Diapositive 1

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Effects of dipolar relaxation in chromium BECs
B. Pasquiou (PhD), G. Bismut (PhD), A. de Paz B.
Laburthe, E. Maréchal, L. Vernac, P. Pedri, M.
Efremov (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)
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Specificities of Chromium
Chromium (S3) Van-der-Waals dipole-dipole
interactions
Long range
Dipole-dipole interactions
Anisotropic
Relative strength of dipole-dipole and
Van-der-Waals interactions
Cr
3
Modification of BEC expansion due to
dipole-dipole interactions
Non local anisotropic mean-field
Striction of BEC (non local effect)
TF profile
Parabolic ansatz is still a good ansatz
Eberlein, PRL 92, 250401 (2004)
(similar results in our group)
Pfau,PRL 95, 150406 (2005)
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Collective excitations of a dipolar BEC
Due to the anisotropy of dipole-dipole
interactions, their effects on the BEC depend on
the relative orientation of the magnetic field
and the axis of the trap
Repeat the experiment for two directions of the
magnetic field
Parametric excitations
Frequency shift (differential measurement)
Bismut et al., PRL 105, 040404 (2010)
Aspect ratio
t (ms)
5
Trap geometry dependence of the measured
frequency shift
BEC always stretches along B
Shift of the quadrupole mode frequency ()
Shift of the aspect ratio ()
Sign of quadrupole shift depends on trap geometry
Trap anisotropy
Eberlein, PRL 92, 250401 (2004)
Good agreement with Thomas-Fermi predictions
Large sensitivity of the collective mode to trap
geometry unlike the striction of the BEC
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Influence of the BEC atom number
In our experiment, MDDI is not much larger than
the quantum kinetic energy
Simulations with Gaussian anzatz
It takes three times more atoms for the frequency
shift of the collective mode to reach the TF
predictions than for the striction of the BEC
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When dipolar mean field beats local contact
meanfield
Tune contact interactions using Feshbach
resonances dipolar interactions larger than
contact interactions
T.Lahaye et al, Nature. 448, 672 (2007)
Anisotropic d-wave collapse of (spherical) BEC
when scattering length is reduced (Feshbach
resonance) gt reveals dipolar coupling
Pfau, PRL 101, 080401 (2008)
And, roton, vortices, Mott physics, 1D or 2D
physics, breakdown of integrability in
1D With ? Cr ? Er ? Dy ? Dipolar molecules ?
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What is dipolar relaxation ?
Dipole-dipole interaction potential
Induces several types of collision
Spin exchange
Elastic collision
Inelastic collisions with rotation
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What is dipolar relaxation ?
Only two channels for dipolar relaxation in mS
3
Dipolar relaxation associated with a change in
kinetik energy
Dependance with magnetic field
and with a change in angular momentum
Change of magnetisation associated with rotation
gt (Einstein-de-Haas effect) Spontaneous
creation of vortices ?
Need of an extremely good control of B close to 0
Important to control magnetic field
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Energy scale, length scale, and magnetic field
Molecular binding enery 10 MHz
Magnetic field 3 G
Inhibition of dipolar relaxation due to
inter-atomic (VdW) repulsion
Band excitation in lattice 100 kHz
30 mG
Suppression of dipolar relaxation in optical
lattices
Chemical potential 1 kHz
.3 mG
Inelastic dipolar mean-field
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3 Gauss
Suppression of dipolar relaxation due to
inter-atomic repulsion
spin-flipped atoms gain so much energy they
leave the trap
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Dipolar relaxation in a Cr BEC
Experimental procedure
Typical results
Remains a BEC for 30 ms
Fit of decay gives b
BEC lost
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Evolution of dipolar relaxation with the magnetic
field
Born approximation neglects molecular potentials
ok for B lt 1G and B gt 10 G not in between.
Pfau, Appl. Phys. B, 77, 765 (2003)
Fermi golden rule
Local character of dipolar relaxation, depending
on B
Node in the entrance wavefunction near a6
Determination of chromium scattering lengths
a6 103 4 a0
a4 64 4 a0
See also Shlyapnikov PRL 73, 3247 (1994) Never
observed up to now
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Interpretation from the molecular physics point
of view

Energy
Interparticle distance
Only valid for RC gt a6 Better knowledge of the
inner part of molecular potentials otherwise
required
In
Out
Node in the entrance wavefunction near a6, zero
coupling, minimum in dipolar relaxation
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Dipolar relaxation measuring non-local
correlations
Use of local character of dipolar relaxation
Measure of two particule correlation function by
varying the magnetic field
Pair correlation function for hard-core potential
L. H. Y. Phys. Rev. 106, 1135 (1957)
A probe of long-range correlations here, a
mere two-body effect, yet unacounted for in a
mean-field  product-ansatz  BEC model
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New estimates of Cr scattering lengths
Collaboration Anne Crubellier (LAC, IFRAF)
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Contribution of higher order partial waves
DR in a BEC accounted for by a purely s-wave
theory No surprise, as the pair wave-function
in a BEC is purely l0 What about DR in thermal
gases ? Dipole-dipole
interactions are long-range all partial waves
may contribute
Temperature (µK)

• The 2-body loss parameter is always twice
  smaller in the BEC than in thermal gases.
• Probe for effect of thermal (HBT-like)
  correlations

Dip still hold for thermal gases. At the dip, DR
insensitive to temperature. Partial waves lgt0 do
not contribute to dipolar relaxation
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Contribution of higher order partial waves
All partial waves contribute to elastic dipolar
collisions but For large enough magnetic
fields, only s-wave contributes to dipolar
relaxation. (the input and output wave functions
always oscillate at very different spatial
frequencies)
Overlap calculations Anne Crubellier (LAC, IFRAF)
Red l0 Blue l2 Green l4 Magenta l6
Overlap
Magnetic field
Perspectives - no DR in fermionic dipolar
mixtures for sufficient B - use DR as a
non-local probe for correlations
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30 mGauss
Spin relaxation and band excitation in optical
lattices
spin-flipped atoms go from one band to another
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Reduction of dipolar relaxation in optical
lattices
Load the BEC in a 1D or 2D Lattice
Experimental procedure
Static magnetic field
Lattices height 135 kHz 25 Er
Loading in lattices
Rf sweep 1
Rf sweep 2
Produce BEC m -3
band mapping
BEC m 3, varying time
detect BEC m -3
One expects a reduction of dipolar relaxation, as
a result of the reduction of the density of
states in the lattice
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Reduction of dipolar relaxation in optical
lattices
Pasquiou et al., PRA 81, 042716 (2010)
Pasquiou et al., PRL 106, 015301 (2011)
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What we measure in 1D
Non equilibrium velocity distribution along
tubes Integrability
Band mapping procedure
Measure population in band v 0 and v 1, and
heating from population created in v
2 (collisional de-excitation)
Population in different bands due to dipolar
relaxation
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(almost) complete suppression of dipolar
relaxation in 1D at low field
Fraction of atoms in v1
Energy released
Magnetic field (kHz)
25 Er
Band excitation
Kinetic energy along tubes
Temperature (µK)
12 Er
Strong reduction of DR when Almost complete
suppression below threshold at 1D
Magnetic field (kHz)
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Importance of cylindrical symetry

• Below threshold, suppression of DR is most
  efficient if
• Lattice sites are cylindrical (fully cylindrical
  ?)
• - The magnetic field is parallel to the 1D gases

Dipolar relaxation rate (a.u.)
Dipolar relaxation rate (a.u.)
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(almost) complete suppression of dipolar
relaxation in 1D at low field a consequence of
angular momentum conservation
Above threshold should produce vortices in
each lattice site (EdH effect) (problem of
tunneling) Towards coherent excitation of pairs
into higher lattice orbitals ?
Below threshold a (spin-excited) metastable 1D
quantum gas Interest for spinor physics, spin
excitations in 1D
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.3 mGauss
Magnetization dynamics of spinor condensates
3
2
1
0
-1
-2
-3
spin-flipped atoms loses energy
Similar to M. Fattori et al., Nature Phys. 2, 765
(2006) at large fields and in the thermal regime
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S3 Spinor physics with free magnetization

• - Up to now, spinor physics with S1 and S2 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
• -gt Linear Zeeman effect irrelevant

1
0
-1

• New features with Cr
• - First S3 spinor (7 Zeeman states, four
  scattering lengths, a6, a4, a2, a0)
• Dipole-dipole interactions free total
  magnetization
• Can investigate the true ground state of the
  system
• (need very small magnetic fields)

3
2
1
0
-1
-2
-3
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S3 Spinor physics with free magnetization
7 Zeeman states all trapped four scattering
lengths, a6, a4, a2, a0
3
3
2
1
2
ferromagnetic i.e. polarized in lowest energy
single particle state
0
1
0
-1
-1
-2
-2
-3
-3
Critical magnetic field
Santos PRL 96, 190404 (2006) Ho PRL. 96, 190405
(2006)
Phases are set by contact interactions (a6, a4,
a2, a0) differ by total magnetization
(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)
DDI ensure the coupling between states with
different magnetization
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At VERY low magnetic fields, spontaneous
depolarization of 3D and 1D quantum gases
Experimental procedure
1 mG
0.5 mG
0.25 mG
Produce BEC m-3
 0 mG 
Stern Gerlach experiments
Rapidly lower magnetic field
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Mean-field effect
BEC Lattice
Critical field 0.26 mG 1.25 mG
1/e fitted 0.4 mG 1.45 mG
Field for depolarization depends on density
Optical lattices change only the density, not
the symetry for DDI
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Mean-field effect
In lattices, no changes for depolarisation with
the orientation of B
Optical lattices change only the density, not
the symetry for DDI
Evidence for inter-sites dipolar coupling
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Dynamics analysis
At short times, transfert between mS -3 and mS
-2
a two level system coupled by Vdd
few atoms in mS -2, so collision only in a6
Natural timescale for depolarization
(a few ms)
But still unaccounted for B above dipolar
meanfield
Influence of the trap / temperature ???
Ueda, PRL 96, 080405 (2006) / Kudo Phys. Rev. A
82, 053614 (2010)
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Dynamics analysis
In lattices (in our experimental configuration),
the volume of the cloud is multiplied by 3
Mean field due to dipole-dipole interaction is
reduced
Slower dynamics, even with higher peak densities
Bulk BEC
Non local character of DDI
2D optical lattices
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Single component Bose thermodynamics
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Multi-component Bose thermodynamics
7 Zeeman states all trapped in optical dipole
trap
Phase diagram, non interacting case, cylindrical
Simkin and Cohen, PRA, 59, 1528 (1999) Isoshima
et al., J. Phys. Soc. Jpn,   69, 12, 3864 (2000)
Normal
BEC in majoritary component Th
temperature
BEC in each component
Double phase transition at constant magnetization
magnetization
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Thermal effect (Partial) Loss of BEC when
demagnetization
B0
B20 mG
lower Tc spin degree of freedom is released
Dipolar interaction opens the way to spinor
thermodynamics with free magnetization
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Thermodynamics of a spinor gas with free
magnetization
Above Bc, magnetization well accounted for by non
interacting model
Above Bc, thermal gas depolarizes, but BEC
remains polarized
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Spin population and thermometry (above Bc)
BEC in m-3
Depolarized thermal gas
 bi-modal  spin distribution
Above Bc Only thermal gas depolarizes get rid
of it ? Cooling scheme? (Bragg excitations or
field gradient)
A new thermometry ? (limits to be checked)
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Summary A quench through a zero temperature
(quantum) phase transition
Santos PRL 96, 190404 (2006) Ho PRL. 96, 190405
(2006)
3
3
2
2
1
1
0

• - Operate near B0. Investigate absolute
  many-body ground-state
• - We do not (cannot ?) reach those new ground
  state phases
• Thermal excitations probably dominate

-1
-2
-3
Pasquiou et al., accepted in PRL
Phases set by contact interactions,
magnetization dynamics set by dipole-dipole
interactions  quantum magnetism 
Also new physics in 1D Polar phase is a
singlet-paired phase arXiv1103.5534
(Shlyapnikov-Tsvelik)
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Conclusion Dipolar relaxation in BEC new
measurement of Cr scattering lengths
non-local correlations Dipolar relaxation in
reduced dimensions almost-suppression of
DR 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 / cooling (Collective
excitations effect of non-local mean-field)
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Thank you for your attention
one open Post-doc position in our group
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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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Prospect new cooling method using the spin
degrees of freedom
Above Bc Only thermal gas depolarizes get rid
of it ? (Bragg excitations or field gradient)