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Elastic and inelastic dipolar effects in chromium Bose-Einstein condensates

Elastic and inelastic dipolar effects in chromium Bose-Einstein condensates. Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France. B. Laburthe. B. Pasquiou. P. Pedri. O. Gorceix. E. Maréchal. G. Bismut. A. Crubellier (LAC). L. Vernac. Q. Beaufils.

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Elastic and inelastic dipolar effects in chromium Bose-Einstein condensates

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

  2. Chromium : S=3 Dipole-dipole interactions Long range interactions - 2-body physics (thermalization of polarized fermions) Non local meanfield • Static and dynamic properties of BECs • Stuttgart, Villetaneuse • Intersites effects in optical lattices • Inguscio (Bloch oscillations) • Use for quantum computing • Polar molecules, de Mille • Blockade and entanglement of Rydberg atoms (Browaeys) Non local correlations • Checkerboard phases (Lewenstein) (Resembles ionic Wigner cristals) • Strong correlations in 1D and 2D dipolar systems (Astrakharchik)

  3. Inelastic dipolar effects Anisotropic dipole-dipole interactions Spin degree of freedom coupled to orbital degree of freedom - Feshbach resonances due to dipole-dipole interactions (Stuttgart, Villetaneuse) - Dipolar relaxation (Stuttgart, Villetaneuse) - Spinor physics; spin dynamics (Stamper-Kurn)

  4. How to make a Chromium BEC in 14s and one slide ? 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 1350 °C (Rb 150 °C) (Rb=780 nm) N = 4.106 T=120 μK (Rb=109 or 10) • All optical evaporation • A dipole trap • A BEC • A crossed dipole trap

  5. Modification of BEC expansion due to dipole-dipole interactions TF profile Striction of BEC (non local effect) Parabolic ansatz is still a good ansatz Eberlein, PRL 92, 250401 (2004) Similar results in Stuttgart PRL 95, 150406 (2005) Full symbols : experiment Empty squares : numerical

  6. « Quadrupole » (intermediate) « Monopole » « Quadrupole » (lower) Collective excitations in dipolar BECs (parametric excitation) Smaller effect (4%), but (possibly) better spectroscopic accuracy Ongoing experiment…

  7. Whendipolarmeanfield beats local contact meanfield (i.e. edd>1), implosion of (spherical) condensates (Tune contact interactions using Feshbach resonances (i.e. edd>1) Nature. 448, 672 (2007) Stuttgart: d-wave collapse Anisotropic explosion pattern reveals dipolar coupling. (Breakdown of self similarity) > Pfau, PRL 101, 080401 (2008) And…, Tc, solitons, vortices, Mott physics, 1D or 2D physics, breakdown of integrability in 1D…

  8. Other fascinating phenomena when dipolar mean field beats magnetic field Meanfield picture : Spin(or) precession (Majorana flips) Spin degree of freedom released, with creation of orbital momentum (vortices) Analog of the Einstein –de Haas effect Ueda, PRL 96, 080405 (2006) Similar theoretical results by Santos and Pfau. Some differences and open questions Santos and Pfau PRL 96, 190404 (2006) Dipole inelastic interactions modify the (already rich) S=3 spinor physics, and, most noticeably, its dynamics At the heart of the Einstein-de Haas effect with Cr BECs : dipolar relaxation

  9. What is dipolar relaxation ? rotation ! - Only two channels for dipolar relaxation in m=3: Need of an extremely good control of B close to 0 Rotate the BEC ? (Einstein-de-Haas)

  10. 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 Born approximation Pfau, Appl. Phys. B, 77, 765 (2003) Remains a BEC for ~30 ms Fit of decay givesb See also Shlyapnikov PRL 73, 3247 (1994) Never observed up to now

  11. Interpretation Gap ~ Zero coupling Determination of scattering lengths S=6 and S=4

  12. Collaboration Anne Crubellier (LAC, IFRAF) New estimates of Cr scattering lengths

  13. 100 7 6 5 4 3 2 Two-body loss param (10^(-13) cm^3/s) 10 7 6 5 4 3 2 1 7 4 6 8 2 4 6 8 2 4 6 8 0.1 1 10 Magnetic field (G) DR in a BEC accounted for by a purely s-wave theory. No surprise, as the pair wave-function in a BEC is purely l=0 What about DR in thermal gases ? Dipole-dipole interactions are long-range: all partial waves may contribute • The 2-body loss parameter is always twice smaller in the BEC than in thermal gases • Effect of thermal (HBT-like) correlations The dip in DR is as strong for thermal gases and BECs Partial waves l>0 do not contribute to dipolar relaxation

  14. All partial waves contribute to elastic dipolar collisions… but … For large enough magnetic fields, only s-wave contributes to dipolar relaxation (because the input and output wave functions always oscillate at very different spatial frequencies) Overlap calculations Anne Crubellier (LAC, IFRAF) Red : l=0 Blue: l=2 Green : l=4 Magenta: l=6 Overlap Magnetic field Perspectives : - no DR in fermionic dipolar mixtures - use DR as a non-local probe for correlations

  15. Towards Einstein-de-Haas ? Ideas to ease the magnetic field control requirements Create a gap in the system: B now needs to be controlled around a finite non-zero value • (i) Go to very tightly confined geometries (BEC in 2D or 3D optical lattices) • (ii) Modify output energy (rf fields) Energy to nucleate a « mini-vortex » in a lattice site (~300 kHz) Below Ev no dipolar relaxation allowed. Resonant dipolar relaxation at Ev.

  16. (i) Reduction of dipolar relaxation in reduced dimension (2D gaz) Load the BEC in a 1D Lattice (retro-reflected Verdi laser) Rf sweep 1 Rf sweep 2 Load optical lattice BEC m=+3, vary time Produce BEC m=-3 detect m=-3 1st BZ Band mapping Lose BEC (2D thermal gas) Dipolar relaxation in reduced dimension (2D)

  17. Strong reduction of dipolar relaxation when !!! !!! but instead Prospect : go to 2D or 3D optical lattices

  18. (ii) Controlling the output energy in dipolar relaxation: rf-assisted dipolar relaxation Without rf, no DR in m=-3 Gap ~ Similar mechanism than dipolar relaxation Within first order Born approximation: (Brf parallel to B) Calculation by Paolo Pedri (IFRAF post-doc, now joined our group) Coll. Anne Crubellier (LAC) See also Verhaar, PRA 53 4343 (1996) Never observed

  19. Prospect: operate at to observe resonant DR Dipolar relaxation between dressed states, to control: Coupling: Output energy

  20. Conclusion Rapid and simplified production of (slightly dipolar) Cr BECs (BECs in strong rf fields) Collective excitations (rf association) (d-wave Feshbach resonance) dipolar relaxation rf-assisted relaxation dipolar relaxation in reduced dimensions (MOT of 53Cr) Optical lattice and low-D physics (breakdown of integrability in 1D) DR as a probe for correlations Einstein-de-Haas effect Spinor diagram Production of a (slightly) dipolar Fermi sea Load into optical lattices – superfluidity ? Perspectives

  21. 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)

  22. Why Bessel functions ? (Floquet analysis) Modulate the eigenenergy of an eigenstate: e.g. different Zeeman states Phase modulation -> Bessel functions rf association Rydberg in m-waves Shaken lattice Q. Beaufils et al., arXiv:0812.4355 Pillet PRA, 36, 1132 (1987) Arimondo PRL 99 220403 (2007))

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