1. Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaborator: Anne Crubellier (Laboratoire Aimé Cotton) B. Pasquiou (PhD), G. Bismut (PhD), A. de Paz B. Laburthe, E. Maréchal, L. Vernac, P. Pedri, M. Efremov (Theory), O. Gorceix (Group leader) Effects of dipolar relaxation in chromium BECs

2. Dipole-dipole interactions Anisotropic Long range Chromium (S=3): Van-der-Waals + dipole-dipole interactions R Relative strength of dipole-dipole and Van-der-Waals interactions Cr: Specificities of Chromium

3. 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) Parabolic ansatz is still a good ansatz Non local anisotropic mean-field (similar results in our group)

4. Collective excitations of a dipolar BEC Repeat the experiment for two directions of the magnetic field Parametric excitations: Due to the anisotropy of dipole-dipole interactions, their effects on the BEC depend on the relative orientation of the magnetic field and the axis of the trap Bismut et al., PRL 105, 040404 (2010) t (ms) Aspect ratio Frequency shift (differential measurement)

5. Trap geometry dependence of the measured frequency shift Large sensitivity of the collective mode to trap geometry unlike the striction of the BEC Trap anisotropy Shift of the quadrupole mode frequency (%) Shift of the aspect ratio (%) Eberlein, PRL 92, 250401 (2004) Good agreement with Thomas- Fermi predictions BEC always stretches along B Sign of quadrupole shift depends on trap geometry

6. In our experiment, MDDI is not much larger than the quantum kinetic energy Simulations with 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 Influence of the BEC atom number

7. When dipolar mean field beats local contact meanfield Pfau, PRL 101, 080401 (2008) And…, roton, vortices, Mott physics, 1D or 2D physics, breakdown of integrability in 1D… With… ? Cr ? Er ? Dy ? Dipolar molecules ? Anisotropic d-wave collapse of (spherical) BEC when scattering length is reduced (Feshbach resonance) => reveals dipolar coupling Tune contact interactions using Feshbach resonances : dipolar interactions larger than contact interactions T.Lahaye et al, Nature. 448, 672 (2007)

8. What is dipolar relaxation ? Elastic collision Spin exchange Inelastic collisions with rotation Dipole-dipole interaction potential: Induces several types of collision: 0 1

9. Only two channels for dipolar relaxation in m S = 3: Change of magnetisation associated with rotation => (Einstein-de-Haas effect) Spontaneous creation of vortices ? Need of an extremely good control of B close to 0 Important to control magnetic field - - -3 -2 0 1 2 3 What is dipolar relaxation ? Dipolar relaxation associated with a change in kinetik energy: and with a change in angular momentum: Dependance with magnetic field

10. Energy scale, length scale, and magnetic field Chemical potential : 1 kHz.3 mG Inelastic dipolar mean-field Molecular binding enery : 10 MHz Magnetic field = 3 G ( is the scattering length) Inhibition of dipolar relaxation due to inter-atomic (VdW) repulsion 30 mG Band excitation in lattice : 100 kHz ( is the harmonic oscillator size) Suppression of dipolar relaxation in optical lattices

11. 3 Gauss …spin-flipped atoms gain so much energy they leave the trap -3 -2 0 1 2 3 Suppression of dipolar relaxation due to inter-atomic repulsion

12. Dipolar relaxation in a Cr BEC Fit of decay gives  Remains a BEC for ~30 ms Time (ms) Atom number BEC lost Rf sweep 2 Produce BEC m = -3 detect BEC m = -3 Rf sweep 1 BEC m = +3, varying time Static magnetic field Experimental procedure : Typical results :

13. Evolution of dipolar relaxation with the magnetic field Fermi golden rule a 6 = 103 ± 4 a 0 See also Shlyapnikov PRL 73, 3247 (1994) Never observed up to now Born approximation neglects molecular potentials : ok for B 10 G… not in between. Local character of dipolar relaxation, depending on B Node in the entrance wavefunction near a 6 Determination of chromium scattering lengths a 4 = 64 ± 4 a 0 Pfau, Appl. Phys. B, 77, 765 (2003)

14. Interparticle distance Energy Interpretation from the molecular physics point of view In Out Node in the entrance wavefunction near a 6, zero coupling, minimum in dipolar relaxation Only valid for R C > a 6 Better knowledge of the inner part of molecular potentials otherwise required

15. A probe of long-range correlations : here, a mere two-body effect, yet unacounted for in a mean-field « product-ansatz » BEC model Dipolar relaxation: measuring non-local correlations L. H. Y. Phys. Rev. 106, 1135 (1957) Use of local character of dipolar relaxation Measure of two particule correlation function by varying the magnetic field Pair correlation function for hard-core potential

16. New estimates of Cr scattering lengths Collaboration Anne Crubellier (LAC, IFRAF) Pasquiou et al., PRA 81, 042716 (2010) Beaufils et al., PRA 79, 032706 (2009)

17. - The 2-body loss parameter is always twice smaller in the BEC than in thermal gases. - Probe for effect of thermal (HBT-like) correlations 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 Dip still hold for thermal gases. At the dip, DR insensitive to temperature. Partial waves l>0 do not contribute to dipolar relaxation Contribution of higher order partial waves Temperature (µK)

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

19. 30 mGauss …spin-flipped atoms go from one band to another 2 3 1 Spin relaxation and band excitation in optical lattices

20. Reduction of dipolar relaxation in optical lattices Load the BEC in a 1D or 2D Lattice One expects a reduction of dipolar relaxation, as a result of the reduction of the density of states in the lattice h  h  band mapping Loading in lattices Static magnetic field Rf sweep 2 Produce BEC m = -3 detect BEC m = -3 Rf sweep 1 BEC m = +3, varying time Experimental procedure: Lattices height ~ 135 kHz 25 Er

21. Pasquiou et al., PRA 81, 042716 (2010) Pasquiou et al., PRL 106, 015301 (2011) Reduction of dipolar relaxation in optical lattices

22. What we measure in 1D: Non equilibrium velocity distribution along tubes Integrability Population in different bands due to dipolar relaxation Measure population in band v = 0 and v = 1, and heating from population created in v = 2 (collisional de-excitation) Band mapping procedure

23. -3 -2 0 1 2 3 (almost) complete suppression of dipolar relaxation in 1D at low field Energy released Band excitation Kinetic energy along tubes Strong reduction of DR when Almost complete suppression below threshold at 1D Magnetic field (kHz) Fraction of atoms in v=1 Temperature (µK) 25 Er 12 Er

24. Importance of cylindrical symetry Below threshold, suppression of DR is most efficient if : - Lattice sites are cylindrical (fully cylindrical ?) - The magnetic field is parallel to the 1D gases Dipolar relaxation rate (a.u.)

25. (almost) complete suppression of dipolar relaxation in 1D at low field: 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…

26. .3 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 Magnetization dynamics of spinor condensates

27. 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 irrelevant 0 1 New features with Cr - First S=3 spinor (7 Zeeman states, four scattering lengths, a 6, a 4, a 2, a 0 ) - 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

28. 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 are 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 Critical magnetic field DDI ensure the coupling between states with different magnetization

29. At VERY low magnetic fields, spontaneous depolarization of 3D and 1D quantum gases Produce BEC m=-3 Rapidly lower magnetic field Stern Gerlach experiments 1 mG 0.5 mG 0.25 mG « 0 mG » Magnetic field control below.5 mG (dynamic lock, fluxgate sensors) (50 Hz noise fluctuations, earth Magnetic field, …) (.1mG stability) (no magnetic shield…) (up to 1H stability) Experimental procedure

30. Mean-field effect BECLattice Critical field0.26 mG1.25 mG 1/e fitted0.4 mG1.45 mG Field for depolarization depends on density Optical lattices : change only the density, not the symetry for DDI

31. Mean-field effect Optical lattices : change only the density, not the symetry for DDI In lattices, no changes for depolarisation with the orientation of B Evidence for inter-sites dipolar coupling

32. Dynamics analysis At short times, transfert between m S = -3 and m S = -2 Ueda, PRL 96, 080405 (2006) / Kudo Phys. Rev. A 82, 053614 (2010) Natural timescale for depolarization: (a few ms) ~ a two level system coupled by V dd few atoms in m S = -2, so collision only in a 6 But still unaccounted for B above dipolar meanfield Influence of the trap / temperature ???

33. Dynamics analysis Bulk BEC 2D optical lattices In lattices (in our experimental configuration), the volume of the cloud is multiplied by 3 Mean field due to dipole-dipole interaction is reduced Slower dynamics, even with higher peak densities Non local character of DDI

34. Single component Bose thermodynamics

35. Multi-component Bose thermodynamics Simkin and Cohen, PRA, 59, 1528 (1999) Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000) Phase diagram, non interacting case, cylindrical -3 -2 0 2 1 3 7 Zeeman states; all trapped in optical dipole trap -2 0 1 2 3 -3 magnetization temperature BEC in majoritary component+ Th Normal BEC in each component Double phase transition at constant magnetization

36. Thermal effect: (Partial) Loss of BEC when demagnetization Dipolar interaction opens the way to spinor thermodynamics with free magnetization B=0 B=20 mG lower T c : spin degree of freedom is released

37. Thermodynamics of a spinor gas with free magnetization Above Bc, magnetization well accounted for by non interacting model Above Bc, thermal gas depolarizes, but BEC remains polarized

38. Spin population and thermometry (above Bc) BEC in m=-3 Depolarized thermal gas « bi-modal » spin distribution A new thermometry ? (limits to be checked) Above Bc: Only thermal gas depolarizes… get rid of it ? Cooling scheme? (Bragg excitations or field gradient)

39. Summary: A quench through a zero temperature (quantum) phase transition 2 1 3 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 Also new physics in 1D: Polar phase is a singlet-paired phase arXiv:1103.5534 (Shlyapnikov-Tsvelik) -2 0 1 2 3 -3 Santos PRL 96, 190404 (2006) Ho PRL. 96, 190405 (2006) Pasquiou et al., accepted in PRL

40. Conclusion Dipolar relaxation in BEC: new measurement of Cr scattering lengths non-local correlations Dipolar relaxation in reduced dimensions: almost-suppression of DR 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 / cooling (Collective excitations – effect of non-local mean-field)

41. Thank you for your attention …one open Post-doc position in our group…

42. 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 1425 °C  A Zeeman slower Pure BEC: 10 000 à 30 000 atomes

43. -3 -2 0 2 1 3 Above Bc: Only thermal gas depolarizes… get rid of it ? (Bragg excitations or field gradient) Prospect : new cooling method using the spin degrees of freedom