Rev. Lett. 106, 255303 (2011)
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Density dependent threshold
BEC Lattice
Critical field 0.26 mG 1.25 mG
1/e fitted 0.3 mG 1.45 mG
Phys. Rev. Lett. 106, 255303 (2011)
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)
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Dynamics analysis
PRL 106, 255303 (2011)
Meanfield picture Spin(or) precession
Ueda, PRL 96, 080405 (2006)
Natural timescale for depolarization
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Open questions about equilibrium state
Phases set by contact interactions,
magnetization dynamics set by dipole-dipole
interactions
Santos and Pfau PRL 96, 190404 (2006) Diener and
Ho PRL. 96, 190405 (2006)
Magnetic field
Demler et al., PRL 97, 180412 (2006)

• - Operate near B0. Investigate absolute
  many-body ground-state
• We do not (cannot ?) reach those new ground state
  phases
• Quench should induce vortices
• Role of thermal excitations ?

Polar
Cyclic
!! Depolarized BEC likely in metastable state !!
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• 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

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Loading an optical lattice
Optical lattice periodic (sinusoidal) potential
due to AC Stark Shift of a standing wave
(from I. Bloch)
We load in the Mott regime U10kHz, J100 Hz
J
In practice, 2 per site in the center (Mott
plateau)
(in our case (1 , 1 , 2.6) l/2 periodicity)
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Spontaneous demagnetization of atoms in a 3D
lattice
3D lattice
Critical field 4kHz
Threshold seen 5kHz
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Control the ground state by a light-induced
effective Quadratic Zeeman effect
-3 -2 -1 0 1 2 3
Energy
A s- polarized laser Close to a J?J
transition (100 mW 427.8 nm)
Da mS2
In practice, a p component couples mS states
Note The effective Zeeman effect is crucial for
good state preparation
Typical groundstate at 60 kHz
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Adiabatic (reversible) change in magnetic state
(unrelated to dipolar interactions)
quadratic effect
t
-3
-2
3D lattice (1 atom per site)
Note the spin state reached without a 3D lattice
is completely different !
Large spin-dependent (contact) interactions in
the BEC have a very large effect on the final
state
-1
-2
-3
-2
-1
0
1
-3
BEC (no lattice)
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Magnetization dynamics in lattice
Load optical lattice
quadratic effect
vary time
Role of intersite dipolar relaxation ?
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Magnetization dynamics resonance for two atoms
per site
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
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Measuring population in higher bands (1D) (band
mapping procedure)
m3
m2
Population in different bands due to dipolar
relaxation
PRL 106, 015301 (2011)
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Strong anisotropy of dipolar resonances
Anisotropic lattice sites
At resonance May produce vortices in each
lattice site (EdH effect) (problem of tunneling)
See also PRL 106, 015301 (2011)
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Conclusions (I)
Dipolar interactions modify collective excitations
Anisotropic speed of sound
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Conclusions
Magnetization changing dipolar collisions
introduce the spinor physics with free
magnetization
New spinor phases at extremely low magnetic fields
Tensor light-shift allow to reach new quantum
phases
0D
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)
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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
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