Laboratoire de Physique des Lasers Universit Paris Nord

Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France Elastic and inelastic dipolar effects in chromium BECs B. Laburthe-Tolra

G. Bismut (Ph. D), B. Pasquiou (Ph. D) B. Laburthe, E. Maréchal, L. Vernac, P. Pedri (Theory), O. Gorceix (Group leader) Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaborator: Anne Crubellier (Laboratoire Aimé Cotton) Invited professors: W. de Souza Melo (Brasil), D. Ciampini (Italy), T. Porto (USA) Internships (since 2008): M. Trebitsch, M. Champion, J. P. Alvarez, M. Pigeard, E. Andrieux, M. Bussonier, F. Hartmann, R. Jeanneret, B. Bourget

Types of interactions in BECs Van-der Waals, short range and isotropic. Pure s-wave collisions at low temperature. Effective potential a. S d(R), with a. S scattering lenght, tunable thanks to Feshbach resonances Multicomponent BECs: More than one state, more than one scattering length. Exchange interactions decide which spin configuration reaches the lowest energy Quantum phase transitions Ferromagnetic / Polar/ Cyclic phases Dipole-dipole interactions (magnetic atoms, Cr, Er, Dy, dipolar molecules, Rydberg atoms)

Alkalis: Van-der-Waals interactions (effective d potential) Chromium (S=3): Van-der-Waals plus dipole-dipole Dipole-dipole interactions Long range Anisotropic « Elastic » : « Inelastic » : Non local anisotropic mean-field Coupling between spin and rotation R

Elastic

Relative strength of dipole-dipole and Van-der-Waals interactions Cr: BEC collapses Stuttgart: Tune contact interactions using Feshbach resonances (Pfau, Nature. 448, 672 (2007)) R Stuttgart: d-wave collapse, PRL 101, 080401 (2008) Anisotropic explosion pattern reveals dipolar coupling. (Breakdown of self similarity) BEC stable despite attractive part of dipole-dipole interactions Parabolic ansatz still good. Striction of BEC. (Eberlein, PRL 92, 250401 (2004))

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

Modification of BEC expansion due to dipole-dipole interactions TF profile Striction of BEC (non local effect) Eberlein, PRL 92, 250401 (2004) Pfau, PRL 95, 150406 (2005) (similar results in our group)

Frequency of collective excitations (Castin-Dum) Consider small oscillations, then with Interpretation Sound velocity In the Thomas-Fermi regime, collective excitations frequency independent of number of atoms and interaction strength: Pure geometrical factor (solely depends on trapping frequencies) TF radius

Collective excitations of a dipolar BEC Due to the anisotropy of dipole-dipole interactions, the dipolar mean-field depends on the relative orientation of the magnetic field and the axis of the trap Repeat the experiment for two directions of the magnetic field (differential measurement) Parametric excitations Phys. Rev. Lett. 105, 040404 (2010) A small, but qualitative, difference (geometry is not all)

A consequence of anisotropy : trap geometry dependence of the frequency shift Shift of the quadrupole mode frequency (%) Shift of the aspect ratio (%) Sign of dipolar meanfield depends on trap geometry (oblate / elongated) • Related to the trap anisotropy Phys. Rev. Lett. 105, 040404 (2010) Good agreement with Thomas-Fermi predictions Eberlein, PRL 92, 250401 (2004)

Non local anisotropic meanfield -Static and dynamic properties of BECs Small effects in Cr… Need Feshbach resonances or larger dipoles. With… ? Cr ? Er ? Dy ? Dipolar molecules ? Then…, Tc, solitons, vortices, Mott physics, new phases (checkboard), 1 D or 2 D physics, breakdown of integrability in 1 D… Interest for quantum computation ?

Inelastic

Spin degree of freedom coupled to orbital degree of freedom - Spinor physics and magnetization dynamics Dipole-dipole interactions Anisotropic R

Introduction to dipolar relaxation Angular momentum conservation 3 0 -3 -2 1 2 -1 Rotate the BEC ? Spontaneous creation of vortices ? 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) Important to control magnetic field

Energy scales Molecular binding enery : 10 MHz Trap depth : 1 MHz Band excitation in lattice : 100 k. Hz Chemical potential : 4 k. Hz Vortex : 100 Hz Magnetic field = 3 G 300 m. G 30 m. G 1 m. G . 01 m. G

A journey in dipolar physics through 7 decades of magnetic field intensities (T. Pfau’s Feshbach resonance – pure dipolar fluid) Suppression of dipolar relaxation due to inter-atomic repulsion Spin relaxation and band excitation in optical lattices Magnetization dynamics of spinor condensates

4 Gauss 3 0 -3 -2 1 2 -1 …spin-flipped atoms gain so much energy they leave the trap

Dipolar relaxation in a Cr BEC R Pro du ce BE C m =-3 eep w s f 1 2 ep e w s Rf BEC m=+3, vary time detect BEC m=-3 Fermi golden rule l au Pf p Ap . ys h. P 7, , 7 76 ) 03 0 2 5 ( B , on i t ma i ox pr p a rn Bo PRA 81, 042716 (2010) See also Shlyapnikov PRL 73, 3247 (1994) Never observed up to now

Interpretation Energy Interpartice distance In Rc = Condon radius Out Zero coupling Determination of scattering lengths S=6 and S=4

New estimates of Cr scattering lengths Collaboration Anne Crubellier PRA 81, 042716 (2010) a 6 = 103 ± 4 a 0. a 6 = 102. 5 ± 0. 4 a 0 Feshbach resonance in d-wave PRA 79, 032706 (2009)

Dipolar relaxation: a localized phenomenon L. H. Y. Phys. Rev. 106, 1135 (1957) A probe of correlations : here, a mere two-body effect, yet unacounted for in a mean-field « product-ansatz » BEC model

40 m. Gauss 3 2 1 …spin-flipped atoms go from one band to another

Dipolar relaxation in optical lattices Optical lattices: periodic potential made by AC-stark shift of a standing wave • Lattices provide very tightly confined geometries Energy to nucleate a « mini-vortex » in a lattice site (~120 k. Hz) A gain of two orders of magnitude on the magnetic field requirements to observe rotation due to spin-flip (Einstein-de Haas effect) ! m=3 m=2

Reduction of dipolar relaxation in optical lattices Load the BEC in a 1 D or 2 D Lattice c pti o d oa la al ce tti R eep w s f 1 ep we 2 s Rf L Pro du ce BEC m=+3, vary time BE C m =-3 detect m=-3 One expects a reduction of dipolar relaxation, as a result of the reduction of the density of states in the lattice

PRA 81, 042716 (2010) Phys. Rev. Lett. 106, 015301 (2011)

What we measure in 1 D (band mapping procedure): 3 0 -3 -2 1 2 Non equilibrium velocity ditribution along tubes Integrability -1 m=3 m=2 Population in different bands due to dipolar relaxation Heating due to collisional deexcitation from excited band

What we measure in 1 D: (almost) complete suppression of dipolar relaxation in 1 D at low field in 2 D lattices B. Pasquiou et al. , Phys. Rev. Lett. 106, 015301 (2011)

Theoretical model: Fermi-Golden rule, taking into account: -The width of the excited band (tunneling) -All excited states along the tubes m=3 m=2 Calculated : 2. 10 -19 m 3 s-1 Measured : 5. 10 -20 m 3 s-1 Qualitatively ok. Correlations (and more) ignored

(almost) complete suppression of dipolar relaxation in 1 D at low field in 2 D lattices: a consequence of angular momentum conservation Below threshold: Above threshold : a (spin-excited) metastable 1 D quantum gas ; should produce vortices in each lattice site (Ed. H effect) (problem of tunneling) Interest for spinor physics, spin excitations in 1 D… Towards coherent excitation of pairs into higher lattice orbitals ?

. 4 m. Gauss 3 2 1 0 -1 -2 -3 3 -3 -2 -1 0 1 2 Similar to M. Fattori et al. , Nature Phys. 2, 765 (2006) at large fields and in thermal regime …spin-flipped atoms loses energy

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, no dipole-dipole interactions) - They investigate the ground state for a given magnetization -> Linear Zeeman effect irrelavant New features with Cr -First S=3 spinor - Dipole-dipole interactions free total magnetization - Can investigate the true ground state of the system (need very small magnetic fields) 1 0 -1 3 2 1 0 -1 -2 -3

S=3 Spinor physics with free magnetization 3 -3 -2 -1 0 1 2 ferromagnetic i. e. polarized in lowest energy single particle state Magnetic field 3 2 1 0 -1 -2 -3 7 Zeeman states; all trapped four scattering lengths, a 6, a 4, a 2, a 0 Santos PRL 96, 190404 (2006) Ho PRL. 96, 190405 (2006) a 0/a 6 (at Bc, it costs no energy to go from m=-3 to m=-2 : difference in interaction energy compensates for the loss in Zeeman energy) Phases set by contact interactions (a 6, a 4, a 2, a 0) – differ by total magnetization

Population At VERY low magnetic fields, spontaneous depolarization of 3 D and 1 D quantum gases Pro du ce BE C m vary time =-3 Time ( ms) m. S Rapidly lower magnetic field Magnetic field control below . 5 m. G (dynamic lock) (. 1 m. G stability) (no magnetic shield…) Stern Gerlach experiments

Mean-field effect Field for depolarization depends on density BEC Lattice Critical field 0. 26 m. G 1. 25 m. G 1/e fitted 0. 4 m. G 1. 45 m. G

Remaining atoms in m=-3 Dynamics analysis Magnetic field due to dipoles Ueda, PRL 96, 080405 (2006) Kudo Phys. Rev. A 82, 053614 (2010) Time (ms) Meanfield picture : Spin(or) precession (Majorana flips) When mean field beats magnetic field Natural timescale for depolarization: (a few ms)

A quench through a zero temperature (quantum) phase transition Santos and Pfau PRL 96, 190404 (2006) Diener and Ho PRL. 96, 190405 (2006) 33 2 2 1 1 0 -1 -2 -3 3 -3 -2 -1 0 1 2 - Operate near B=0. Investigate absolute many-body ground-state - We do not (cannot ? ) reach those new ground state phases !! - Thermal excitations probably dominate Phases set by contact interactions, magnetization dynamics set by dipole-dipole interactions « quantum magnetism »

Population Thermal effect: (Partial) Loss of BEC when demagnetization Spin degree of freedom is released ; lower Tc m. S ( Time ms) As gas depolarises, temperature is constant, but condensate fraction goes down !

Thermal effect: (Partial) Loss of BEC when demagnetization Spin degree of freedom is released ; lower Tc B=0 B=20 m. G PRA, 59, 1528 (1999) J. Phys. Soc. Jpn, 69, 12, 3864 (2000) lower Tc: a signature of decoherence Dipolar interaction open the way to spinor thermodynamics with free magnetization

Conclusion Collective excitations – effect of non-local mean-field Dipolar relaxation in BEC – new measurement of Cr scattering lengths correlations Dipolar relaxation in reduced dimensions - towards Einstein-de-Haas rotation in lattice sites Spontaneous demagnetization in a quantum gas - New phase transition – first steps towards spinor ground state (Spinor thermodynamics with free magnetization – application to thermometry) (d-wave Feshbach resonance) (rf-assisted relaxation) (MOT of fermionic 53 Cr) (BECs in strong rf fields) (rf association)