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Spontaneous Demagnetization of Ultra-Cold Chromium Atoms at Low Magnetic Fields

This study explores the effects of dipole-dipole interactions (DDIs) in a 52Cr Bose-Einstein condensate (BEC) and their evidence in a polarized BEC at low magnetic fields. It investigates the existence of a critical magnetic field where the BEC undergoes a quantum phase transition due to contact interactions and examines the thermodynamics of a spin 3 gas. The paper also discusses the modification of the BEC expansion and collective excitations in a dipolar BEC.

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Spontaneous Demagnetization of Ultra-Cold Chromium Atoms at Low Magnetic Fields

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  1. Spontaneousdemagnetization of ultra cold chromiumatoms atlowmagneticfields B. Pasquiou (PhD), G. Bismut (PhD) B. Laburthe, E. Maréchal, L. Vernac, P. Pedri, O. Gorceix (Group leader) We study the effects of Dipole-Dipole Interactions (DDIs) in a 52 Cr BEC

  2. Spontaneousdemagnetization of ultra cold chromiumatoms atlowmagneticfields 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 below Bcthe BEC is not ferromagnetic anymore a quantum phase transition due to contact interactions III- Thermodynamics of a spin 3 gas how thermodynamics is modified when the spin degree of freedom is released

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

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

  5. 1 0 -1 Other effect of DDIs: they can change magnetization of the atomic sample Dipole-dipole interaction potential with spin operators: Induces several types of collision: Spin exchange 1 ( ) + + S S S S S S Elastic collision + - - + 1 z 2 z 1 2 1 2 2 Inelastic collisions 3 ( ) - + + 2 zS r S r S - + + - 1 z 1 1 4 ( ) + + 2 zS r S r S +3 -1 - + + - 2 z 2 2 Cr +2 -2 rotation induced change in magnetization: +1 -3 Cr BEC in -3 => Einstein-de-Haas effect magnetization becomes free Optical trap

  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 1 0 -1 3 • New features with Cr • - First S=3 spinor (7 Zeeman states, four scattering lengths, a6, a4, a2, a0) • Dipole-dipole interactions free total magnetization • We can investigate the true ground state of the system (need very small magnetic fields) 2 1 0 -1 -2 -3 Two different B regims: B > Bc: ferromagnetic BEC and B < Bcnon-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 below Bcthe BEC is not ferromagnetic anymore a quantum phase transition due to contact interactions III- Thermodynamics of a spin 3 gas how thermodynamics is modified when the spin degree of freedom is released

  8. S=3 Spinor physics below Bc: emergence of new quantum phases S=3: four scattering lengths, a6, a4, a2, a0 3 2 ferromagnetic i.e. polarized in lowest energy single particle state 1 0 -1 -2 -3 Santos et Pfau PRL 96, 190404 (2006) Diener et Ho PRL 96, 190405 (2006) polar phase Critical magnetic field Bc Quantum phases are set by contact interactions (a6, a4, a2, a0) and differ by total magnetization at Bc, it costs no energy to go from mS=-3 to mS=-2 : stabilization in interaction energy compensates for the Zeeman energy excitation DDIs ensure the coupling between states with different magnetization below Bca non-feromagnetic phase is favored

  9. S=3 Spinor physics below Bc:spontaneous demagnetization of 3D and 1D quantum gases Rapidly lower magnetic field below Bc measure spin populations with Stern Gerlach experiment Experimental procedure: Bi>>Bc 1 mG (a) BEC in m=-3 0.5 mG (b) 0.25 mG (c) « 0 mG » (d) B=Bc -3 -2 -1 0 1 2 3 Bf < Bc 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 ! + Nthermal << Ntot Performances: 0.1 mG stability without magnetic shield, up to 1Hour stability Pasquiou et al., PRL 106, 255303 (2011)

  10. S=3 Spinor physics below Bc:local density effect Note Spinor Physics in 1 D can be qualitatively different see Shlyapnikov and Tsvelik New Journal of Physics 13 065012 (2011) Bcdepends on density 2D Optical lattices increase the peak density by about 5 Pasquiou et al., PRL 106, 255303 (2011)

  11. S=3 Spinor physics below Bc:dynamic analysis Simple model At short times, transfert between mS = -3 and mS = -2 ~ a two level system coupled by Vdd Bulk BEC Corresponding timescale for demagnetization: good agreement with experiment both for bulk BEC (t =3 ms) and 1 D quantum gases (t = 10 ms) But dynamics still unaccounted for : 2D optical lattices In lattices (in our experimental configuration), the volume of the cloud is multiplied by 3 Non local character of DDIs Slower dynamics, even with higher peak densities Mean field due to dipole-dipole interaction is reduced Pasquiou et al., PRL 106, 255303 (2011)

  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 below Bcthe BEC is not ferromagnetic anymore a quantum phase transition due to contact interactions III- Thermodynamics of a spin 3 gas how thermodynamics is modified when the spin degree of freedom is released

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

  14. S=3 Spinor physics above Bc: magnetization versus T B = 0.9 mG > Bc Above Bc, the BEC is ferromagnetic: only atoms in mS=-3 condense (i.e. in the absolute ground state of the system) BEC in m=-3 the kink in magnetization reveals BEC thermal gas Tc1 Solid line: results of theory without interactions and free magnetization Tc1is the critical temperature for BEC of the spinor gas (in the mS=-3 component) The good agreement shows that the system behaves as if there were no interactions (expected for S=1)

  15. S=3 Spinor physics above Bc: spin populations and thermometry BEC in mS= -3 A new thermometry Boltzmanian fit 8000 6000 population 4000 2000 Tspin more accurate at low T -3 -2 -1 0 1 2 3 m S depolarized thermal gas bimodal distribution Only thermal gas depolarizesCooling scheme if selective losses for mS > -3 e.g. field gradient « bi-modal » spin distribution

  16. S=3 Spinor physics below Bc:thermodynamics change B < Bc B < Bc B > Bc B >> Bc for T < Tc2 BEC in all mS ! Tc2 Tc1 for B < Bc, magnetization remains constant after the demagnetization process independant of T B=Bc(Tc2) for Tc2 < T < Tc1 BEC only in mS = -3 This reveals the non-ferromagnetic nature of the BEC below Bc Pasquiou et al., ArXiv:1110.0786 (2011)

  17. Thermodynamics of a spinor 3 gas: Results of theory with fixed magnetization and no interactions Tc1(M) A phase (normal) Evolution for a free magnetization 1.0 Evolution at fixed magnetization A double phase transition 0.8 0.6 B phase BEC in mS=-3 0.4 C phase BEC in each component 0.2 Tc2(M) 0 -1 -2 -3 Magnetization

  18. Thermodynamics of a spinor 3 gas: outline of our results evolution for M fixed (exp: for B < Bc) In green: Results of a theory with no interactions and constant magnetization evolution for free M (exp: for B > Bc) A phase: normal (thermal) B phase: BEC in one component C phase: multicomponent BEC In purple: our data measurement of Tc1(M), by varying B histograms: spin populations Pasquiou et al., ArXiv:1110.0786 (2011)

  19. Conclusion: what does free magnetization bring ? Above Bc - Spinor thermodynamics with free magnetization of a ferromagnetic gas - Application to thermometry / cooling A quench through a (zero temperature quantum) phase transition Below Bc first steps towards spinor ground state The non ferromagnetic phase is set by contact interactions, but magnetization dynamics is set by dipole-dipole interactions • 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

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

  21. When dipolar mean field beats local contact meanfield 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) Anisotropic d-wave collapse of (spherical) BEC when scattering length is reduced (Feshbach resonance) => reveals dipolar coupling Pfau, PRL 101, 080401 (2008) And: roton, vortices, Mott physics, 1D or 2D physics, breakdown of integrability in 1D… With Cr, Dy, Dipolar molecules ?

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