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A. de Paz (PhD), A. Sharma, E. Maréchal, L. Vernac, O. Gorceix, B. Laburthe P. Pedri (Theory)

Dipolar chromium BECs , and magnetism. A. de Paz (PhD), A. Sharma, E. Maréchal, L. Vernac, O. Gorceix, B. Laburthe P. Pedri (Theory). Have left: B. Pasquiou (PhD), G. Bismut (PhD ), A. Chotia, M. Efremov , Q. B eaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu

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A. de Paz (PhD), A. Sharma, E. Maréchal, L. Vernac, O. Gorceix, B. Laburthe P. Pedri (Theory)

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  1. DipolarchromiumBECs, and magnetism A. de Paz (PhD), A. Sharma, E. Maréchal, L. Vernac, O. Gorceix, B. Laburthe P. Pedri (Theory) Have left: B. Pasquiou (PhD), G. Bismut (PhD), A. Chotia, 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. Van-der-Waals (contact) interactions R Chromium : an artificially large spin (S=3): (magnetic) dipole-dipole interactions Long range Anisotropic Short range Isotropic

  3. R Hydrodynamic properties of dipolar BECs Large dipolar interactions: spherical BEC collapses 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 (BEC, Innsbruck), or Dy (BEC, Fermi sea, Stanford) … and heteronuclear molecules coming up … For Cr, BEC stable despite attractive part of dipole-dipole interactions • Small (but interesting) effects observed – at the % level : • Striction – Stuttgart, PRL 95, 150406 (2005) • - Collective excitations - Villetaneuse, PRL 105, 040404 (2010) • - Anisotropic speed of sound, Villetaneuse, PRL 109, 155302 (2012)

  4. This talk : The impact of dipole-dipole interactions on multicomponent (« spinor ») BEC Magnetism Anistropy : Interactions couple spin and orbital degrees of freedom Long-range interaction : Intersite coupling in lattices Study magnetism with large spins (S=3) • 0 Introduction to spinor physics • 1 Spinor physics of a Bose gas with free magnetization • 2 (Quantum) magnetism in opical lattices

  5. Introduction to spinor physics Chapman, Sengstock… Exchange energy Coherent spin oscillation Klempt Stamper-Kurn Domains, spin textures, spin waves, topological states Stamper-Kurn, Chapman, Sengstock, Shin… Quantum phase transitions Stamper-Kurn, Lett, Gerbier

  6. High Spin Fermions coming up… Spin oscillations (F=9/2 K atoms, Sengstock) Pomeranchuk-like cooling (Yb atoms) New SU(N) symmetry (alkaline-earth atoms) (see talk F. Schreck) Rey, Gorshkov, Gurarie…

  7. Main new features with Cr Main ingredients for spinor physics S=3 S=1,2,… 7 Zeeman states 4 scattering lengths New structures 1 Spin-dependent contact interactions Spin exchange 0 -1 Strong spin-dependent contact interactions Purely linear Zeeman effect And Dipole-dipole interactions Quadratic Zeeman effect

  8. R Dipolar interactions introduce magnetization-changing collisions without with 1 1 0 Dipole-dipole interactions 0 -1 -1

  9. Dipolar relaxation, rotation, and magnetic field 3 2 1 0 -1 Angular momentum conservation -2 -3 1D Rotate the BEC ? Spontaneous creation of vortices ? Einstein-de-Haas effect Important to control magnetic field Ueda, PRL 96, 080405 (2006) Santos PRL 96, 190404 (2006) Gajda, PRL 99, 130401 (2007) B. Sun and L. You, PRL 99, 150402 (2007) B(mG)

  10. S=3 Spinor physics with free magnetization • 1 Spinorphysics of a Bose gaswith free magnetization (bulk) • 2 (Quantum) magnetism in opticallattices Technical challenges : Good control of magnetic field needed (down to 100 mG) Active feedback with fluxgate sensors Low atom number – 10 000 atoms in 7 Zeeman states

  11. 3 2 1 0 -1 -2 -3 Spin temperature equilibriates with mechanical degrees of freedom At low magnetic field: spin thermally activated -3 -2 -1 0 1 2 3 We measure spin-temperature by fitting the mS population (separated by Stern-Gerlach technique) Related to Demagnetization Cooling expts, Pfau, Nature Physics 2, 765 (2006)

  12. Spontaneous magnetization due to BEC T>Tc T<Tc -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 a bi-modal spin distribution Thermal population in Zeeman excited states BEC only in mS=-3 (lowest energy state) Cloud spontaneously polarizes ! A non-interacting BEC is ferromagnetic Newmagnetism, differs from solid-state PRL 108, 045307 (2012)

  13. Below a critical magnetic field: the BEC ceases to be ferromagnetic ! B=100 µG B=900 µG • Magnetization remains small even when the condensate fraction approaches 1 • !! Observation of a depolarized condensate !! Necessarily an interaction effect PRL 108, 045307 (2012)

  14. -1 Cr spinor properties at low field 3 3 2 2 1 1 -2 0 0 -1 -1 -2 -2 -3 -3 -3 Large magnetic field : ferromagnetic Low magnetic field : polar/cyclic Santos PRL 96, 190404 (2006) Ho PRL. 96, 190405 (2006) -2 -3 Good agreement between field below which we see demagnetization and Bc PRL 106, 255303 (2011)

  15. Open questions about equilibrium state Phases set by contact interactions, magnetizationdynamics set by dipole-dipole interactions Santos and Pfau PRL 96, 190404 (2006) Diener and Ho PRL. 96, 190405 (2006) Magnetic field Demler et al., PRL 97, 180412 (2006) Cyclic Polar !! Depolarized BEC likely in metastable state !! • - Operate near B=0. Investigate absolute many-body ground-state • We do not (cannot ?) reach those new ground state phases • Quench should induce vortices… • Role of thermal excitations ?

  16. 0 Introduction to spinorphysics • 1 Spinorphysics of a Bose gaswith free magnetization • 2 (Quantum) magnetism in opicallattices

  17. Study quantum magnetism with dipolar gases ? Hubard model at half filling, Heisenberg model of magnetism (effective spin model) Dipole-dipole interactions between real spins Magnetization changing collisions

  18. Magnetization dynamics resonance for a Mott state with two atoms per site (~15 mG) 3 2 1 Rf sweep 1 Rf sweep 2 0 -1 Load optical lattice -2 -3 m=+3, wait time Produce BEC m=-3 detect m=-3 Dipolar resonance when released energy matches band excitation Mott state locally coupled to excited band arXiv: 1212.5469 (2012)

  19. From now on : stay away from dipolar magnetization dynamics resonances, Spin dynamics at constant magnetization (<15mG) Magnetization changing collisions Can be suppressed in optical lattices Differs from Heisenberg magnetism: Related research with polar molecules: A. Micheli et al., Nature Phys. 2, 341 (2006). A.V. Gorshkov et al., PRL, 107, 115301 (2011), See also D. Peter et al., PRL. 109, 025303 (2012)

  20. Control the initial state by a tensor light-shift 0 -1 -3 -2 -1 0 1 2 3 -2 A s- polarized laser Close to a JJ transition (100 mW 427.8 nm) -3 D=a mS2 Quadratic effect allows state preparation

  21. Adiabatic state preparation in 3D lattice Load optical lattice quadratic effect quadratic effect vary time t -3 -2 Initiate spin dynamics by removing quadratic effect

  22. Short times : fast oscillations due to spin-dependent contact interactions -1 -2 -3 G= ( 250 µs) Up to now unknown source of damping (sudden melting of Mott insulator ?) (period  220 µs) PRELIMINARY

  23. Long time-scale spin dynamics in lattice : intersite dipolar exchange Intersite dipolar interaction (much slower than on-site dynamics) Magnetization is constant Intersite dynamics disappears in presence of a gradient

  24. Effect of doublons ? Spin dynamics for (at most) one atom per site Oscillations arise from interactions between doubled-occupied sites Slow spin dynamics for one particle per site: Intersite dipole-dipole coupling

  25. Theoretical understanding : dipolar spin exchange (Very) long time-scale dynamics due to intersite dipolar exchange between singlons MS=(-3, -2, -1, 0) 1/e timescale = 25 ms 10 20 30 40 50 Spin oscillations due to intersite dipolar exchange between doublons Time (ms) Calculation Paolo Pedri Exact diagonalisation Plaquette 3x2 336 states Timescale = 4 ms Faster coupling because larger effecive spin

  26. Conclusions Bulk Magnetism: spinor physics with free magnetization New spinor phases at extremely low magnetic fields Lattice Magnetism: Magnetization dynamics is resonant Intersite dipolar spin-exchange

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

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