Spin-3 dynamics study in a chromium BEC Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France Olivier GORCEIX CLEO/Europe-EQEC Conference Munich – 23 May 2011

Interactions in BECs Van der Waals / contact interactions : short range and isotropic at low T Effective potential a S  (R), with a S = scattering length in channel S, a S is magnetically tunable through Feshbach resonances Dipole-dipole interactions : long range and anisotropic magnetic atoms Cr, Er, Dy; dipolar molecules; Rydberg atoms Chromium atoms carry a magnetic moment of 6µ B MDDI are 36 times bigger than in alkali BECs We produce and study 52 Cr Bose-Einstein Condensates

Dipole-dipole interaction potential Anisotropic Chromium (S=3): contact AND dipole-dipole interactions R Non local anisotropic mean-field Coupling between spin and rotation

PART ONE OF THE TALK DIPOLAR RELAXATION INHIBITION SPIN DYNAMICS IN AN OPTICAL LATTICE How a 2D lattice can stabilize an unstable BEC ?

DR causes heating then losses and the magnetic field strength controls DR Inelastic collisions - dipolar relaxation DR Zeeman energy ladder in B

Angular momentum conservation Induces rotation in the BEC ? Spontaneous creation of vortices ? Einstein-de-Haas effect Two allowed channels for ground state atoms Inelastic collisions - dipolar relaxation DR K. Gawryluk et al. PRL 106, (2011) M. Gajda, PRL 99, (2007) B. Sun and L. You, PRL 99, (2007) Plus many other… B

Dipolar relaxation in optical lattices – Experimental procedure Adiabatic loading of the ground state M = - 3 BEC in a 1D or a 2D lattice Rf induced transition to the metastable state M = +3 Hold time while DR takes place RF sweep back to M = -3 Detection Produce BEC m=-3 detect m=-3 get the DR rate Rf sweep 1Rf sweep 2 BEC m=+3, hold time Load optical lattice adiabatic Band mapping

Lattices provide tightly confined geometries (tubes or pancakes) They introduce a new energy scale and they change the initial and final states space. Dipolar relaxation in optical lattices Above B c, DR releases energy and creates a « mini-vortex » in a lattice site Optical lattices: periodic potential = ac-Stark shift in a far-detuned standing wave m=3 m=2 B

B ≈ 40 mG Spin-flipped atoms get promoted from the lowest band to the excited bands when B is over the threshold set by Spin relaxation and band excitation in optical lattices B

What do we measure in 1D ? (band mapping for B above threshold) Velocity distribution along the tubes Population in different bands due to dipolar relaxation m=3 m= Heating due to collisional de- excitation from excited band

Dipolar relaxation inhibition in 1D (below B c ) Conversely (almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices B. Pasquiou et al., Phys. Rev. Lett. 106, (2011)

Above threshold: Vortices are expected to pop up (EdH effect) but they fade away by tunneling PRA 81, (2010) Phys. Rev. Lett. 106, (2011) Log scale !! 3D trap pancakes tubes Below threshold: a (spin-excited) metastable 1D quantum gas (>100ms) ; Interest for spinor physics, spin excitations in 1D…

PART TWO OF THE TALK SPONTANEOUS DEMAGNETIZATION OF A SPINOR BEC What happens at extremely low magnetic fields ? ie when This happens for B <few 0.1 mG

S=3 Spinor physics with free magnetization - To date, spinor studies have been restricted to S=1 and S=2 -Up to now, all spinor dynamics studies were restricted to constant magnetization As required by contact interactions - eg in Rb a pair of colliding atoms stays in the M = m S1 +m S2 = 0 multiplicity 0 1 New features with Cr -First S=3 spinor - Dipole-dipole interactions free the magnetization - Possible investigation of the true many-body ground state of the system (which requires stable and very small magnetic fields)

when B ≈ 4 mG the chemical potential is much smaller than the Zeeman splittings Ferromagnetic phase of the spinor condensate Above threshold Starting point : BEC in the m= -3 single particle ground state Procedure: lower B for example to 1mG Detection TOF + Stern-Gerlach Ferromagnetic / polarized phase

when the final B ≈ 0.4 mG then the chemical potential becomes on the order of Zeeman splittings …spin-flipped atoms gain energy Spontaneous demagnetization of the spinor condensate Above threshold Below threshold Starting point : BEC in the m= -3 single particle ground state Procedure: lower the magnetic field Detection TOF + Stern-Gerlach

S=3 multi-component BEC with free magnetization Santos PRL 96, (2006) Ho PRL. 96, (2006) Zeeman states; all trapped four scattering lengths: a 6, a 4, a 2, a 0 Spontaneous demagnetization : the reason why it happens ! at B c, it costs no energy to go from m= -3 to m= -2 : loss in interaction energy compensates for the gain in Zeeman energy) Contact interactions decide which spin configuration has the lowest energy Phases set by contact interactions differ by their magnetization Magnetic field a 0 /a 6 ferromagnetic i.e. polarized in the lowest energy single particle state Phase transitions can occur between: Ferromagnetic / Polar/ Cyclic phases

Mean-field effect: when does the transition take place ? BECLattice Critical field0.26 mG1.25 mG Demag time3ms10ms Critical field for depolarization depends on the density (exp check for linearity) Magnetic field control below 0.5 mG (actively stabilized) (0.1mG stability) (no magnetic shield…)

Dynamics of the depolarization Time (ms) Remaining atoms in m=-3 Timescale for depolarization: (a few in 3D to 10 ms in the 2D lattice) Spontaneous demagnetization : how it happens ? What triggers the transistion ? Phases are set by contact interactions, while (de)magnetization dynamics is due to and set by dipole-dipole interactions « quantum magnetism » B. Pasquiou et al., Phys. Rev. Lett. (in the press) and arXiv:

Conclusion Dipolar relaxation in bulk BECs and in reduced dimensions Spontaneous demagnetization in a quantum gas -phase transition -first steps towards evidence for spinor S=3 ground state structure -spinor thermodynamics with free magnetization Outlook Towards a demonstration of Einstein-de-Haas effect - rotation in 3D lattice sites Excitation spectrum (poster tomorrow and PRL 105, (2010)) Project : quantum gas of dipolar fermionic 53 Cr

Acknowledgements Financial support: Conseil Régional d’Ile de France (Contrat Sésame) Ministère de l’Enseignement Supérieur et de la Recherche (CPER, FNS and ANR) European Union (FEDER) IFRAF CNRS Université Paris Nord

Ph.D students: Gabriel Bismut Benjamin Pasquiou www-lpl.univ-paris13.fr:8082 Permanent staff: Bruno Laburthe-Tolra, Etienne Maréchal, Paolo Pedri, Laurent Vernac and O. G. Former members Arnaud Pouderous, Radu Chicireanu, Quentin Beaufils, Thomas Zanon, Jean-ClaudeKeller, René Barbé Group members : The Cold Atom Group in Paris Nord

E.Maréchal, OG, P. Pedri, Q. Beaufils (PhD), B. Laburthe, L. Vernac, B. Pasquiou (PhD), G. Bismut (PhD), D. Ciampini (invited), M. Champion, JP Alvarez (trainees) Post-doc position available (Q4 2011) apply now!! www-lpl.univ-paris13.fr:8082