1. B. Pasquiou (PhD), G. Bismut (PhD) B. Laburthe, E. Maréchal, L. Vernac, P. Pedri, O. Gorceix (Group leader) Spontaneous demagnetization of ultra cold chromium atoms at low magnetic fields We study the effects of Dipole-Dipole Interactions (DDIs) in a 52 Cr BEC

2. Spontaneous demagnetization of ultra cold chromium atoms at low magnetic fields I- Dipole – dipole interactions how have they been evidenced in a polarized BEC what we are seeing new when going to low B fields II- Existence of a critical magnetic field III- Thermodynamics of a spin 3 gas how thermodynamics is modified when the spin degree of freedom is released below B c the BEC is not ferromagnetic anymore a quantum phase transition due to contact interactions

3. Dipole-dipole interactions (DDIs) Anisotropic Long Range Relative strength of dipole-dipole and Van-der-Waals interactions Different interactions in a BEC alkaline for 87 Rb chromium dysprosium for the BEC is unstable polar molecules GPE : R Van-der-Waals interactions Isotropic Short Range polarized BEC

4. Pfau,PRL 95, 150406 (2005) Some effects of DDIs on BECs for  dd < 1 (Cr) TF profile Eberlein, PRL 92, 250401 (2004) Striction of the BEC (non local effect)  dd adds a non local anisotropic mean-field Modification of the BEC expansion Collective excitations of a dipolar BEC Bismut et al., PRL 105, 040404 (2010) t (ms) Aspect ratio The effects of DDIs are experimentally evidenced by differential measurements, for two orthogonal orientations of the B field all the atoms are in the same Zeeman state DDIs change in the few % range the physics of polarized BEC

5. Other effect of DDIs: they can change magnetization of the atomic sample Elastic collision Spin exchange Inelastic collisions Dipole-dipole interaction potential with spin operators: Induces several types of collision: 0 1          222 111 212121 2 2 4 3 2 1 SrSrzS SrSr SSSSSS z z zz -2 -3 Cr +3 +2 +1 Cr BEC in -3 magnetization becomes free change in magnetization: rotation induced Optical trap => Einstein-de-Haas effect

6. 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 (VdW), no DDIs - The ground state for a given magnetization was investigated -> 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 - We can investigate the true ground state of the system (need very small magnetic fields) 0 1 -2 -3 2 3 Two different B regims: B > B c : ferromagnetic BEC and B < B c non-ferromagnetic BEC

7. Spontaneous demagnetization of ultra cold chromium atoms at low magnetic fields I- Dipole – dipole interactions how have they been evidenced in a polarized BEC what we are seeing new when going to low B fields II- Existence of a critical magnetic field III- Thermodynamics of a spin 3 gas how thermodynamics is modified when the spin degree of freedom is released below B c the BEC is not ferromagnetic anymore a quantum phase transition due to contact interactions

8. S=3 Spinor physics below B c : emergence of new quantum phases Santos et Pfau PRL 96, 190404 (2006) Diener et Ho PRL 96, 190405 (2006) -2 0 1 2 3 -3 S=3: four scattering lengths, a 6, a 4, a 2, a 0 at B c, it costs no energy to go from m S =-3 to m S =-2 : stabilization in interaction energy compensates for the Zeeman energy excitation Quantum phases are set by contact interactions (a 6, a 4, a 2, a 0 ) and differ by total magnetization ferromagnetic i.e. polarized in lowest energy single particle state Critical magnetic field B c DDIs ensure the coupling between states with different magnetization below B c a non-feromagnetic phase is favored polar phase

9. S=3 Spinor physics below B c : spontaneous demagnetization of 3D and 1D quantum gases BEC in m=-3 Rapidly lower magnetic field below B c measure spin populations with Stern Gerlach experiment 1 mG 0.5 mG 0.25 mG « 0 mG » Experimental procedure: -3-20123 (a) (b) (c) (d) B=B c B i >>B c B f < B c Performances: 0.1 mG stability without magnetic shield, up to 1Hour stability Magnetic field control below.5 mG dynamic lock, fluxgate sensors reduction of 50 Hz noise fluctuations, earth Magnetic field, "elevators" BEC in all Zeeman components ! Pasquiou et al., PRL 106, 255303 (2011) + N thermal << N tot

10. 3D BEC1D Quantum gas Critical field0.26 mG1.25 mG 1/e fitted0.3 mG1.45 mG B c depends on density 2D Optical lattices increase the peak density by about 5 S=3 Spinor physics below B c : local density effect Note Spinor Physics in 1 D can be qualitatively different see Shlyapnikov and Tsvelik New Journal of Physics 13 065012 (2011) Pasquiou et al., PRL 106, 255303 (2011)

11. 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 DDIs S=3 Spinor physics below B c : dynamic analysis Pasquiou et al., PRL 106, 255303 (2011) Corresponding timescale for demagnetization: good agreement with experiment both for bulk BEC (  =3 ms) and 1 D quantum gases (  = 10 ms) At short times, transfert between m S = -3 and m S = -2 ~ a two level system coupled by V dd Simple model But dynamics still unaccounted for :

12. Spontaneous demagnetization of ultra cold chromium atoms at low magnetic fields I- Dipole – dipole interactions how have they been evidenced in a polarized BEC what are we seeing new when going to low B fields II- Existence of a critical magnetic field III- Thermodynamics of a spin 3 gas how thermodynamics is modified when the spin degree of freedom is released below B c the BEC is not ferromagnetic anymore a quantum phase transition due to contact interactions

13. Summarize of our experimental situation Ultra cold gas of spin 3 52 Cr atoms at low magnetic fields 7 components spinor Optical trap, (almost) same trapping potential for the 7 Zeeman states Single component Bose thermodynamicsMulti-component Bose thermodynamics Simkin and Cohen, PRA, 59, 1528 (1999) Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000) spin degree of freedom unfrozen mG at 400 nK -2 0 1 2 3 -3 -2 0 2 1 3 Similar to M. Fattori et al., Nature Phys. 2, 765 (2006) at large B fields and in the thermal regime average trap frequency

14. S=3 Spinor physics above B c : magnetization versus T B = 0.9 mG > B c Solid line: results of theory without interactions and free magnetization the kink in magnetization reveals BEC T c1 Above B c, the BEC is ferromagnetic: only atoms in m S =-3 condense The good agreement shows that the system behaves as if there were no interactions (expected for S=1) thermal gas BEC in m=-3 T c1 is the critical temperature for BEC of the spinor gas (in the m S =-3 component) (i.e. in the absolute ground state of the system)

15. BEC in m S = -3 depolarized thermal gas « bi-modal » spin distribution A new thermometry Only thermal gas depolarizes Cooling scheme if selective losses for m S > -3 e.g. field gradient S=3 Spinor physics above B c : spin populations and thermometry 8000 6000 4000 2000 -3-20123 m S population Boltzmanian fit T spin more accurate at low T bimodal distribution

16. S=3 Spinor physics below B c : thermodynamics change B > B c B < B c B >> B c T c1 T c2 for T c2 < T < T c1 BEC only in m S = -3 for T < T c2 BEC in all m S ! for B < B c, magnetization remains constant after the demagnetization process independant of T This reveals the non-ferromagnetic nature of the BEC below B c B=B c (T c2 ) Pasquiou et al., ArXiv:1110.0786 (2011)

17. Magnetization B phase BEC in m S =-3 A phase (normal) C phase BEC in each component Thermodynamics of a spinor 3 gas: Results of theory with fixed magnetization and no interactions 0-2-3 0.2 0.4 0.6 0.8 1.0 A double phase transition Evolution at fixed magnetization Evolution for a free magnetization T c1 (M) T c2 (M)

18. Thermodynamics of a spinor 3 gas: outline of our results In green: Results of a theory with no interactions and constant magnetization A phase: normal (thermal) B phase: BEC in one component C phase: multicomponent BEC evolution for free M (exp: for B > B c ) evolution for M fixed (exp: for B < B c ) In purple: our data measurement of T c1 (M), by varying B histograms: spin populations Pasquiou et al., ArXiv:1110.0786 (2011)

19. Conclusion: what does free magnetization bring ? A quench through a (zero temperature quantum) phase transition -We do not (cannot ?) reach the new ground state phase - Thermal excitations probably dominate but… - … effects of DDIs on the quantum phases have to be evaluated The non ferromagnetic phase is set by contact interactions, but magnetization dynamics is set by dipole-dipole interactions first steps towards spinor ground state - Spinor thermodynamics with free magnetization of a ferromagnetic gas - Application to thermometry / cooling Above B c Below B c

20. Thank you for your attention … PhD student welcome in our group…

21. 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, Dy, Dipolar molecules ? Anisotropic d-wave collapse of (spherical) BEC when scattering length is reduced (Feshbach resonance) => reveals dipolar coupling Contact interactions can be tuned using Feshbach resonances: dipolar interactions then can get larger than contact interactions T.Lahaye et al, Nature. 448, 672 (2007)