Collective excitations in a dipolar Bose-Einstein Condensate Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France Former PhD students and post-docs: Q. Beaufils, T. Zanon, R. Chicireanu, A. Pouderous Former members of the group: J. C. Keller, R. Barbé B. Pasquiou O. Gorceix P. Pedri B. Laburthe L. Vernac E. Maréchal G. Bismut

Why are dipolar gases interesting? Strongly anisotropic Magnetic Dipole-Dipole Interactions (MDDI) repulsive interactions attractive interactions Angle between dipoles Long range radial dependence Great interest in ultracold gazes of dipolar molecules

What’s so special about Chromium? 6 valence electrons (S=3): strong magnetic dipole of Dimensionless quantity: strength of MDDI relative to s-wave scattering Large dipole-dipole interactions: 36 times larger than for alcali atoms. Magnetic dipole of Only two groups have a Chromium BEC: in Stuttgart and Villetaneuse

How to make a Chromium BEC in 14s and one slide ? 425 nm 427 nm 650 nm 7S37S3 5 S,D 7P37P3 7P47P4  An atom: 52 Cr N = T=120 μK (1) (2) Z  An oven  A small MOT  A dipole trap  A crossed dipole trap  All optical evaporation  A BEC (Rb=10 9 or 10 ) (Rb=780 nm) Oven at 1350 °C (Rb 150 °C)  A Zeeman slower Q. Beaufils et al., PRA 77, (2008)

Outline  I) Hydrodynamics of a Dipolar BEC  II) Experimental results for collective excitations  III) How to measure the systematic effects

Similar results in Stuttgart PRL 95, (2005) I) 1 - One first effect of dipole dipole interactions: Modification of the BEC aspect ratio Thomas Fermi profile Striction of BEC (non local effect) Parabolic ansatz is still a good ansatz The magnetic field is turned of 90° Shift of the aspect ratio σ x y z y z x

I) 2 - Dynamic properties of interactions in a BEC 2 quadrupole modes Lowest modes 1 monopole mode Highest mode Out of equilibrium: 3 collective modes

I) 2 - Dynamic properties of interactions in a BEC 2 quadrupole modes Lowest modes 1 monopole mode Highest mode Out of equilibrium: 3 collective modes

I) 2 - Dynamic properties of interactions in a BEC 2 quadrupole modes Lowest modes 1 monopole mode Highest mode Out of equilibrium: 3 collective modes Theory: Superfluid hydrodynamics of a BEC in the Thomas-Fermi regime Continuity equation Euler Equation

I) 3 - Introducing a dipolar mean field Theory: Non local mean-field The frequencies of the collective modes depend on the orientation of the magnetic field relative to the trap axis. dependent on the orientation of the magnetic dipoles We measure a relative shift Frequency shift proportional to

II) 1 - How to excite one collective mode of the BEC 15ms modulation of the IR power with a 20% amplitude at a frequency ω close to the intermediate collective mode resonance. The cloud then oscillates freely for a variable time Imaging process with TOF of 5ms Aλ/2 plate controls the trap geometry : angle Φ Parametric excitations: Modulation of the « stiffness » of the trap by modulating its depth

II) 2- Oscillations of the aspect ratio of the BEC after parametric excitations Trap geometry close to cylindrical symmetry Very low (3%) noise on the TF radii High damping due to the large anharmonicity of the trap Change between two directions of the magnetic field We measure

II) 3 - Trap geometry dependence of the measured frequency shift Large sensitivity of the collective mode to trap geometry at the vicinity of spherical symmetry, unlike the striction of the BEC Good agreement With theoretical predictions Related to the trap anisotropy Relative shift of the quadrupole mode frequency Relative shift of the aspect ratio

II 1 - Influence of the BEC atom number smaller number of atoms Gaussian anzatz in order to take the quantum kinetic energy into account. In our experiment, it is not negligible compared to the mean-field due to MDDI. Large number of atoms (>10000) Thomas Fermi Regime Parabolic density profile No more in the Thomas Fermi Regime Parabolic anzatz is not valid

Results of simulations with the 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 Simulations with Gaussian anzatz Blue and Red Two different trap geometries

III) 1 - Measurement of the trap frequencies parametric oscillations of the trap depth + Potential gradient Excitation of center of mass motion Center of mass motion only depends on external potential Direct measurement of the trap frequencies A good way of measuring systematic shifts of trap frequencies

III) 2 - Origins of the systematic shifts on the trap frequencies In a Gaussian trap: magnetic gradient induced frequency shift => Trap geometry dependent Shift Light shift of Cr is slightly dependent on the laser polarization orientation with respect to the static magnetic field. Relative associated shift independent of the trap geometry. Acceleration due to magnetic potential gradient Waist of the trap along the gradient

III) 3 - Experimental results for the systematic shifts of the trap frequencies Fit by Excitation of center of mass motion Measurement of the trap frequencies The magnetic field is turned of 90° Measurement of relative systematic shift

Summary  Characterization of the effect of MDDI on a collective mode of a Cr BEC.  Good agreement with TF predictions for a large enough number of Atoms.  Large sensitivity to trap geometry.  Useful tool to characterize a BEC beyond the TF regime, for lower numbers of atoms.  First measurement of the tensorial light shift of Chromium.

Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaboration: Anne Crubellier (Laboratoire Aimé Cotton) B. Pasquiou O. Gorceix Q. Beaufils Paolo Pedri B. Laburthe L. Vernac J. C. Keller E. Maréchal G. Bismut

Trap geometry (aspect ratio) dependent shifts Theoretical results with a parabolic anzatz Eberlein, PRL 92, (2004) with assumed cylindrical symmetry of the trap See also: Pfau, PRA 75, (2007) for non axis-symmetric traps

Collective excitations of a BEC Collisionless hydrodynamics of a BEC in the Thomas- Fermi regime Continuity equation Euler Equation Time evolution of the BEC Scaling law Superfluid velocity with

Equation of Motion From the s-wave pseudopotential with a being the s-wave scattering lenght. Three solution for the linearized equation: Two « quadrupole » modes In our case the two lowest modes One « monopole » mode In our case the highest mode with and