Dipolar chromium BECs, and magnetism

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

Chromium (S=3): Van-der-Waals plus dipole-dipole interactions d 6 B Dipole-dipole interactions V S g 4 13cos ( ) 0 dd J B 1 R 3 Long range Anisotropic R Partially attractive, partially repulsive Interactions couple spin and orbital degrees of freedom

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

Relative strength of dipole-dipole and Van-der-Waals interactions 1 BEC collapses dd dd 0 mm V 1 a V dd VdW Stuttgart: Tune contact interactions using Feshbach resonances (Nature. 448, 67 (007)) R Anisotropic explosion pattern reveals dipolar coupling. Stuttgart: d-wave collapse, PRL 101, 080401 (008) See also Er PRL, 108, 10401 (01) See also Dy, PRL, 107, 190401 (01) and Dy Fermi sea PRL, 108, 15301 (01) and heteronuclear molecules 1 BEC stable despite attractive part of dipole-dipole interactions dd Cr: dd 0.16

Polarized («scalar») BEC Hydrodynamics Collective excitations, sound, superfluidity Multicomponent («spinor») BEC Magnetism Phases, spin textures Chromium (S=3): involve dipole-dipole interactions V S g 4 13cos ( ) 0 dd J B 1 R 3 Long-ranged Anisotropic R Hydrodynamics: non-local mean-field Magnetism: Atoms are magnets

5 Cr BEC experiment Vacuum 4 10-11 mbar Oven at 1500 C Zeeman slower MOT 100 µk 10 6 atoms Evaporative cooling 100 nk 10 4 atoms Oven at 1500 C Many lasers! Magnetic field control < 100 µg Small condensates (10 4 atoms)

1 Hydrodynamic properties of a weakly dipolar BEC - Collective excitations - Bragg spectroscopy 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) 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 3 dd ( r) Vdd ( r r ') n( r ') d r ' Striction of BEC (non local effect) Eberlein, PRL 9, 50401 (004) Pfau,PRL 95, 150406 (005) (similar results in our group)

Frequency of collective excitations (Castin-Dum) Consider small oscillations, then d dt H. with H 3 1 1 1 3 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)

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

Aspect ratio 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 Parametric excitations Repeat the experiment for two directions of the magnetic field (differential measurement) 1. 1.0 0.8 0.6 PRL 105, 040404 (010) 5 t( ms) A small, but qualitative, difference (geometry is not all) 10 15 dd 0 Note : dipolar shift very sensitive to trap geometry : a consequence of the anisotropy of dipolar interactions

Bragg spectroscopy Probe dispersion law Quasi-particles, phonons E( k) ck k 1 c is sound velocity c is also critical velocity Landau criterium for superfluidity Moving lattice on BEC d healing length Bogoliubov spectrum k k k 0 c Rev. Mod. Phys. 77, 187 (005) E ( E n g ) Lattice beams with an angle. Momentum exchange k kl sin( / )

Fraction of excited atoms Anisotropic speed of sound 0.15 0.10 0.05 0.00 0 1000 000 Frequency difference (Hz) 3000 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 0% effect, much larger than the (~%) modification of the mean-field due to DDI An effect of the momentum-sensitivity of DDI 4 d 3 ( ) (3cos k 1) Vk k Ek ( Ek n0 ( gc gd (3cos k 1)) B k k c (mm/s) Theo Exp Parallel 3.6 3.4 Good agreement between theory and experiment; Finite size effects at low q Perpendicular 3.8 (See also prediction of anisotropic superfluidity of D dipolar gases : Phys. Rev. Lett. 106, 065301 (011))

Fraction of excited atoms Aspect ratio Conclusions (1) Hydrodynamic properties with weak dipole-dipole interactions Striction Stuttgart, PRL 95, 150406 (005) Collective excitations Villetaneuse, PRL 105, 040404 (010) 1. 1.0 0.8 0.6 5 10 15 0 Anisotropic speed of sound 0.15 0.10 0.05 Bragg spectroscopy Villetaneuse Accepted in PRL (01) 0.00 0 1000 000 Frequency difference (Hz) 3000 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) -

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

Main ingredients for spinor physics Main new features with Cr 3 Spin-dependent contact interactions Spin exchange m S, m S=1,, S tot 0 4 (a a0 m 0, m S 0 1 3 S 0, m 1 0-1 tot 0 S=3 7 Zeeman states 4 scattering lengths New structures Strong spin-dependent contact interactions Purely linear Zeeman effect Engineer artificial quadratic effect using tensor light shift And Quadratic Zeeman effect Dipole-dipole interactions

Dipolar interactions introduce magnetization-changing collisions without Vdd V S g 4 Dipole-dipole interactions 13cos ( ) 0 dd J B 1 R 3 1 0-1 R 3 1 0-1 - -3 with Vdd

B=0: Rabi -3 - -1 0 1 3 V dd In a finite magnetic field: Fermi golden rule (losses) -3 - -1 0 1 3 V g B dd f B (x1000 compared to alkalis)

Dipolar relaxation and rotation 1 3,3 3, 0 1-1 - -3 3,3 Ueda, PRL 96, 080405 (006) Santos PRL 96, 190404 (006) Gajda, PRL 99, 130401 (007) B. Sun and L. You, PRL 99, 15040 (007) Rotate the BEC? Spontaneous creation of vortices? Einstein-de-Haas effect Angular momentum conservation m S m E m S l 0 g B B Important to control magnetic field

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

g (r) Energy From the molecular physics point of view: a delocalized probe V eff R c ( R) l( l 1) R l l 0 1 3,3 g B f J B 3,,3 R C l( l 1) mg B in S B ( R ) c Interpartice distance PRA 81, 04716 (010) B = 3 G R c -body physics R vdw 1 6 5 4 3 0.1 B =.3 mg Rc many-body physics 1/3 n 6 5 4 3 4 5 6 7 8 9 10 3 4 5 6 7 8 9 100 Distance r (nm)

S=3 Spinor physics with free magnetization Alkalis : - S=1 and S= 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, 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 10 000 atoms in 7 Zeeman states

S=3 Spinor physics with free magnetization Alkalis : - S=1 and S= 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, a 0 ) - No hyperfine structure - Free magnetization Magnetic field matters! 1 Spinor physics of a Bose gas with free magnetization (Quantum) magnetism in opical lattices

Spin Temperature ( K) Spin temperature equilibriates with mechanical degrees of freedom At low magnetic field: spin thermally activated g B k T B B 1.4 1. 3 1 0-1 - -3-3 - -1 0 1 3 We measure spin-temperature by fitting the m S population (separated by Stern-Gerlach technique) Related to Demagnetization Cooling expts, Pfau, Nature Physics, 765 (006) 1.0 0.8 0.6 0.4 0. 0. 0.4 0.6 0.8 1.0 Time of flight Temperature ( K) 1.

T>Tc Thermal population in Zeeman excited states Spontaneous magnetization due to BEC BEC only in m S =-3 (lowest energy state) Cloud spontaneously polarizes! T<Tc -3 - -1 0 1 3-3 - -1 0 1 3 a bi-modal spin distribution A non-interacting BEC is ferromagnetic New magnetism, differs from solid-state (singlet pairing) Magnetization Condensate fraction 1.0 0.8 0.6 0.4 0. 0.0-0.5-1.0-1.5 -.0 -.5-3.0 0.0 0. 0. 0.4 0.4 0.6 0.6 Temperature ( K) 0.8 Temperature ( K) B 900G 0.8 1.0 1.0 1. 1. PRL 108, 045307 (01)

Magnetization Condensate fraction Below a critical magnetic field: the BEC ceases to be ferromagnetic! 0.0-0.5 B=100 µg 1.0 0.8-1.0-1.5 -.0 B=900 µg 0.6 0.4 -.5 0. -3.0 0.0 0.4 0.8 Temperature ( K) -Magnetization remains small even when the condensate fraction approaches 1!! Observation of a depolarized condensate!! 1. 0.0 0.1 0. 0.3 Temperature ( K) 0.4 0.5 Necessarily an interaction effect PRL 108, 045307 (01)

3 1 0-1 - -3-3 - -1 Large magnetic field : ferromagnetic Cr spinor properties at low field -3 - -1 0 1 Low magnetic field : polar/cyclic 3 g B J B c n a a 0 6 4 m " 6 " -3 " 4 " - Santos PRL 96, 190404 (006) Ho PRL. 96, 190405 (006) PRL 106, 55303 (011)

Final m=-3 fraction Density dependent threshold 1.0 0.8 g B J B c n a a 0 6 4 m 0.6 BEC Lattice 0.4 0. 0.0 0 1 BEC BEC in lattice 3 4 Magnetic field (mg) 5 Critical field 0.6 mg 1.5 mg 1/e fitted 0.3 mg 1.45 mg On-going discussions with M. Brewczyk and M. Gajda Load into deep D optical lattices to boost density. Field for depolarization depends on density Note: Possible new physics in 1D: Polar phase is a singlet-paired phase Shlyapnikov-Tsvelik NJP, 13, 06501 (011)

Magnetization Dynamics analysis 0.0-0.5-1.0-1.5 Rapidly lower magnetic field -.0 -.5-3.0 50 100 150 Bulk BEC In D lattice PRL 106, 55303 (011) 00 50 Time (ms) Natural timescale for depolarization: Meanfield picture : Spin(or) precession 1/3 0 V ( ) dd r n S gj B n 4 Ueda, PRL 96, 080405 (006)

Magnetic field Open questions about equilibrium state Santos and Pfau PRL 96, 190404 (006) Diener and Ho PRL. 96, 190405 (006) Demler et al., PRL 97, 18041 (006) Phases set by contact interactions, magnetization dynamics set by dipole-dipole interactions Polar 1 1,0,0,0,0,0,1 - 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? (a) (b) (c) (d) -3 - -1 0 1 3!! Depolarized BEC likely in metastable state!! Cyclic 1 1,0,0,0,0,1,0

Magnetization Conclusions () Spinor physics with free magnetization 0.0 Spontaneous Magnetization of the cloud at BEC New magnetism -0.5-1.0-1.5 -.0 -.5-3.0 0.0 0.4 0.8 Temperature ( K) 1. (a) (b) (c) (d) -3 - -1 0 1 3 New spinor phases at extremely low magnetic fields Interplay between magnetic field, contact interactions and dipolar interactions Magnetism!

T/Tc Phase diagram B B c B B c Quasi- Boltzmann distribution 1.4 1. A 1.0 0.8 0.6 0.4 B Bi-modal spin distribution 0. C 0.0 0.0-0.5-1.0-1.5 -.0 -.5-3.0 Spinor condensate Magnetization Phase diagram adapted from J. Phys. Soc. Jpn, 69, 1, 3864 (000) See also PRA, 59, 158 (1999)

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 Magnetism in 3D optical lattices - Spin and magnetization dynamics - Depolarized ground state at low magnetic field

Study quantum magnetism with dipolar gases? Hubard model at half filling, Heisenberg model of magnetism (effective spin model) 1 nn i j H Jij ( Si. S j ) 4 z i j Dipole-dipole interactions between real spins 1 S1zS z 3 zs1z 4 zs r 1 r S S S S 1 r r S S 1 S S 1. V dd zz 1 z z H Jij ( Si. S j ) i j xy 1 H Jij ( Si. S j Si. S j ) i j 1 1 gj B 3 4 R 0 S. S 3( S. ur)( S. ur) Anisotropy Does not rely on Mott physics Magnetization changing collisions S S 1

m=3 fraction S S 1 Magnetization dynamics resonance for two atoms per site (~15 mg) 0.8 0.7 0.6-3 -1-0 1 3 0.5 0.4 Dipolar resonance when released energy matches band excitation 36 38 40 4 44 46 Magnetic field (khz) Towards coherent excitation of pairs into higher lattice orbitals? (Rabi oscillations) Mott state locally coupled to excited band

S S 1 Strong anisotropy of dipolar resonances Atom number 14x10 3 1 10 8 6 4 40 60 80 100 10 140 Magnetic field (khz) 160 180 00 Anisotropic lattice sites At resonance V r 3 ( x iy) Sd 5 r May produce vortices in each lattice site (Einstein-de-Haas effect) Coll. M. Gajda (problem of tunneling) See also PRL 106, 015301 (011)

Fraction in m=+3 S S 1 Note: Lineshape of dipolar resonances probes number of atoms per site 1. 0.6 0.4 1.0 0.8 0.6 0. atoms per site 0.4 3 atoms per site 0. 0.0 3 and more atoms per sites loaded in lattice for faster loading Probe of atom squeezing in Mott state 36 38 40 B(kHz) 4 Few-body physics! The 3-atom state which is reached has entangled spin and orbital degrees of freedom 44 3,3,3 0,0,0,3,3 spin orbit 0.0,0,0

Energy From now on : stay away from dipolar magnetization dynamics resonances, Spin dynamics at constant magnetization (<15mG) Control the initial state by a tensor light-shift Quadratic effect allows state preparation m S 3 1-3 - -1 0 1 3 0 A s polarized laser Close to a JJ transition (100 mw 47.8 nm) -1 m S 0 30 60 90 10 150 - -3 In practice, a component couples m S states Magnetic field (khz)

Adiabatic state preparation in 3D lattice t ( atomes / site) - -3 Initiate spin dynamics by removing quadratic effect m S, m 6 5 S 6, mtot 4 S 4, mtot 4 11 11 S 1, 3, 1 1, 3 4 B B c na a m 6 4

Fraction dans m=- magnétization On-site spin oscillations (due to contact oscillations) -1 - -3 vary time -.0 0.9 0.8 0.7 0.6-1.5 4 B B c na a m 6 4 0.5 0.0 0.1 0. 0.3 0.4 0.5 temps (ms) (perdiod 0 µs) ( 50 µs) Up to now unknown source of damping

populations Long time-scale spin dynamics in lattice 0.6 vary time 0.5 0.4 m=-3 m=- Sign for intersite dipolar interaction? (two orders of magnitude slower than on-site dynamics) 0.3 0. 0 5 10 Time (ms) 15 0 1 S S S S 1 1

Magnetization -1.5 -.0 -.5 At extremely low magnetic field (<1.5 mg): Spontaneous demagnetization of atoms in a 3D lattice Critical field Threshold seen 3D lattice 4kHz 5kHz 4 g B J B c n a a 0 6 4 m -3.0 5 10 Magnetic field (khz) 15 " 6 " " 4 " S 6, m 6 S 4, m 4-3 -

Magnetization pop(m=-3)/pop(m=-) Conclusions (3) Magnetism in optical lattices Resonant magnetization dynamics Towards Einstein-de-Haas effect Anisotropy Few body vs many-body physics 1.4 0.6 0.4 0. 1. 1.0 0.8 0.6 atoms per site 0.4 3 atoms per site 0. 1. 0.0 36 38 40 4 44 0.0 1.0 0.8 0.6 0.4 Away from resonances: spin oscillations at constant magnetization Spin-exchange Dipolar exchange 0 5 10 time (ms) Spontaneous depolarization at low magnetic field Towards low-field phase diagram 15 0-1.5 -.0 -.5-3.0 5 10 Magnetic field (khz) 15

Dipolar BECs: A non-standard superfluid Anisotropic properties Spinor Dipolar BECs: Study magnetism New spinor phases Spins in lattices Study quantum magnetism Spin dynamics

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