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de Paz ( PhD ), A. Chotia , A. Sharma, B. Laburthe-Tolra , E. Maréchal, L. Vernac ,

Magnetization dynamics of a dipolar BEC in a 3D optical lattice. de Paz ( PhD ), A. Chotia , A. Sharma, B. Laburthe-Tolra , E. Maréchal, L. Vernac , P. Pedri ( Theory ), O. Gorceix (Group leader).

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de Paz ( PhD ), A. Chotia , A. Sharma, B. Laburthe-Tolra , E. Maréchal, L. Vernac ,

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  1. Magnetization dynamics of a dipolar BEC in a 3D optical lattice • de Paz (PhD), A. Chotia, A. Sharma, • B. Laburthe-Tolra, E. Maréchal, L. Vernac, • P. Pedri (Theory), • O. Gorceix (Group leader) Have left: B. Pasquiou (PhD), G. Bismut (PhD), M. Efremov , Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaborators:Anne Crubellier (Laboratoire Aimé Cotton), J. Huckans, M. Gajda

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

  3. BEC stable despite attractive part of dipole-dipole interactions BEC collapses R Relative strength of dipole-dipole and Van-der-Waals interactions Stuttgart: Tune contact interactions using Feshbach resonances (Nature. 448, 672 (2007)) Anisotropic explosion pattern reveals dipolar coupling. Stuttgart: d-wave collapse, PRL 101, 080401 (2008) See also Er PRL, 108, 210401 (2012) See also Dy, PRL, 107, 190401 (2012) … and Dy Fermi sea PRL, 108, 215301 (2012) … and heteronuclear molecules… Cr:

  4. Hydrodynamic properties of a BEC with weak dipole-dipole interactions Saddle shape Striction Stuttgart, PRL 95, 150406 (2005) Collective excitations Villetaneuse, PRL 105, 040404 (2010) Anisotropic speed of sound Bragg spectroscopy Villetaneuse arXiv: 1205.6305 (2012) Interesting but weak effects in a scalar Cr BEC

  5. R Polarized (« scalar ») BEC Hydrodynamics Collective excitations, sound, superfluidity Multicomponent (« spinor ») BEC Magnetism Phases, spin textures… Chromium (S=3): involve dipole-dipole interactions Long-ranged Anisotropic Hydrodynamics: non-local mean-field Magnetism: Atoms are magnets

  6. Focus on : Magnetization dynamics in a 3D optical lattice : • 3 regimes : • B is of the order of the lattice band excitations. Observation of dipolar resonances and of band excitations mediated by dipole interactions. • Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution. • B is below the first excitation band : Observation of intersite dynamics, with constant magnetization. • B is very low : spontaneous depolarization.

  7. 2 1 m=+3 Rf sweep Time sequence : V0 ≈ 25 Er T 20 ms BEC In m=-3 Observation of spin changing collisions resonances and band excitations: - BEC atom number N=10^4 atoms. - Loaded adiabatically in a 3 D anisotropic optical lattice. Typical frequencies: wx = 2p 170 kHz wy = 2p 50 kHz wz = 2p 110 kHz Lattice in horizontal plane Mott distribution With our parameters Stern Gerlach analysis +B amplitude and direction is set

  8. Two dipolar relaxation channels for two atoms in m=+3, sharing a same lattice site 3 2 1 Here, z is fixed by the B field orientation. 0 -1 -2 -3

  9. 2 1 If B is higher than the lattice depth (25 Er), dipolar relaxation leads to losses. This case allows to measure the number of site with single occupancy. B is lower than the trap depth Simple measure of site with two atoms or more B is higher than the trap depth Atoms remaining in m=-3 time Mott distribution

  10. If B is lower than the lattice depth : magnetization dynamics with no loss. Dynamics very sensitive to the magnetic field orientation and value.

  11. Observation of resonances due to dipolar relaxation (fixed time T=12 ms) Anisotropic lattice sites

  12. Predication of the resonances position: For channel 2 : B along OX • Two particles in a harmonic anisotropic potentialwith frequencies wx, wy and wz. • Consider the relative orbital motion • Initial relative orbital motion |nX=0, nY=0, nZ=0> • Coupling to final relative orbital motion of the atomic pair |nx,ny,nz> Initial Final

  13. Typical frequencies: wx = 2p 170 kHz wy = 2p 50 kHz wz = 2p 110 kHz Red curve : Lowest energy resonance at wL=wY With (nY+nZ) even • Width of the resonances enlarged by the tunneling • Lower energy resonance around 50 kHz : • Tunneling very small (100 Hz) • Focus on this lowest energy resonance.

  14. Lower energy resonance. Probe of the atom number distribution. Shift due to contact interactions Black curve : two atoms / site. Contact interaction : shift and splitting of the resonance. Molecular Basis :

  15. Note: Lineshape of dipolar resonances probes number of atoms per site Fraction in m=+3 B(kHz) 3 and more atoms per sites loaded in lattice for faster loading orbit spin Probe of atom squeezing in Mott state Few-body physics ! The 3-atom state which is reached has entangled spin and orbital degrees of freedom

  16. Focus on : Magnetization dynamics in a 3D optical lattice : • 3 regimes : • B is of the order of the lattice depth. Observation of dipolar resonances and of band excitations mediated by dipole interactions. • Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution. • B is below the first excitation band : Observation of intersite dynamics, with constant magnetization. • B is very low : spontaneous depolarization.

  17. From now on : stay away from dipolar magnetization dynamics resonances, Spin dynamics at constant magnetization (<15mG) New tool : Control the initial state by a tensor light-shift 1 Quadratic light shift effect allows state preparation 0 -1 -3 -2 -1 0 1 2 3 -2 Energy A s- polarized laser Close to a JJ transition (100 mW 427.8 nm) -3 D=a mS2 In practice, a p component couples mS states

  18. Adiabatic state preparation in 3D lattice quadratic effect t -3 -2 (2 atomes / site) Initiate spin dynamics by removing quadratic effect G=

  19. On-site spin oscillations Load optical lattice quadratic effect vary time (due to contact oscillations) -1 -2 -3 G= ( 250 µs) (period  220 µs) Up to now unknown source of damping

  20. Long time-scale spin dynamics in lattice Load optical lattice quadratic effect vary time Sign for intersite dipolar interaction ? (two orders of magnitude slower than on-site dynamics)

  21. Coherent spin oscillations at lower lattice depth The very long time scale excludes on-site oscillations where spin-exchange collisions dominate

  22. Probing spin oscillations from superfluid to Mott (Probes coherence length) (probes coherent spin oscillations) Intersite coherent spin oscillation seems to need phase coherence between sites Superfluid more robust Probes magnetism from superfluid to insulator

  23. Focus on : Magnetization dynamics in a 3D optical lattice : • 3 regimes : • B is of the order of the lattice depth. Observation of dipolar resonances and of band excitations mediated by dipole interactions. • Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution. • B is below the first excitation band : Observation of intersite dynamics, with constant magnetization. • B is very low : spontaneous depolarization.

  24. At extremely low magnetic field (<1.5 mG): Spontaneous demagnetization of atoms in a 3D lattice -2 -3 PRL 106, 255303 (2011) ( in bulk BEC)

  25. Summary - Magnetism in lattice Resonant magnetization dynamics Few body vs many body physics Away from resonances: spin oscillations Spin-exchange : intrasite and inter site dynamics Not robust in Mott regime Spontaneous depolarization at low magnetic field Towards low-field phase diagram

  26. Thanks for your attention!. • de Paz, A. Chotia, A. Sharma B. Pasquiou, G. Bismut, • B. Laburthe-Tolra, E. Maréchal, L. Vernac, • P. Pedri, M. Efremov, O. Gorceix

  27. de Paz, A. Chotia, A. Sharma B. Pasquiou, G. Bismut, • B. Laburthe-Tolra, E. Maréchal, L. Vernac, • P. Pedri, M. Efremov, O. Gorceix

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