Have left: B. Pasquiou (PhD), G. Bismut (PhD), M. Efremov, Q. Beaufils (PhD), J.C. Keller, T. Zanon, R. Barbé, A. Pouderous (PhD), R. Chicireanu (PhD) Collaborator: Anne Crubellier (Laboratoire Aimé Cotton) A.de Paz (PhD), A. Chotia, A. Sharma, B. Laburthe-Tolra, E. Maréchal, L. Vernac, P. Pedri (Theory), O. Gorceix (Group leader) Dipolar chromium BECs

Dipole-dipole interactions Anisotropic Long range Chromium (S=3): 6 electrons in outer shell have their spin aligned Van-der-Waals plus dipole-dipole interactions R Hydrodynamics Magnetism

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

N = T=120 μK How to make a Chromium BEC 425 nm 427 nm 650 nm 7S37S3 5 S,D 7P37P3 7P47P4  An atom: 52 Cr  An oven  A small MOT  A dipole trap  A crossed dipole trap  All optical evaporation  A BEC Oven at 1425 °C  A Zeeman slower (1) (2) Z

1 – Hydrodynamic properties of a weakly dipolar BEC - Collective excitations - Bragg spectroscopy 2 – Magnetic properties of a dipolar BEC - Thermodynamics - Phase transition to a spinor BEC - Magnetism in a 3D lattice

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

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

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

Collective excitations of a dipolar BEC Repeat the experiment for two directions of the magnetic field (differential measurement) Parametric excitations Phys. Rev. Lett. 105, (2010) A small, but qualitative, difference (geometry is not all) 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 Note : dipolar shift very sensitive to trap geometry : a consequence of the anisotropy of dipolar interactions

Bragg spectroscopy Probe dispersion law Quasi-particles, phonons Rev. Mod. Phys. 77, 187 (2005) c is sound velocity c is also critical velocity Landau criterium for superfluidity healing length Bogoliubov spectrum    Moving lattice on BEC Lattice beams with an angle. Momentum exchange

Anisotropic speed of sound Width of resonance curve: finite size effects (inhomogeneous broadening) Speed of sound depends on the relative angle between spins and excitation

A 20% effect, much larger than the (~2%) modification of the mean-field due to DDI Anisotropic speed of sound An effect of the momentum-sensitivity of DDI (See also prediction of anisotropic superfluidity of 2D dipolar gases : Phys. Rev. Lett. 106, (2011)) c (mm/s) TheoExp Parallel Perpendicular32.8 Good agreement between theory and experiment; Finite size effects at low q

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

1 – Hydrodynamic properties of a weakly dipolar BEC - Collective excitations - Bragg spectroscopy 2 – Magnetic properties of a dipolar BEC - Thermodynamics - Phase transition to a spinor BEC - Magnetism in a 3D lattice

Dipolar interactions introduce magnetization-changing collisions Dipole-dipole interactions R without with

B=0: Rabi In a finite magnetic field: Fermi golden rule (losses) (x1000 compared to alkalis)

Important to control magnetic field Rotate the BEC ? Spontaneous creation of vortices ? Einstein-de-Haas effect Angular momentum conservation Dipolar relaxation, rotation, and magnetic field Ueda, PRL 96, (2006) Santos PRL 96, (2006) Gajda, PRL 99, (2007) B. Sun and L. You, PRL 99, (2007)

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

Interpartice distance Energy From the molecular physics point of view: a delocalized probe PRA 81, (2010) 2-body physics B = 3 G B =.3 mG many-body physics

S=3 Spinor physics with free magnetization Alkalis : - S=1 and S=2 only - Constant magnetization (exchange interactions)  Linear Zeeman effect irrelevant New features with Cr: -S=3 spinor (7 Zeeman states, four scattering lengths, a 6, a 4, a 2, a 0 ) -No hyperfine structure - Free magnetization Magnetic field matters ! Technical challenges : Good control of magnetic field needed (down to 100  G) Active feedback with fluxgate sensors Low atom number – atoms in 7 Zeeman states

1 Spinor physics of a Bose gas with free magnetization -Thermodynamics: how magnetization depends on temperature -Spontaneous depolarization of the BEC due to spin-dependent interactions 2 Magnetism in opical lattices -Depolarized ground state at low magnetic field -Spin and magnetization dynamics S=3 Spinor physics with free magnetization Alkalis : - S=1 and S=2 only - Constant magnetization (exchange interactions)  Linear Zeeman effect irrelevant New features with Cr: -S=3 spinor (7 Zeeman states, four scattering lengths, a 6, a 4, a 2, a 0 ) -No hyperfine structure - Free magnetization Magnetic field matters !

Spin temperature equilibriates with mechanical degrees of freedom We measure spin-temperature by fitting the m S population (separated by Stern-Gerlach technique) At low magnetic field: spin thermally activated

Spontaneous magnetization due to BEC BEC only in m S =-3 (lowest energy state) Cloud spontaneously polarizes ! Thermal population in Zeeman excited states Non-interacting multicomponent Bose thermodynamics: a BEC is ferromagnetic Phys. Rev. Lett. 108, (2012) T>Tc T<Tc a bi-modal spin distribution

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

Santos PRL 96, (2006) Large magnetic field : ferromagneticLow magnetic field : polar/cyclic Ho PRL. 96, (2006) Cr spinor properties at low field Phys. Rev. Lett. 106, (2011)

Density dependent threshold BECLattice Critical field0.26 mG1.25 mG 1/e fitted0.3 mG1.45 mG Load into deep 2D optical lattices to boost density. Field for depolarization depends on density Phys. Rev. Lett. 106, (2011) Note: Possible new physics in 1D: Polar phase is a singlet-paired phase Shlyapnikov-Tsvelik NJP, 13, (2011)

Dynamics analysis Meanfield picture : Spin(or) precession Ueda, PRL 96, (2006) Natural timescale for depolarization: PRL 106, (2011) Produce BEC m=-3 Rapidly lower magnetic field

Open questions about equilibrium state Santos and Pfau PRL 96, (2006) Diener and Ho PRL. 96, (2006) Phases set by contact interactions, magnetization dynamics set by dipole-dipole interactions - 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 ? !! Depolarized BEC likely in metastable state !! Demler et al., PRL 97, (2006) Polar Cyclic Magnetic field

1 Spinor physics of a Bose gas with free magnetization -Thermodynamics: Spontaneous magnetization of the gas due to ferromagnetic nature of BEC -Spontaneous depolarization of the BEC due to spin-dependent interactions 2 Magnetism in 3D opical lattices -Depolarized ground state at low magnetic field -Spin and magnetization dynamics

Loading an optical lattice 2D 3D Optical lattice = periodic (sinusoidal) potential due to AC Stark Shift of a standing wave (from I. Bloch) (in our case (1, 1, 2.6)* /2 periodicity) We load in the Mott regime U=10kHz, J=100 Hz U J In practice, 2 per site in the center (Mott plateau)

Spontaneous demagnetization of atoms in a 3D lattice 3D lattice Critical field 4kHz Threshold seen 5kHz -3 -2

Control the ground state by a light-induced effective Quadratic Zeeman effect A  polarized laser Close to a J  J transition (100 mW nm) In practice, a  component couples m S states Typical groundstate at 60 kHz Energy  m S 2 Note : The effective Zeeman effect is crucial for good state preparation

Large spin-dependent (contact) interactions in the BEC have a very large effect on the final state Adiabatic (reversible) change in magnetic state (unrelated to dipolar interactions) t quadratic effect BEC (no lattice) 3D lattice (1 atom per site) Note: the spin state reached without a 3D lattice is completely different !

Magnetization dynamics in lattice vary time Load optical lattice quadratic effect Role of intersite dipolar relaxation ?

Magnetization dynamics resonance for two atoms per site Dipolar resonance when released energy matches band excitation Towards coherent excitation of pairs into higher lattice orbitals ? (Rabi oscillations) Mott state locally coupled to excited band Resonance sensitive to atom number

Measuring population in higher bands (1D) (band mapping procedure): Population in different bands due to dipolar relaxation m=3 m= PRL 106, (2011)

Strong anisotropy of dipolar resonances Anisotropic lattice sites See also PRL 106, (2011) At resonance May produce vortices in each lattice site (EdH effect) (problem of tunneling)

Conclusions (I) Dipolar interactions modify collective excitations Anisotropic speed of sound

Magnetization changing dipolar collisions introduce the spinor physics with free magnetization 0D Magnetism in optical lattices magnetization dynamics in optical lattices can be made resonant could be made coherent ? towards Einstein-de-Haas (rotation in lattice sites) New spinor phases at extremely low magnetic fields Conclusions Tensor light-shift allow to reach new quantum phases

A. de Paz, A. Chotia, A. Sharma, B. Pasquiou (PhD), G. Bismut (PhD), B. Laburthe, E. Maréchal, L. Vernac, P. Pedri, M. Efremov, O. Gorceix