A. de Paz (PhD), A. Chotia, A. Sharma, B. Laburthe-Tolra, E. - PowerPoint PPT Presentation

Dipolar chromium BECs, and magnetism A. 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

Effect of interactions on condensates Attractive interactions Repulsive interactions Stable condensate Implosion of BEC for large Phonon spectrum atom number Small solitons Superfluidity Rice… ENS, JILA… Spin dependent interactions Magnetism Berkeley…

Chromium (S=3): Van-der-Waals plus dipole-dipole interactions   d 6 B Dipole-dipole interactions     1    2   2 2 0 V S g 1 3cos ( ) Long range  dd J B 3 4 R Anisotropic  R Partially attractive , Interactions couple spin and partially repulsive orbital degrees of freedom

Different dipolar systems « Magnetic atom » Dipole-dipole interactions   d B 1   2 137  2 Molecule with (field induced-) electric dipole moment  d ea 0   4 8 n 10  2 Rydberg atoms d n ea 0

Relative strength of dipole-dipole and Van-der-Waals interactions   2 m V    0 m dd   1  BEC collapses dd 2 12 a V dd VdW 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) R 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…   1 BEC stable despite attractive part of dipole-dipole interactions dd   0.16 Cr: dd

Polarized (« scalar ») BEC Multicomponent (« spinor ») BEC Hydrodynamics Magnetism Phases, spin textures… Collective excitations, sound, superfluidity Chromium (S=3): involve dipole-dipole interactions     Long-ranged 1    2   2 2 0 V S g 1 3cos ( )   dd J B 3 4 R Anisotropic R Hydrodynamics: Magnetism: non-local mean-field Atoms are magnets

52 Cr BEC experiment Vacuum 4 10 -11 mbar MOT Oven at 1500 °C 100 µK Zeeman slower 10 6 atoms Oven at 1500 °C Evaporative cooling Many lasers ! 100 nK 10 4 atoms Magnetic field control < 100 µG Small condensates (10 4 atoms)

1 – Hydrodynamic properties of a weakly dipolar BEC - Collective excitations - Bragg spectroscopy 2 – Magnetic properties of a dipolar BEC - Spinor physics of a Bose gas with free magnetization - (Quantum) magnetism in opical lattices

Interaction-driven expansion of a BEC A lie: Imaging BEC after time-of-fligth is a measure of in-situ momentum distribution Self-similar, (interaction-driven) Castin-Dum expansion Phys. Rev. Lett. 77 , 5315 (1996) TF radii after expansion related to interactions Cs BEC with tunable interactions (from Innsbruck))

Modification of BEC expansion due to dipole-dipole interactions     3 ( ) r V ( r r n r d r ') ( ') ' TF profile dd dd Striction of BEC (non local effect) Eberlein, PRL 92 , 250401 (2004) (similar results in our group) Pfau,PRL 95 , 150406 (2005)

Frequency of collective excitations (Castin-Dum) Consider small oscillations, then         2 2 2 3  1 1 1   2 d          2 2 2 H  3  H . with 2 2 2 2 dt         2 2 2 3   3 3 3 In the Thomas-Fermi regime, collective excitations frequency independent of number of atoms and interaction strength: Pure geometrical factor (solely depends on trapping frequencies)

Observation of one collective mode (Ox) Radius (µm) 22 Rayon (Ox) 20 18 16 (Oy) Radius (µm) 14 20 Rayon (Oy) 15 0 2 4 6 8 temps (ms) Time (ms) (parametric excitation)

Collective excitations of a dipolar BEC Parametric excitations Due to the anisotropy of dipole-dipole interactions, the Repeat the experiment for two dipolar mean-field depends on the relative orientation of the directions of the magnetic field magnetic field and the axis of the trap (differential measurement) 1.2 Aspect ratio 1.0 0.8 PRL 105 , 040404 (2010) 0.6 5 10 15 20 ( ) t ms     A small, but qualitative, difference (geometry is not all)  dd Note : dipolar shift very sensitive to trap geometry : a consequence of the anisotropy of dipolar interactions

Bragg spectroscopy Probe dispersion law  c is sound velocity E k ( ) ck c is also critical velocity k   1 Quasi-particles, phonons Landau criterium for superfluidity Moving lattice on BEC  d   healing length Rev. Mod. Phys. 77 , 187 (2005) Lattice beams with an angle. Momentum exchange Bogoliubov spectrum      k 2 k sin( / 2) E E ( 2 n g ) L k k k 0 c

Anisotropic speed of sound Fraction of excited atoms 0.15 0.10 0.05 0.00 0 1000 2000 3000 Frequency difference (Hz) Width of resonance curve: finite size effects (inhomogeneous broadening) Speed of sound depends on the relative angle between spins and excitation

Anisotropic speed of sound A 20% effect, much larger than the (~2%) modification of the mean-field due to DDI An effect of the momentum-sensitivity of DDI  2 4 d          2 V k ( ) (3cos 1) 2 E E ( 2 n g ( g (3cos 1)) k 3 k k k 0 c d k  Good agreement between B k theory and experiment; k Finite size effects at low q c (mm/s) Theo Exp Parallel 3.6 3.4 Perpendicular 3 2.8 (See also prediction of anisotropic superfluidity of 2D dipolar gases : Phys. Rev. Lett. 106 , 065301 (2011))

Conclusions (1) Hydrodynamic properties with weak dipole-dipole interactions Striction Stuttgart, PRL 95 , 150406 (2005) Collective excitations 1.2 Aspect ratio 1.0 Villetaneuse, PRL 105 , 040404 (2010) 0.8 0.6 5 10 15 20 Fraction of excited atoms 0.15 Anisotropic speed of sound Bragg spectroscopy 0.10 Villetaneuse Accepted in PRL (2012) 0.05 0.00 0 1000 2000 3000 Frequency difference (Hz) Interesting but weak effects in a scalar Cr BEC (far from Feshbach resonance)

Much more to come with… Cr ? Er ? Dy ? Molecules ? Induced dipoles (Rydberg atoms) ? Examples: - rotonic excitation spectrum, associated instabilities - solitons - New vortex lattice structures - New quantum phases in optical lattices (supersolidity, checkerboard) - …

1 – Hydrodynamic properties of a weakly dipolar BEC - Collective excitations - Bragg spectroscopy 2 – Magnetic properties of a dipolar BEC - Spinor physics of a Bose gas with free magnetization - (Quantum) magnetism in opical lattices

Introduction to spinor physics Chapman, Exchange energy Sengstock… Coherent spin oscillation Quantum effects!   1 Klempt     0,0 1, 1 1,1 Stamper- 2 Kurn Domains, spin textures, spin waves, topological states Stamper-Kurn, Chapman, Sengstock, Shin… Stamper-Kurn, Quantum phase transitions Lett

Main ingredients for spinor physics Main new features with Cr S=3 S=1,2,… 7 Zeeman states 4 scattering lengths Spin-dependent contact New structures interactions Spin exchange Strong spin-dependent    m 0 , m 0 contact interactions S S 2 1      S 2 , m 0 S 0 , m 0 tot tot 3 3 Purely linear Zeeman effect 1 Engineer artificial quadratic effect     2 4 ( a a    0 using tensor light shift 2 0    m -1 And Quadratic Zeeman effect Dipole-dipole interactions

Dipolar interactions introduce magnetization-changing collisions V without dd 1 0 Dipole-dipole interactions -1     1    2   2 2 0 V S g 1 3cos ( )  dd J B 3 4 R 3 V with dd 2 1  0 -1 R -2 -3

B=0: Rabi -3 -2 -1 0 1 2 3   V dd In a finite magnetic field: Fermi golden rule (losses) 3     2     2 V g B 1 dd f B 0 -1 (x1000 compared to alkalis) -2 -3

Dipolar relaxation and rotation Angular momentum conservation     m m 0 S l   1   3 , 3 3 , 2 2 , 3 2    S     E m g B 2 B 3 2 1 0 -1 -2 -3 Rotate the BEC ? Important to control Spontaneous creation of vortices ? magnetic field Einstein-de-Haas effect Ueda, PRL 96 , 080405 (2006) Santos PRL 96 , 190404 (2006) Gajda, PRL 99 , 130401 (2007) B. Sun and L. You, PRL 99 , 150402 (2007)

Magnetic field B=1G  Particle leaves the trap 3 B=10 mG  Energy gain matches band 2 excitation in a lattice 1 0 -1 -2 B=.1 mG  Energy gain equals to -3 chemical potential in BEC