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Elastic and inelastic dipolar effects in chromium BECs. Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France. B. Laburthe-Tolra. B. Pasquiou. P. Pedri. E. Maréchal. O. Gorceix . G. Bismut. L. Vernac. A. Crubellier (LAC- Orsay).

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elastic and inelastic dipolar effects in chromium becs

Elastic and inelasticdipolareffects in chromiumBECs

Laboratoire de Physique des Lasers

Université Paris Nord

Villetaneuse - France

B. Laburthe-Tolra

B. Pasquiou

P. Pedri

E. Maréchal

O. Gorceix

G. Bismut

L. Vernac

A. Crubellier (LAC- Orsay)

Former PhD students and post-docs:Q. Beaufils, T. Zanon, R. Chicireanu, A. Pouderous

Former members of the group: J. C. Keller, R. Barbé

slide2

Chromium : S=3

Dipole-dipole interactions

Long range

Anisotropic

Non local anisotropic meanfield

  • Static and dynamic properties of BECs
slide3

Inelastic dipolar effects

Anisotropic dipole-dipole interactions

Spin degree of freedom coupled to orbital degree of freedom

- Dipolar relaxation

- Spinor physics and magnetization dynamics

slide4

Outline

1 Elastic

Collective excitations in a Cr BEC

2 Inelastic

Control of dipolar relaxation in opticallattices

Spontaneousdemagnetizationdynamics in opticallattices

slide5

Modification of BEC expansion due to dipole-dipole interactions

TF profile

Striction of BEC

(non local effect)

Parabolic ansatz

is still a good ansatz

Eberlein, PRL 92, 250401 (2004)

Pfau,PRL 95, 150406 (2005)

slide6

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

Parametric excitations:

Repeat the experiment for two directions of the magnetic field (differential measurement)

slide7

Trap geometry dependence of the measured frequency shift

BEC always stretches along B

Sign of quadrupole shift depends on trap geometry

Shift of the quadrupole mode frequency (%)

Shift of the aspect ratio (%)

  • Related to the 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

slide8

Outline

1 Elastic

Collective excitations in a Cr BEC

2 Inelastic

Control of dipolar relaxation in opticallattices

Spontaneousdemagnetizationdynamics in opticallattices

slide9

Angle between dipoles

Dipolar relaxation

3

2

1

0

-1

Angular momentum conservation

-2

-3

- Two channels for dipolar relaxation in m=3 (no DR in m=-3):

Rotate the BEC ?

Spontaneous creation of vortices ?

(Einstein-de-Haas effect)

Need of an extremely good control of B close to 0

Santos, PRL 96, 190404 (2006)

See also Ueda, PRL 96, 080405 (2006)

how to observe the einstein de haas effect
How to observe the Einstein-de Haas effect ?

Ideas to ease the magnetic field control requirements

Create a gap in the system:

B now needs to be controlled around a finite non-zero value

  • Go to very tightly confined geometries

(BEC in 2D optical lattices)

Energy to nucleate a « mini-vortex » in a lattice site

(~120 kHz)

A gain of two orders of magnitude on the magnetic field requirements !

slide11

Dipolar relaxation in a Cr BEC

3

2

1

Rf sweep 1

Rf sweep 2

0

-1

-2

Produce BEC m=-3

-3

BEC m=+3, vary time

detect BEC m=-3

Fit of decay givesb

Born approximation Pfau, Appl. Phys. B, 77, 765 (2003)

Determines scattering lengths

See also Shlyapnikov PRL 73, 3247 (1994)

Never observed up to now

slide12

Reduction of dipolar relaxation in optical lattices

Load the BEC in a 1D or 2D Lattice (retro-reflected Verdi laser)

Rf sweep 1

Rf sweep 2

Load optical lattice

BEC m=+3, vary time

Produce BEC m=-3

detect m=-3

Look at heating; deduce b

One expects a reduction of dipolar relaxation, as a result of the reduction of the density of states in the lattice

slide13

3D

2D

Dipolar relaxation rate parameter 10-19 m3 s-1

1D

Strong reduction of dipolar relaxation when

Almost complete suppression below a threshold at 1D

slide14

Suppression of dipolar relaxation in 1D: the result of cylindrical symmetry

(angular momentum conservation)

q

Dipolar relaxation rate (u.a.)

  • Below threshold, suppresion of DR is most efficient if :
  • Lattice sites are cylindrical
  • - The magnetic field is parallel to the 1D gases

0.8

0.6

Dipolar relaxation rate (u.a.)

0.4

Above threshold : should produce vortices in each lattice site (EdH effect)

… in progress …

(problem of tunneling)

0.2

q

slide15

Outline

1 Elastic

Collective excitations in a Cr BEC

2 Inelastic

Control of dipolar relaxation in opticallattices

Spontaneousdemagnetizationdynamics in 1D gases

slide16

Spinor ground state at low magnetic field

S=3

7 Zeeman states; all trapped

four scattering lengths, a6, a4, a2, a0

A rich spinor diagram at low magnetic field

Different quantum phases at relatively « large » magnetic fields (mG) due to very different scattering lengths

Santos and Pfau

PRL 96, 190404 (2006)

Diener and Ho

PRL. 96, 190405 (2006)

3

3

2

2

1

1

0

0

-1

-1

-2

-2

-3

-3

Magnetizationdynamics set by dipole-dipole interactions

slide17

At VERY low magnetic fields, spontaneous depolarization of 1D quantum gases

Load optical lattice

vary time

Produce BEC m=-3

Rapidly lower magnetic field

Stern Gerlach experiments

slide18

A quench through a phase transition ?

Fraction in m=-3

Magnetic field (kHz)

3

2

1

0

-1

-2

-3

slide19

Magnetization dynamics in an increased meanfield

« Critical » field depends on chemical potential

Fraction in m=-3

Magnetic field (kHz)

Td

Strong heating in lattice, unrelated to depolarization, still unaccounted for

…in progresss…

Remains below Td

Td

Temperature (mK)

Time (ms)

slide20

(many more?) open questions:

Tensor light-shift:

3

-3

2

-2

1

-1

0

Effect of non zero temperature ?

Effects on dynamics, phase diagram…

Santos

PRA 75, 053606 (2007)

In which timescale will we reach the new phase ?

How to describe dipolar relaxation ?

Effects of 1D ?

slide21

Conclusion

Collective excitations – good agreement with theory

Dipolar relaxation in reduced dimensions - towards Einstein-de-Haas

Spontaneous demagnetization in a quantum gas

– first steps towards spinor ground state

(BECs in strong rf fields)

(rf-assisted relaxation)

(rf association)

(d-wave Feshbach resonance)

(MOT of 53Cr)

Production of a (slightly) dipolar Fermi sea

Load into optical lattices – superfluidity ?

Perspectives

slide22

L. Vernac

E. Maréchal

J. C. Keller

G. Bismut

Paolo Pedri

B. Laburthe

B. Pasquiou

Q. Beaufils

O. Gorceix

Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu

Collaboration:Anne Crubellier (Laboratoire Aimé Cotton)

slide23

Influence of the BEC atom number

  • In our experiment, MDDI is not much larger than 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