The anisotropic excitation spectrum of a chromium Bose-Einstein Condensate

Laboratoire de Physique des LasersUniversité Sorbonne Paris Cité

Villetaneuse - France

Olivier GORCEIX

44th EGASGöteborg – July 11, 2012

Interactions within a BECVan der Waals / contact interactions :

isotropic and short ranged

Effective potentiel proportionnal to aS (R), with aS = scattering length, aS adjustable thanks to Feshbach resonances

Dipole-dipole interactions: anisotropic and long-ranged highly magnetic atoms Cr, Er, Dy, dipolar molecules; Rydberg atoms

Chromium atoms carry a permanent magnetic dipole of 6µB

MDDI are 36 times bigger than in alkali BECs but still

dd (Cr)=0.159 while dd (Rb)=0.0044

where dd quantifies the ratio dipolar / contact interactions

Dipole-dipole interaction potential

22 203

11 3cos ( )

4dd J BV S gR

Anisotropy

Chrome (S=3): both contact AND dipolar interactions

R

Mean field becomes non local and anisotropic

Spin and rotation are coupled

is equal to 0.16

Pfau et al,PRL 95, 150406 (2005)

First reported effects of DDIs on BECs with Cr BECs

Eberlein et al, PRL 92, 250401 (2004)

Striction of the BEC(non local effect)

Vdd adds a non localanisotropic mean-field

B

Anisotropy in theBEC expansion

Bismut et al., PRL 105, 040404 (2010)

0.16dd

The effects of DDIsare experimentallyevidenced bydifferentialmeasurements,for two orthogonalorientations of the B field

DDIs change inthe few % rangethe physics ofa ground state BEC

DDIs

1st PART

COLLECTIVE OSCILLATIONS

Impact of the dipolar interactions on their frequencies

A small correction induced by dipolar interactions

repulsion attraction

Collective excitations of a dipolar BEC

We repeat the experiment for two orthogonal orientations

of B

1.2

1.0

0.8

0.6

2015105

Asp

ect

rati

o

Parametric excitation

MDDI are anisotropic, they impact on the q-pole excitation eigenfrequencies of a trapped BEC

In this mode, oscillations along y and z are in opposition

( )t ms

15 000 atoms

Trap geometry dependence of the measured frequency shift

Trap anisotropy

Shift of the quadrupole

mode frequency (%)

Shift of the aspect ratio

(%)

Theory PRL 92, 250401 (2004)

Good agreement with Thomas-Fermi predictions

BEC always stretches along B

While the sign of the quadrupole shift depends on the trap geometry

0.16dd

This exp:Bismut et al., PRL 105, 040404 (2010)

2nd PART

RAMAN-BRAGG SPECTROSCOPY OF A DIPOLAR BEC

Sound velocity anisotropy induced by dipolar interactions

A more pronounced dipolar effect

Rev. Mod. Phys. 77, 187 (2005)

c is the sound velocity

c is also the critical velocity

for superfluidity in the Landau model

healing length

0( 2 )k k k cE E n g Bogoliubov spectrum

1k

m

kEk 2

22 /12 0 kgnE ck

Quasi-particles, phonons kck 1k free particles

kk E

when

where gc= 4ħ2a /m

Excitation spectrum of a BEC with pure contact interactions

224

( ) (3cos 1)3 k

dV k

A 20% effect expected on the speed of sound !Much larger than the (~3%) effects for striction and collective excitations

Excitation spectrum of the BEC with DDIs

kB

1cos312 20 kddckkk gnEE

if , and if ,0k //cc 2/ k cc

0( 2 )k k k cE E n g becomes:

2.11

21///

dd

ddcc

0.16dd

k

or B┴

frequencies and Angular separation

absorption image after TOF of 5 ms

Profile at resonance ie when ħ (q)

Raman-Bragg spectroscopy of a BEC

k

Ene

rgy

1 2

0.8k

Moving lattice upon the BEC

Lattice beams crossing with an angle and a detunedcauses resonant momentum exchange when

2 sin( / 2)Lk k

From the excitation spectrum we infer the speed of sound

=14° Phonon regime

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 spin and excitation wavevector

c┴ ≠ c

Anisotropic speed of sound

Theo Exp

Parallel 3.6 mm/s 3.4 mm/s

Perpendicular 3 mm/s 2.8 mm/s

Good agreement between theory and experiment:

Bismut el al, arXiv :1205.6305

At ultralow T ≈ 300nK and B ≈ 40 nT the chemical potential becomes greater than the Zeeman splitting -> NEW PHYSICS

-3-2-1 0

2 1

3

Magnetism and thermodynamics - spinor physics

Above and Below threshold

TOF + Stern-Gerlach

Spin 3 phase diagramSpontaneous demagnetization

Pasquiou et al, PRL 106, 255303 and 108, 045307

Conclusion

Dipolar interactions induce anisotropy in the BEC excitation spectra - collective modes;- phonon dispersion law : sound velocity

Magnetism and thermodynamics of a spin 3 BEC with free magnetisation

Perspectives

Extension of our work on magnetism to strongly correlated states in 3D optical lattticesEinstein-de-Haas effect: spin-rotation couplingImproved spatial resolution for in situ imaging of magnetization domains

Extension to a Fermi sea of 53Cr atoms

E.Maréchal, OG, P. Pedri, Q. Beaufils (PhD), B. Laburthe, L. Vernac, B. Pasquiou (PhD), G. Bismut (PhD)

The chromium BEC crewThe chromium BEC crewwww-lpl.univ-paris13.fr:8082

Thank you for your attention

… PhD students welcomed in our group…