Magnetization dynamics in dipolar chromium BECs B. Pasquiou (PhD), G. Bismut (PhD), A. de Paz B. Laburthe, E. Maréchal, L. Vernac, P. Pedri, M. Efremov (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) 1 1 1 1

Non local anisotropic mean-field Chromium (S=3): Van-der-Waals plus dipole-dipole interactions Dipole-dipole interactions Long range Anisotropic R Non local anisotropic mean-field Relative strength of dipole-dipole and Van-der-Waals interactions Cr: 2

Collective excitations Striction Stuttgart, PRL 95, 150406 (2005) Collective excitations Villetaneuse, PRL 105, 040404 (2010) Anisotropic d-wave collapse when scattering length is reduced (Feshbach resonance) Stuttgart, PRL 101, 080401 (2008)

Spin degree of freedom coupled to orbital degree of freedom - Spinor physics and magnetization dynamics without 1 Dipole-dipole interactions -1 with 3 2 R 1 -1 -2 -3

In a finite magnetic field: Fermi golden rule B=0: Rabi -3 -2 -1 0 1 2 3 In a finite magnetic field: Fermi golden rule -3 -2 -1 1 2 3

Dipolar relaxation, rotation, and magnetic field Angular momentum conservation -3 -2 -1 1 2 3 Rotate the BEC ? Spontaneous creation of vortices ? Einstein-de-Haas effect Important to control magnetic field Ueda, PRL 96, 080405 (2006) Santos PRL 96, 190404 (2006) Gajda, PRL 99, 130401 (2007) B. Sun and L. You, PRL 99, 150402 (2007) 6 6

From the molecular physics point of view Energy Interpartice distance Rc = Condon radius PRA 81, 042716 (2010)

Energy scale, length scale, and magnetic field Molecular binding enery : 10 MHz Magnetic field = 3 G Inhibition of dipolar relaxation due to inter-atomic (VdW) repulsion ( is the scattering length) Band excitation in lattice : 100 kHz 30 mG Suppression of dipolar relaxation in optical lattices ( is the harmonic oscillator size) Chemical potential : 1 kHz .3 mG Inelastic dipolar mean-field

3 Gauss Suppression of dipolar relaxation due to inter-atomic repulsion -3 -2 -1 1 2 3 …spin-flipped atoms gain so much energy they leave the trap

Feshbach resonance in d-wave PRA 79, 032706 (2009) Dipolar relaxation in a Cr BEC Rf sweep 1 Rf sweep 2 Produce BEC m=-3 BEC m=+3, vary time detect BEC m=-3 Fermi golden rule Born approximation Pfau, Appl. Phys. B, 77, 765 (2003) PRA 81, 042716 (2010) a6 = 103 ± 4 a0. Feshbach resonance in d-wave PRA 79, 032706 (2009) See also Shlyapnikov PRL 73, 3247 (1994) a6 = 102.5 ± 0.4 a0 10 10

Dipolar relaxation: measuring non-local correlations L. H. Y. Phys. Rev. 106, 1135 (1957) A probe of long-range correlations : here, a mere two-body effect, yet unacounted for in a mean-field « product-ansatz » BEC model 11

30 mGauss Spin relaxation and band excitation in optical lattices 2 3 1 Spin relaxation and band excitation in optical lattices …spin-flipped atoms go from one band to another

Reduction of dipolar relaxation in optical lattices Load the BEC in a 1D or 2D Lattice Produce BEC m=-3 detect m=-3 Rf sweep 1 Rf sweep 2 BEC m=+3, vary time Load optical lattice One expects a reduction of dipolar relaxation, as a result of the reduction of the density of states in the lattice 13

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

(almost) complete suppression of dipolar relaxation in 1D at low field -3 -2 -1 1 2 3 Energy released Band excitation Kinetic energy along tubes B. Pasquiou et al., Phys. Rev. Lett. 106, 015301 (2011)

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

.3 mGauss Magnetization dynamics of spinor condensates -3 -2 -1 2 1 3 3 2 1 -1 -2 -3 …spin-flipped atoms loses energy Similar to M. Fattori et al., Nature Phys. 2, 765 (2006) at large fields and in the thermal regime

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 1 -1 3 New features with Cr - First S=3 spinor (7 Zeeman states, four scattering lengths, a6, a4, a2, a0) Dipole-dipole interactions free total magnetization Can investigate the true ground state of the system (need very small magnetic fields) 2 1 -1 -2 -3 18

S=3 Spinor physics with free magnetization -1 2 1 -2 2 1 -1 -1 -2 -2 -3 -3 -3 Large magnetic field : ferromagnetic Low magnetic field : polar/cyclic -2 -3 Phases set by contact interactions (a6, a4, a2, a0) – differ by total magnetization Santos PRL 96, 190404 (2006) Ho PRL. 96, 190405 (2006) 19

Magnetic field control below .5 mG (dynamic lock, fluxgate sensors) At VERY low magnetic fields, spontaneous depolarization of 3D and 1D quantum gases 1 mG 0.5 mG Produce BEC m=-3 0.25 mG « 0 mG » Stern Gerlach experiments Rapidly lower magnetic field Magnetic field control below .5 mG (dynamic lock, fluxgate sensors) (.1mG stability) (no magnetic shield…) 20

Mean-field effect BEC Lattice Critical field 0.26 mG 1.25 mG 1/e fitted 0.4 mG 1.45 mG Field for depolarization depends on density

Dynamics analysis Meanfield picture : Spin(or) precession (Majorana flips) When mean field beats magnetic field Ueda, PRL 96, 080405 (2006) Kudo Phys. Rev. A 82, 053614 (2010) (a few ms) Natural timescale for depolarization:

A quench through a zero temperature (quantum) phase transition -2 -1 1 2 3 -3 Santos and Pfau PRL 96, 190404 (2006) Diener and Ho PRL. 96, 190405 (2006) -3 -2 -1 2 1 3 3 2 1 - 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 » Also new physics in 1D: Polar phase is a singlet-paired phase arXiv:1103.5534 (Shlyapnikov-Tsvelik) 23

Only thermal gas depolarizes… Prospect : new cooling method using the spin degrees of freedom -3 -2 -1 2 1 3 Above Bc: Only thermal gas depolarizes… get rid of it ? (Bragg excitations or field gradient)

Conclusion Dipolar relaxation in BEC – new measurement of Cr scattering lengths non-local 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) (Collective excitations – effect of non-local mean-field)

…one open Post-doc position in our group… G. Bismut (PhD), B. Pasquiou (PhD) , A. de Paz B. Laburthe, E. Maréchal, L. Vernac, P. Pedri, M. Efremov (Theory), O. Gorceix (Group leader) …one open Post-doc position in our group… 26 26 26 26

Thermal effect: (Partial) Loss of BEC when demagnetization Spin degree of freedom is released ; lower Tc B=0 B=20 mG PRA, 59, 1528 (1999) J. Phys. Soc. Jpn,   69, 12, 3864 (2000) Dipolar interaction opens the way to spinor thermodynamics with free magnetization 27

Single component Bose thermodynamics

Multi-component Bose thermodynamics -3 -2 -1 2 1 3 Multi-component Bose thermodynamics -2 -1 1 2 3 -3 7 Zeeman states; all trapped PRA, 59, 1528 (1999) J. Phys. Soc. Jpn,   69, 12, 3864 (2000) temperature magnetization

Non interacting spinor Double phase transition at constant magnetization Condensate fraction temperature temperature magnetization Magnetization Magnetic field No demagnetization at low temperature Temperature

How to make a Chromium BEC An atom: 52Cr An oven A Zeeman slower 425 nm 427 nm 650 nm 7S3 5S,D 7P3 7P4 A small MOT Oven at 1425 °C N = 4.106 T=120 μK 750 700 650 600 550 500 450 (1) (2) Z A dipole trap All optical evaporation A BEC A crossed dipole trap

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BEC with Cr atoms in an optical trap PRA 73, 053406 (2006) PRA 77, 053413 (2008) PRA 77, 061601(R) (2008) 33

Thermal effect: (Partial) Loss of BEC when demagnetization Spin degree of freedom is released ; lower Tc temperature Normal « A phase » A BEC in majority component « B phase » A BEC in each component magnetization PRA, 59, 1528 (1999) J. Phys. Soc. Jpn,   69, 12, 3864 (2000) lower Tc: a signature of decoherence 34

Thermodynamics of a spinor gas with free magnetization Above Bc, magnetization well accounted for by non interacting model Above Bc, thermal gas depolarizes, but BEC remains polarized

Spin population and thermometry (above Bc) BEC in m=-3 Depolarized thermal gas A new thermometry ? (limits to be checked) « bi-modal » spin distribution

Threshold for dipolar relaxation in 1D: (almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices B. Pasquiou et al., Phys. Rev. Lett. 106, 015301 (2011) 37