The anisotropic excitation spectrum of a chromium Bose-Einstein Condensate Laboratoire de Physique des Lasers Université Sorbonne Paris Cité Villetaneuse - France Olivier GORCEIX 44th EGAS Göteborg – July 11, 2012

Interactions within a BEC Van der Waals / contact interactions : isotropic and short ranged Effective potentiel proportionnal to a S  (R), with a S = scattering length, a S 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 6µ B MDDI are 36 times bigger than in alkali BECs but still  dd (Cr)=0.159 while  dd (Rb)= where  dd quantifies the ratio dipolar / contact interactions

Dipole-dipole interaction potential 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, (2005) First reported effects of DDIs on BECs with Cr BECs Eberlein et al, PRL 92, (2004) Striction of the BEC (non local effect) V dd adds a non local anisotropic mean-field Anisotropy in the BEC expansion Bismut et al., PRL 105, (2010) The effects of DDIs are experimentally evidenced by differential measurements, for two orthogonal orientations of the B field DDIs change in the few % range the physics of a 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 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 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, (2004) Good agreement with Thomas- Fermi predictions BEC always stretches along B While the sign of the quadrupole shift depends on the trap geometry This exp: Bismut et al., PRL 105, (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 Bogoliubov spectrum Quasi-particles, phonons free particles when where g c = 4  ħ 2 a /m Excitation spectrum of a BEC with pure contact interactions

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 if, and if, becomes:

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    Moving lattice upon the BEC Lattice beams crossing with an angle and a detuned causes resonant momentum exchange when From the excitation spectrum we infer the speed of sound  =14° Phonon regime 

Anisotropic speed of sound 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 TheoExp Parallel3.6 mm/s3.4 mm/s Perpendicular3 mm/s2.8 mm/s Good agreement between theory and experiment: Bismut el al, arXiv :

At ultralow T ≈ 300nK and B ≈ 40 nT the chemical potential becomes greater than the Zeeman splitting -> NEW PHYSICS Magnetism and thermodynamics - spinor physics Above and Below threshold TOF + Stern-Gerlach Spin 3 phase diagram Spontaneous demagnetization Pasquiou et al, PRL 106, and 108,

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 latttices Einstein-de-Haas effect: spin-rotation coupling Improved spatial resolution for in situ imaging of magnetization domains Extension to a Fermi sea of 53 Cr atoms

E.Maréchal, OG, P. Pedri, Q. Beaufils (PhD), B. Laburthe, L. Vernac, B. Pasquiou (PhD), G. Bismut (PhD) The chromium BEC crew www-lpl.univ-paris13.fr:8082

Thank you for your attention … PhD students welcomed in our group…