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Collective excitations in a dipolar Bose-Einstein Condensate

Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France. Collective excitations in a dipolar Bose-Einstein Condensate. B. Pasquiou. E. Maréchal. P. Pedri. O. Gorceix. B. Laburthe. G. Bismut. L. Vernac.

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Collective excitations in a dipolar Bose-Einstein Condensate

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

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

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

  4. How to make a Chromium BEC in 14s and one slide ? 7P4 7P3 650 nm 425 nm 5S,D 427 nm 7S3 (2) (1) 600 550 Z 500 450 500 550 600 650 700 750 • An atom: 52Cr • An oven • A Zeeman slower • A small MOT Oven at 1350 °C (Rb 150 °C) (Rb=780 nm) N = 4.106 T=120 μK (Rb=109 or 10) Q. Beaufils et al., PRA 77, 061601 (2008) • All optical evaporation • A dipole trap • A BEC • A crossed dipole trap

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

  6. 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 z z The magnetic field is turned of 90° Shift of the aspect ratio σ y y x x Similar results in Stuttgart PRL 95, 150406 (2005)

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

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

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

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

  11. 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

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

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

  14. II 1 - Influence of the BEC atom number smaller number of atoms Large number of atoms (>10000) No more in the Thomas Fermi Regime Thomas Fermi Regime Parabolic anzatz is not valid Parabolic density profile • 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.

  15. Simulations with Gaussian anzatz Blue and Red Two different trap geometries 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

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

  17. 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

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

  19. 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.

  20. 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)

  21. Trap geometry (aspect ratio) dependent shifts Theoretical results with a parabolic anzatz See also: Pfau, PRA 75, 015604 (2007) for non axis-symmetric traps Eberlein, PRL 92, 250401 (2004) with assumed cylindrical symmetry of the trap

  22. 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

  23. Equation of Motion with and 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

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