1. Elastic and inelastic dipolar effects in chromium BECs Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France B. Laburthe-Tolra

2. Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaborator: Anne Crubellier (Laboratoire Aimé Cotton) Invited professors: W. de Souza Melo (Brasil), D. Ciampini (Italy), T. Porto (USA) Internships (since 2008): M. Trebitsch, M. Champion, J. P. Alvarez, M. Pigeard, E. Andrieux, M. Bussonier, F. Hartmann, R. Jeanneret, B. Bourget G. Bismut (PhD), B. Pasquiou (PhD) B. Laburthe, E. Maréchal, L. Vernac, P. Pedri (Theory), O. Gorceix (Group leader)

3. Types of interactions in BECs Van-der Waals, short range and isotropic. Pure s-wave collisions at low temperature. Effective potential a S  (R), with a S scattering lenght, tunable thanks to Feshbach resonances Dipole-dipole interactions (magnetic atoms, Cr, Er, Dy, dipolar molecules, Rydberg atoms) Quantum phase transitions Ferromagnetic / Polar/ Cyclic phases Multicomponent BECs: More than one state, more than one scattering length. Exchange interactions decide which spin configuration reaches the lowest energy

4. Dipole-dipole interactions Anisotropic Long range Alkalis: Van-der-Waals interactions (effective  potential) Chromium (S=3): Van-der-Waals plus dipole-dipole R « Elastic »: Non local anisotropic mean-field « Inelastic »: Coupling between spin and rotation

5. Elastic

6. Relative strength of dipole-dipole and Van-der-Waals interactions Stuttgart: d-wave collapse, PRL 101, 080401 (2008) Anisotropic explosion pattern reveals dipolar coupling. (Breakdown of self similarity) Stuttgart: Tune contact interactions using Feshbach resonances (Pfau, Nature. 448, 672 (2007)) BEC collapses Parabolic ansatz still good. Striction of BEC. (Eberlein, PRL 92, 250401 (2004)) BEC stable despite attractive part of dipole-dipole interactions Cr: R

7. Interaction-driven expansion of a BEC A lie: Imaging BEC after time-of-fligth is a measure of in-situ momentum distribution Cs BEC with tunable interactions (from Innsbruck)) Self-similar, Castin-Dum expansion Phys. Rev. Lett. 77, 5315 (1996) TF radii after expansion related to interactions

8. Pfau,PRL 95, 150406 (2005) Modification of BEC expansion due to dipole-dipole interactions TF profile Eberlein, PRL 92, 250401 (2004) Striction of BEC (non local effect) (similar results in our group)

9. Frequency of collective excitations Consider small oscillations, then with In the Thomas-Fermi regime, collective excitations frequency independent of number of atoms and interaction strength: Pure geometrical factor (solely depends on trapping frequencies) (Castin-Dum) Interpretation Sound velocity TF radius

10. Collective excitations of a dipolar BEC Repeat the experiment for two directions of the magnetic field (differential measurement) Parametric excitations Phys. Rev. Lett. 105, 040404 (2010) A small, but qualitative, difference (geometry is not all) Due to the anisotropy of dipole-dipole interactions, the dipolar mean-field depends on the relative orientation of the magnetic field and the axis of the trap

11. A consequence of anisotropy : trap geometry dependence of the frequency shift Related to the trap anisotropy Shift of the quadrupole mode frequency (%) Shift of the aspect ratio (%) Eberlein, PRL 92, 250401 (2004) Good agreement with Thomas-Fermi predictions Sign of dipolar mean- field depends on trap geometry (oblate / elongated) Phys. Rev. Lett. 105, 040404 (2010)

12. Non local anisotropic meanfield -Static and dynamic properties of BECs Small effects in Cr… Need Feshbach resonances or larger dipoles. With… ? Cr ? Er ? Dy ? Dipolar molecules ? Then…, Tc, solitons, vortices, Mott physics, new phases (checkboard), 1D or 2D physics, breakdown of integrability in 1D… Interest for quantum computation ?

13. Inelastic

14. Spin degree of freedom coupled to orbital degree of freedom - Spinor physics and magnetization dynamics Dipole-dipole interactions Anisotropic R

15. Important to control magnetic field Rotate the BEC ? Spontaneous creation of vortices ? Einstein-de-Haas effect Angular momentum conservation Introduction to dipolar relaxation -3 -2 0 1 2 3 Ueda, PRL 96, 080405 (2006) Santos PRL 96, 190404 (2006) Gajda, PRL 99, 130401 (2007) B. Sun and L. You, PRL 99, 150402 (2007)

16. Energy scales Trap depth : 1 MHz 30 mG Band excitation in lattice : 100 kHz 300 mG Chemical potential : 4 kHz 1 mG Vortex : 100 Hz.01 mG Molecular binding enery : 10 MHz Magnetic field = 3 G

17. (T. Pfau’s Feshbach resonance – pure dipolar fluid) Suppression of dipolar relaxation due to inter-atomic repulsion Spin relaxation and band excitation in optical lattices Magnetization dynamics of spinor condensates A journey in dipolar physics through 7 decades of magnetic field intensities

18. 4 Gauss …spin-flipped atoms gain so much energy they leave the trap -3 -2 0 1 2 3

19. Dipolar relaxation in a Cr BEC Produce BEC m=-3 detect BEC m=-3 Rf sweep 1Rf sweep 2 BEC m=+3, vary time See also Shlyapnikov PRL 73, 3247 (1994) Never observed up to now Born approximation Pfau, Appl. Phys. B, 77, 765 (2003) PRA 81, 042716 (2010) Fermi golden rule

20. In Out Interpretation Zero coupling Determination of scattering lengths S=6 and S=4 Interpartice distance Energy R c = Condon radius

21. New estimates of Cr scattering lengths Collaboration Anne Crubellier PRA 81, 042716 (2010) Feshbach resonance in d-wave PRA 79, 032706 (2009) a 6 = 103 ± 4 a 0. a 6 = 102.5 ± 0.4 a 0

22. A probe of correlations : here, a mere two-body effect, yet unacounted for in a mean-field « product-ansatz » BEC model Dipolar relaxation: a localized phenomenon L. H. Y. Phys. Rev. 106, 1135 (1957)

23. 40 mGauss …spin-flipped atoms go from one band to another 2 3 1

24. Lattices provide very tightly confined geometries Dipolar relaxation in optical lattices Energy to nucleate a « mini-vortex » in a lattice site (~120 kHz) A gain of two orders of magnitude on the magnetic field requirements to observe rotation due to spin-flip (Einstein-de Haas effect) ! Optical lattices: periodic potential made by AC-stark shift of a standing wave m=3 m=2

25. Reduction of dipolar relaxation in optical lattices Load the BEC in a 1D or 2D Lattice Produce BEC m=-3 detect m=-3 Rf sweep 1Rf sweep 2 BEC m=+3, vary time Load optical lattice One expects a reduction of dipolar relaxation, as a result of the reduction of the density of states in the lattice

26. PRA 81, 042716 (2010) Phys. Rev. Lett. 106, 015301 (2011)

27. What we measure in 1D (band mapping procedure): Non equilibrium velocity ditribution along tubes Integrability Population in different bands due to dipolar relaxation m=3 m=2 -3 -2 0 1 2 3 Heating due to collisional de- excitation from excited band

28. What we measure in 1D: (almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices B. Pasquiou et al., Phys. Rev. Lett. 106, 015301 (2011)

29. m=3 m=2 Theoretical model: Fermi-Golden rule, taking into account: -The width of the excited band (tunneling) -All excited states along the tubes Calculated : 2. 10 -19 m 3 s -1 Measured : 5. 10 -20 m 3 s -1 Qualitatively ok. Correlations (and more) ignored

30. (almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices: a consequence of angular momentum conservation Above threshold : should produce vortices in each lattice site (EdH effect) (problem of tunneling) Towards coherent excitation of pairs into higher lattice orbitals ? Below threshold: a (spin-excited) metastable 1D quantum gas ; Interest for spinor physics, spin excitations in 1D…

31. .4 mGauss …spin-flipped atoms loses energy -2 0 1 2 3 -3 -2 0 2 1 3 Similar to M. Fattori et al., Nature Phys. 2, 765 (2006) at large fields and in the thermal regime

32. S=3 Spinor physics with free magnetization - Up to now, spinor physics with S=1 and S=2 only - Up to now, all spinor physics at constant magnetization (exchange interactions, no dipole-dipole interactions) - They investigate the ground state for a given magnetization -> Linear Zeeman effect irrelavant 0 1 New features with Cr -First S=3 spinor - Dipole-dipole interactions free total magnetization - Can investigate the true ground state of the system (need very small magnetic fields) 0 1 -2 -3 2 3

33. S=3 Spinor physics with free magnetization Santos PRL 96, 190404 (2006) Ho PRL. 96, 190405 (2006) -2 0 1 2 3 -3 -2 0 2 1 3 7 Zeeman states; all trapped four scattering lengths, a 6, a 4, a 2, a 0 (at B c, it costs no energy to go from m=-3 to m=-2 : difference in interaction energy compensates for the loss in Zeeman energy) Phases set by contact interactions (a 6, a 4, a 2, a 0 ) – differ by total magnetization Magnetic field a 0 /a 6 ferromagnetic i.e. polarized in lowest energy single particle state

34. At VERY low magnetic fields, spontaneous depolarization of 3D and 1D quantum gases Produce BEC m=-3 vary time Rapidly lower magnetic field Stern Gerlach experiments Magnetic field control below.5 mG (dynamic lock) (.1mG stability) (no magnetic shield…) Time (ms) Population mSmS

35. Mean-field effect BECLattice Critical field0.26 mG1.25 mG 1/e fitted0.4 mG1.45 mG Field for depolarization depends on density

36. Dynamics analysis Time (ms) Remaining atoms in m=-3 Meanfield picture : Spin(or) precession (Majorana flips) When mean field beats magnetic field Ueda, PRL 96, 080405 (2006) Kudo Phys. Rev. A 82, 053614 (2010) Natural timescale for depolarization: (a few ms) Magnetic field due to dipoles

37. -2 0 1 2 3 -3 A quench through a zero temperature (quantum) phase transition 2 1 3 Santos and Pfau PRL 96, 190404 (2006) Diener and Ho PRL. 96, 190405 (2006) Phases set by contact interactions, magnetization dynamics set by dipole-dipole interactions « quantum magnetism » - Operate near B=0. Investigate absolute many-body ground-state - We do not (cannot ?) reach those new ground state phases !! - Thermal excitations probably dominate -3 -2 0 2 1 3

38. Thermal effect: (Partial) Loss of BEC when demagnetization Spin degree of freedom is released ; lower T c Time (ms) Population mSmS As gas depolarises, temperature is constant, but condensate fraction goes down !

39. Thermal effect: (Partial) Loss of BEC when demagnetization Spin degree of freedom is released ; lower T c PRA, 59, 1528 (1999) J. Phys. Soc. Jpn, 69, 12, 3864 (2000) lower T c : a signature of decoherence Dipolar interaction open the way to spinor thermodynamics with free magnetization B=0 B=20 mG

40. Conclusion Collective excitations – effect of non-local mean-field Dipolar relaxation in BEC – new measurement of Cr scattering lengths correlations Dipolar relaxation in reduced dimensions - towards Einstein-de-Haas rotation in lattice sites Spontaneous demagnetization in a quantum gas - New phase transition – first steps towards spinor ground state (Spinor thermodynamics with free magnetization – application to thermometry) (d-wave Feshbach resonance) (BECs in strong rf fields) (rf-assisted relaxation) (rf association) (MOT of fermionic 53 Cr)