1. E. Maréchal, O. Gorceix, P. Pedri, Q. Beaufils, B. Laburthe, L. Vernac, B. Pasquiou (PhD), G. Bismut (PhD) Excitation of a dipolar BEC and Quantum Magnetism We study the effects of Dipole-Dipole Interactions (DDIs) in a 52 Cr BEC M. Efremov IFRAF post doc A. de Paz 1st year PhD student Radu Chicireanu former PhD student J.C. Keller R. Barbé former members A. Crubelier collaboration (theory)

2. 6 electrons in the outer shells Specificities of chromium S=3 in the ground state permanent magnetic moment 6 µ B paramagnetic gas with rather strong dipole-dipole interactions (DDIs) DDIs change the physics of a polarized BEC (all atoms in the same Zeeman substate) DDIs allow the cold gas magnetization to change

3. High temperature oven (T=1350°C in our case) Obtaining a chromium BEC Preliminary works of J. Mc Clelland (NIST) - Tilman Pfau, J. Mlynek Trapping Transition at 425 nm High inelastic loss rates due to light assisted collisions choice of the materials needs to double a Ti:Sa laser low atom number MOT Experiment at Stuttgart (Tilman Pfau) High dipolar relaxation rateBEC only possible in an optical trap Accumulation in metastable states is efficientRed light repumpers required Our way to BEC: direct loading of an optical trap in metastable states optimization of the loading with depumping to a new metastable state + use of RF sweep

4. Physics of a dipolar BEC at Villetaneuse polarized BEC in the ground state m S =-3 polarized BEC in the excited state m S =+3 unpolarized ultra cold gas Study of dipolar relaxation in 3D, 2D, 1D, and 0D Spin Flip lower B field BEC excitations ("quadrupole" mode) S=3 spinor gas with free magnetization BEC excitations (phonons, free particle,…) multi-component BEC D wave Fescbach resonance RF association of molecules Ground State RF induced degeneracy Bragg spectroscopy trap modulation

5. I- Dipole – dipole interactions in a polarized chromium BEC how DDIs have been evidenced in ground state BECs why larger effects are expected with the excitations (phonons, free particles, …) how do we observe them II- Demagnetization of ultracold chromium gases at "ultra" low magnetic field study of S=3 spinor gas with free magnetization how thermodynamics is modified when the spin degree of freedom is released observation of a phase transition due to contact interactions: below a critical B field we observe a multi-component BEC Summary of the talk

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

7. J. Stuhler, PRL 95, 150406 (2005) Some effects of DDIs on Cr BECs 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 The effects of DDIs are experimentally evidenced by differential measurements, for two orthogonal orientations of the B field DDIs TF profile

8. Collective excitations of a dipolar BEC Bismut et al., PRL 105, 040404 (2010) t (ms) Aspect ratio DDIs change in the few % range the ground state physics of a polarized BEC DDIs induce changes smaller than  dd ! Some effects of DDIs on Cr BECs Trap anisotropy Shift of the quadrupole mode frequency (%) Shift of the aspect ratio (%)

9. A new and larger effect of DDIs: modification of the excitation spectrum of a Cr BEC Experiment: probe dispersion law c is the sound velocity c depends on In the BEC ground state the effects of DDIs are averaged due to their anisotropic nature New idea: probe the effects of DDIs on other kind of excitations of the BEC the dipolar mean field depends on trap geometry the excitation spectrum is given by the Fourier Transform of the interactions Quasi-particles, phonons measure the modification of c due to DDIs: 15% ? all dipoles contribute in the same way attractive and repulsive contributions of DDIs almost compensate

10. Excitation spectrum of a BEC with pure contact interactions Rev. Mod. Phys. 77, 187 (2005) c is the sound velocity c is also the critical velocity is the healing length Bogoliubov spectrum: Quasi-particles, phonons Free particles

11. A 20% shift due to DDIs expected on the speed of sound ! much larger than the (~3%) effects measured on the ground state and the "quadrupole" mode An effect of the momentum-sensitivity of DDIs: Excitation spectrum of a BEC in presence of DDIs if, and if, becomes:

12. Excitation spectrum of a BEC: the local density approximation (LDA) * the BEC is trapped, the density is not uniform * the BEC has a non zero width momentum distribution validity of LDA: = the theory giving predictions that you can compare with with LDA not valid at small k two sources of broadening: the excitation spectrum of the BEC has a non zero width and the effect of DDIs is going to be less than naively expected… LDA = consider the gas locally uniform

13.    Two laser beams detuned: Momentum and energy transfer Excitation of a BEC: principle of Bragg Spectroscopy Bragg beams very far detuned from atomic resonances For a given , tune  to find a good excitation, and register the excitation spectrum nm   = 100 Hz to 100 kHz

14. Bragg Spectroscopy: experimental realization Two lasers "in phase" are required We use two AOMs driven by a digital double RF source providing two RF signals in phase For given (accessible) values of , we register excitation spectra    6° to 14°, 28°, 83° optical access we measure the excited fraction for a given  excited and non-excited parts spatially separated by momentum transfer

15. Bragg Spectroscopy: experimental difficulties * choice of  t = the excitation duration (of the Bragg pulse) * poor spatial separation of the excited fraction at low k if  t is too small, we add a Fourier broadening if  t is too large, the mechanical effect of the trap comes into play to have a good spatial separation after expansion k becomes hard to reach in our case (we don't work with an elongated BEC) non excited fraction  t << T trap / 4 not quite possible at low k…  t >> 1 /  f non excited fraction

16. Bragg Spectroscopy: experimental difficulties poor separation of the excited fraction at low k ! data analysis complicated, noisy data no excitation  = 6°  = 14°  = 83°

17. Width of resonance curve: finite size effects (inhomogeneous broadening) The excitation spectra depends on the relative angle between spins and excitation Bragg Spectroscopy of a dipolar BEC: experimental results Excitation spectra at  =14°  From the different spectra, registered for a given , we deduce the value of: = shift of the excitation spectrum due to DDIs

18. Bragg Spectroscopy of a dipolar BEC: experimental results 1 1 2 3 4 1 0 0.1 0.2

19. Villetaneuse Collective excitations Striction Anisotropic speed of sound Conclusion: a 52 Cr BEC is a "non-standard superfluid" Stuttgart Expansion

20. I- Dipole – dipole interactions in a polarized chromium BEC how DDIs have been evidenced in ground state BECs why larger effects are expected with the excitations how do we observe them II- Demagnetization of ultracold chromium gases at "ultra" low magnetic field Study of S=3 spinor gas with free magnetization how thermodynamics is modified when the spin degree of freedom is released observation of a quantum phase transition due to contact interactions: below a critical B field we observe a multi-component BEC Summary of the talk

21. DDIs can change the 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: Optical trap

22. DDIs can change the magnetization of the atomic sample Inelastic collisions Dipole-dipole interaction potential with spin operators: Induces several types of collision:          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 rotation induced => Einstein-de-Haas effect

23. 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

24. Ultra cold gas of spin 3 52 Cr atoms at "ultra" low magnetic fields The spin degree of freedom is unfrozen when: 7 components spinor Optical trap, (almost) same trapping potential for the 7 Zeeman states mG at 400 nK allows the magnetization to change Two different B regims for the ground state are predicted: when B > B c, the Zeeman interactions dominate: one component (ferromagnetic) BEC when B < B c, the contact interactions dominate: multi-component (non-ferromagnetic) BEC -2 -3 Above B c : is 52 Cr close to a non-interacting S=3 gas with free magnetization ? Why B c ? What do we observe below B c ?

25. S=3 spinor gas: the non interacting picture (I) 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) -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 T c is lowered

26. Magnetization B phase BEC in m S =-3 A phase (normal) C phase BEC in each component 0-2-3 0.2 0.4 0.6 0.8 1.0 For Na: a double phase transition expected Evolution at fixed magnetization Evolution for a free magnetization T c1 (M) T c2 (M) S=3 spinor gas: the non interacting picture (II) For Cr: One BEC component, in mS= -3 the absolute ground state of the system Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000)

27. Our results: 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 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 condensation of the spinor gas (in the m S =-3 component) (i.e. in the absolute ground state of the system) B > B c Pasquiou et al., ArXiv:1110.0786 (2011) Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000)

28. measurement of T c1 (M), by varying B Pasquiou et al., ArXiv:1110.0786 (2011) Our results (II): measurements of T c1 B > B c The good agreement shows that the system behaves as if there were no interactions (expected for S=1) Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000) histograms: spin populations

29. 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 8000 6000 4000 2000 -3-20123 m S population Boltzmanian fit T spin more accurate at low T ! bimodal distribution Our results (III): spin populations and thermometry B > B c Pasquiou et al., ArXiv:1110.0786 (2011)

30. S=3 Spinor physics below B c : emergence of new quantum phases -2 0 1 2 3 -3 As a 6 > a 4, it costs no energy at B c to go from m S =-3 to m S =-2 : the stabilization in interaction energy compensates for the Zeeman energy excitation the BEC is ferromagnetic i.e. polarized in lowest energy single particle state Above B c -2 0 1 2 3 -3 Below B c All the atoms in m S = -3 interactions only in the molecular potential S tot = 6 because m s tot = -6 The repulsive contact interactions set by a 6 If atoms are transferred in m S = -2 then they can interact in the molecular potential S tot = 4 because m s tot = -4 The repulsive contact interactions are set by a 6 and a 4 the BEC is non ferromagnetic i.e. it is a multicomponent BEC

31. S=3 Spinor physics below B c : new quantum phases Santos et Pfau PRL 96, 190404 (2006) Diener et Ho PRL 96, 190405 (2006) For an S=3 BEC, contact interactions are set by four scattering lengths, a 6, a 4, a 2, a 0 Quantum phases are results of an interplay between Zeeman and contact interactions Quantum phases are set by contact interactions 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 polar phase unknown nematic phase

32. S=3 Spinor physics below B c : spontaneous demagnetization of the BEC BEC in m S =-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 1 Hour stability Magnetic field control below.5 mG (!!) dynamic lock, fluxgate sensors reduction of 50 Hz noise fluctuations feedback on earth magnetic field, "elevators" BEC in all Zeeman components ! Pasquiou et al., PRL 106, 255303 (2011) + N thermal << N tot

33. 3D BEC1D Quantum gas B c expected0.26 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)

34. 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 of the demagnetization 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, transfer between m S = -3 and m S = -2 ~ a two level system coupled by V dd Simple model But dynamics still unaccounted for: BcBc

35. 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 independent 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) hint for double phase transition

36. Thermodynamics of a spinor 3 gas: outline of our results A phase: normal (thermal) B phase: BEC in one component C phase: multi-component BEC evolution for B > B c evolution 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) B c reached

37. 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 exotic spinor ground state - Spinor thermodynamics with free magnetization of a ferromagnetic gas - Application to thermometry / cooling Above B c Below B c

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