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Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. BarbÃ©, A. Pouderous, R. Chicireanu Collaborator: Anne Crubellier (Laboratoire AimÃ© Cotton)

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Magnetization dynamics in dipolar chromium BECs

B. Pasquiou (PhD), G. Bismut (PhD), A. de Paz

B. Laburthe, E. MarÃ©chal, L. Vernac,

P. Pedri, M. Efremov (Theory),

O. Gorceix (Group leader)

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

Collaborator:Anne Crubellier (Laboratoire AimÃ© Cotton)

R

Chromium (S=3): Van-der-Waals plus dipole-dipole interactions

Dipole-dipole interactions

Long range

Anisotropic

Non local anisotropic mean-field

Relative strength of dipole-dipole and Van-der-Waals interactions

Cr:

Striction

Stuttgart, PRL 95, 150406 (2005)

Collective excitations

Villetaneuse, PRL 105, 040404 (2010)

Anisotropic d-wave collapse when scattering length is reduced (Feshbach resonance)

Stuttgart, PRL 101, 080401 (2008)

R

Spin degree of freedom coupled to orbital degree of freedom

- Spinor physics and magnetization dynamics

without

with

1

Dipole-dipole interactions

0

-1

3

2

1

0

-1

-2

-3

B=0: Rabi

3

2

1

0

-1

-2

-3

-3 -2 -1 0 1 2 3

In a finite magnetic field: Fermi golden rule

Dipolar relaxation, rotation, and magnetic field

3

2

1

0

-1

Angular momentum conservation

-2

-3

Rotate the BEC ?

Spontaneous creation of vortices ?

Einstein-de-Haas effect

Important to control magnetic field

Ueda, PRL 96, 080405 (2006)

Santos PRL 96, 190404 (2006)

Gajda, PRL 99, 130401 (2007)

B. Sun and L. You, PRL 99, 150402 (2007)

From the molecular physics point of view

Energy

Interpartice distance

Rc = Condon radius

PRA 81, 042716 (2010)

( is the scattering length)

( is the harmonic oscillator size)

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

3

2

1

0

-1

-2

-3

Suppression of dipolar relaxation due to inter-atomic repulsion

â€¦spin-flipped atoms gain so much energy they leave the trap

Dipolar relaxation in a Cr BEC

Rf sweep 1

Rf sweep 2

Produce BEC m=-3

BEC m=+3, vary time

detect BEC m=-3

Fermi golden rule

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

PRA 81, 042716 (2010)

a6 = 103 Â± 4 a0.

Feshbach resonance in d-wave PRA 79, 032706 (2009)

See also Shlyapnikov PRL 73, 3247 (1994)

a6 = 102.5 Â± 0.4 a0

Dipolar relaxation: measuring non-local correlations

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 Â«Â product-ansatzÂ Â» BEC model

3

2

1

Spin relaxation and band excitation in optical lattices

â€¦spin-flipped atoms go from one band to another

Reduction of dipolar relaxation in optical lattices

Load the BEC in a 1D or 2D Lattice

Rf sweep 1

Rf sweep 2

Load optical lattice

BEC m=+3, vary time

Produce BEC m=-3

detect m=-3

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

PRA 81,

042716 (2010)

Phys. Rev. Lett.

106, 015301 (2011)

(almost) complete suppression of dipolar relaxation in 1D at low field

3

2

1

0

-1

-2

-3

Energy released

Band excitation

Kinetic energy along tubes

B. Pasquiou et al., Phys. Rev. Lett. 106, 015301 (2011)

(almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices:

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 1Dâ€¦

3

2

1

0

-1

-2

-3

Magnetization dynamics of spinor condensates

3

2

1

0

-1

-2

-3

â€¦spin-flipped atoms loses energy

Similar to M. Fattori et al., Nature Phys. 2, 765 (2006) at large fields and in the thermal regime

S=3 Spinor physics with free magnetization

- - Up to now, spinor physics with S=1 and S=2 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
- -> Linear Zeeman effect irrelavant

1

0

-1

3

- New features with Cr
- - First S=3 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)

2

1

0

-1

-2

-3

S=3 Spinor physics with free magnetization

-1

3

3

2

1

-2

2

1

0

0

-1

-1

-2

-2

-3

-3

-3

Large magnetic field : ferromagnetic

Low magnetic field : polar/cyclic

-2

-3

Phases set by contact interactions (a6, a4, a2, a0)

â€“ differ by total magnetization

Santos PRL 96,

190404 (2006)

Ho PRL. 96,

190405 (2006)

Magnetic field control below .5 mG (dynamic lock, fluxgate sensors)

(.1mG stability)

(no magnetic shieldâ€¦)

At VERY low magnetic fields,

spontaneous depolarization of 3D and 1D quantum gases

1 mG

0.5 mG

Produce BEC m=-3

0.25 mG

Â«Â 0 mGÂ Â»

Stern Gerlach experiments

Rapidly lower magnetic field

Mean-field effect

Field for depolarization depends on density

Dynamics analysis

Meanfield picture : Spin(or) precession (Majorana flips)

When mean field beats magnetic field

Ueda, PRL 96, 080405 (2006)

Kudo Phys. Rev. A 82, 053614 (2010)

(a few ms)

Natural timescale for depolarization:

3

2

1

0

-1

3

-2

-3

2

1

0

-1

-2

-3

A quench through a zero temperature (quantum) phase transition

Santos and Pfau

PRL 96, 190404 (2006)

Diener and Ho

PRL. 96, 190405 (2006)

3

2

1

- - Operate near B=0. Investigate absolute many-body ground-state
- - We do not (cannot ?) reach those new ground state phases
- Thermal excitations probably dominate

Phases set by contact interactions,

magnetizationdynamics set by

dipole-dipole interactions

Â«Â quantum magnetismÂ Â»

Also new physics in 1D:

Polar phase is a singlet-paired phase

arXiv:1103.5534 (Shlyapnikov-Tsvelik)

3

2

1

0

-1

-2

-3

Prospect : new cooling method using the spin degrees of freedom

Above Bc:

Only thermal gas depolarizesâ€¦

get rid of it ?

(Bragg excitations

or field gradient)

Conclusion

Dipolar relaxation in BEC â€“ new measurement of Cr scattering lengths

non-localcorrelations

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

rotation in lattice sites

Spontaneous demagnetization in a quantum gas

- New phase transition

â€“ first steps towards spinor ground state

(Spinor thermodynamics with free magnetization

â€“ application to thermometry)

(Collective excitations â€“ effect of non-local mean-field)

G. Bismut (PhD), B. Pasquiou (PhD) , A. de Paz

B. Laburthe, E. MarÃ©chal, L. Vernac,

P. Pedri, M. Efremov(Theory),

O. Gorceix (Group leader)

â€¦one open Post-doc position in our groupâ€¦

Thermal effect: (Partial) Loss of BEC when demagnetization

Spin degree of freedom is released ; lower Tc

B=0

B=20 mG

PRA, 59, 1528 (1999) J. Phys. Soc. Jpn, Â Â 69, 12, 3864 (2000)

Dipolar interaction opens the way to spinor thermodynamics with free magnetization

Single component Bose thermodynamics

3

2

1

0

-1

-2

-3

Multi-component Bose thermodynamics

3

2

7 Zeeman states; all trapped

1

0

-1

PRA, 59, 1528 (1999) J. Phys. Soc. Jpn, Â Â 69, 12, 3864 (2000)

-2

-3

temperature

magnetization

Non interacting spinor

Double phase transition at constant magnetization

Condensate fraction

temperature

temperature

magnetization

Magnetization

Magnetic field

No demagnetization at low temperature

Temperature

7P4

7P3

650 nm

600

425 nm

550

5S,D

(2)

(1)

500

427 nm

Z

450

500

550

600

650

700

750

7S3

- An atom: 52Cr

- An oven

- A Zeeman slower

- A small MOT

Oven at 1425 Â°C

N = 4.106

T=120 Î¼K

- A dipole trap

- All optical evaporation

- A BEC

- A crossed dipole trap

BEC with Cr atoms in an optical trap

PRA 73, 053406 (2006)

PRA 77, 053413 (2008)

PRA 77, 061601(R) (2008)

Thermal effect: (Partial) Loss of BEC when demagnetization

Spin degree of freedom is released ; lower Tc

temperature

Normal

Â«Â A phaseÂ Â»

A BEC in majority component

Â«Â B phaseÂ Â»

A BEC in each component

magnetization

PRA, 59, 1528 (1999) J. Phys. Soc. Jpn, Â Â 69, 12, 3864 (2000)

lower Tc: a signature of decoherence

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

Spin population and thermometry (above Bc)

BEC in m=-3

Depolarized thermal gas

A new thermometry ?

(limits to be checked)

Â«Â bi-modalÂ Â» spin distribution

Threshold for dipolar relaxation in 1D:

(almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices

B. Pasquiou et al., Phys. Rev. Lett. 106, 015301 (2011)