1. Elastic and inelastic dipolar effects in chromium BECs 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-Tolra L. Vernac E. Maréchal G. Bismut A. Crubellier (LAC- Orsay)

2. BEC: a quantum (super-)fluid Macroscopic occupation of ground state Van-der-Waals 1/r 6 interactions, short range, isotropic Quasi-particles, phonons Landau criterium for superfluidity Rev. Mod. Phys. 77, 187 (2005)

3. Types, and control, of interactions 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) Tunable through NMR techniques (PRL 89, 130401 (2002)). Quantum phase transitions Ferromagnetic / Polar/ Cyclic phases Quantum magnetism Nematic phases in liquid cristals Multicomponent BECs: more than one scattering length. Exchange interactions decide which spin configuration reaches the lowest energy state.

4. Dipole-dipole interactions Non local anisotropic meanfield Chromium: S=3 -Static and dynamic properties of BECs Anisotropic Long range Alkalis: Van-der-Waals interactions (effective  potential) Chromium: Van-der-Waals plus dipole-dipole Spin degree of freedom coupled to orbital degree of freedom - Spinor physics and magnetization dynamics

5. Introduction One hydrodynamic dipolar effect Magnetization dynamics near a quantum phase transition Experimental setup Control of dipolar relaxation

6. N = 4.10 6 T=120 μK How to make a Chromium BEC 425 nm 427 nm 650 nm 7S37S3 5 S,D 7P37P3 7P47P4  An atom: 52 Cr 750700650600550500 600 550 500 450 (1) (2) Z  An oven  A small MOT  A dipole trap  A crossed dipole trap  All optical evaporation  A BEC Oven at 1350 °C  A Zeeman slower

7. Hot oven Good vacuum Many lasers 1 M€, 4 years

9. PRA 77, 061601(R) (2008) PRA 77, 053413 (2008)PRA 73, 053406 (2006) BEC with Cr atoms in an optical trap

10. Introduction: BEC, dimensions, interactions One hydrodynamic dipolar effect Magnetization dynamics near a quantum phase transition Experimental setup Control of dipolar relaxation

11. Free 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 Self-similar, Castin-Dum expansion TF radii after t.o.f. related to interactions

12. 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) V dd : finite size effect !

13. Collective excitations of a dipolar BEC Collective excitations frequency independent of number of atoms and intetaction strength: Pure geometrical factor At lowest energies, wavelength of excitation is 1/(the size of the BEC)

14. Castin-Dum and frequency of collective excitations Consider small oscillations, then with In the Thomas Fermi regime, collective excitations frequencies solely depend on trapping frequencies

15. 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

16. When dipolar mean field beats local contact meanfield implosion of (spherical) condensates Stuttgart: d-wave collapse Pfau, PRL 101, 080401 (2008) Anisotropic explosion pattern reveals dipolar coupling. (Breakdown of self similarity) And…, Tc, solitons, vortices, Mott physics, 1D or 2D physics, breakdown of integrability in 1D… With… ? Cr ? Er ? Dy ? Dipolar molecules ? (Tune contact interactions using Feshbach resonances Nature. 448, 672 (2007) ) >

17. Introduction: BEC, dimensions, interactions One hydrodynamic dipolar effect Magnetization dynamics near a quantum phase transition Experimental setup Control of dipolar relaxation

18. Need of an extremely good control of B close to 0 Rotate the BEC ? Spontaneous creation of vortices ? Einstein-de-Haas effect Ueda, PRL 96, 080405 (2006) See also Santos, PRL 96, 190404 (2006) Angular momentum conservation Dipolar relaxation : PRA 81, 042716 (2010) (B~0.1 mG) -3 -2 0 1 2 3

19. Go to very tightly confined geometries (BEC in 2D optical lattices) How to observe the Einstein-de Haas effect ? Energy to nucleate a « mini-vortex » in a lattice site An idea 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 (~120 kHz) A gain of two orders of magnitude on the magnetic field requirements ! Optical lattices: periodic potential made by AC-stark shift of a standing wave

20. 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 Dipolar relaxation in 1D lattice: PRA 81, 042716 (2010)

21. What we measure in 1D: 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. arXiv:1010.3241arXiv:1010.3241

22. What we measure in 1D: (almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices. arXiv:1010.3241arXiv:1010.3241

23. (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…

24. Dipolar relaxation in a Cr BEC Fit of decay gives  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 Remains a BEC for ~30 ms Born approximation Pfau, Appl. Phys. B, 77, 765 (2003) PRA 81, 042716 (2010)

25. In Out Interpretation Zero coupling Determination of scattering lengths S=6 and S=4 Interpartice distance Energy

26. New estimates of Cr scattering lengths Collaboration Anne Crubellier (LAC, IFRAF) PRA 81, 042716 (2010) PRA 79, 032706 (2009)

27. Perspectives : go to very low fields what happens when R c >n (-1/3) ? Many-body spinor physics… with changing magnetization… Dipolar relaxation: a local phenomenon

28. Introduction: BEC, dimensions, interactions One hydrodynamic dipolar effect Magnetization dynamics near a quantum phase transition Experimental setup Control of dipolar relaxation

29. S=3 Spinor physics Ueda, PRL 96, 080405 (2006) Similar theoretical results by Santos and Pfau, PRL 96, 190404 (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 energ y to go from m=-3 to m=-2) Phases set by contact interactions (a 6, a 4, a 2, a 0 ) – differ by total magnetization (role of dipolar interactions !)

30. 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 Many difficulties related to extremely low energy scales Magnetic field control below.5 mG (dynamic lock) Technical noise ? Time (ms) Population mSmS

31. Mean-field effect BECLattice Critical field0.26 mG1.25 mG 1/e fitted0.4 mG1.15 mG Field for depolarization depends on density

32. Dynamics analysis Time (ms) Remaining atoms in m=-3 Depolarization at higher field for BEC in lattice… but depolarization is slower, presumably due to swelling of the cloud loaded in lattice (depolarization timescale set by the strength of dipole-dipole interactions (magnetic) meanfield) Meanfield picture : Spin(or) precession (Majorana flips) When mean field beats magnetic field Ueda, PRL 96, 080405 (2006)

33. -2 0 1 2 3 -3 A quench through a quantum phase transition ? -3 -2 0 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 » In 1D for attractive interactions: Condensate of bosons pairs Chandrasekhar limit (Shlyapnikov, Tsvelic) We do not (cannot ?) reach those new ground state phases !!

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

35. Thermal effect: (Partial) Loss of BEC when demagnetization Spin degree of freedom is released ; lower T c temperature Condensate fraction PRA, 59, 1528 (1999) J. Phys. Soc. Jpn, 69, 12, 3864 (2000) Normal « B phase » A BEC in each component « A phase » A BEC in majority component magnetization temperature

36. Conclusion Collective excitations – good agreement with theory Dipolar relaxation in reduced dimensions - towards Einstein-de-Haas Spontaneous demagnetization in a quantum gas – first steps towards spinor ground state (d-wave Feshbach resonance) (BECs in strong rf fields) (rf-assisted relaxation) (rf association) (MOT of 53 Cr) Production of a (slightly) dipolar Fermi sea Load into optical lattices – superfluidity ? Perspectives

37. 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)

38. Single component Bose thermodynamics

39. Multi-component Bose thermodynamics PRA, 59, 1528 (1999) J. Phys. Soc. Jpn, 69, 12, 3864 (2000) -3 -2 0 2 1 3 7 Zeeman states; all trapped -2 0 1 2 3 -3 magnetization temperature

40. Double phase transition at constant magnetization No demagnetization at low temperature temperature Condensate fraction Magnetic field Temperature Magnetization Non interacting spinor magnetization temperature