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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).

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## Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaborator: Anne Crubellier (La

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**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)**R**Chromium (S=3): Van-der-Waals plus dipole-dipole interactions Dipole-dipole interactions Long range Anisotropic Non local anisotropic mean-field Relative strength of dipole-dipole and Van-der-Waals interactions Cr:**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)**R**Spin degree of freedom coupled to orbital degree of freedom - Spinor physics and magnetization dynamics without with 1 Dipole-dipole interactions 0 -1 3 2 1 0 -1 -2 -3**B=0: Rabi**3 2 1 0 -1 -2 -3 -3 -2 -1 0 1 2 3 In a finite magnetic field: Fermi golden rule**Dipolar relaxation, rotation, and magnetic field**3 2 1 0 -1 Angular momentum conservation -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)**From the molecular physics point of view**Energy Interpartice distance Rc = Condon radius PRA 81, 042716 (2010)**( is the scattering length)**( is the harmonic oscillator size) 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 Band excitation in lattice : 100 kHz 30 mG Suppression of dipolar relaxation in optical lattices Chemical potential : 1 kHz .3 mG Inelastic dipolar mean-field**3**3 Gauss 2 1 0 -1 -2 -3 Suppression of dipolar relaxation due to inter-atomic repulsion …spin-flipped atoms gain so much energy they leave the trap**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**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**3**2 1 30 mGauss 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 Rf sweep 1 Rf sweep 2 Load optical lattice BEC m=+3, vary time Produce BEC 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)**(almost) complete suppression of dipolar relaxation in 1D at**low field 3 2 1 0 -1 -2 -3 Energy released Band excitation Kinetic energy along tubes B. Pasquiou et al., Phys. Rev. Lett. 106, 015301 (2011)**(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**2 1 0 -1 -2 -3 .3 mGauss Magnetization dynamics of spinor condensates 3 2 1 0 -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 0 -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 0 -1 -2 -3**S=3 Spinor physics with free magnetization**-1 3 3 2 1 -2 2 1 0 0 -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)**Magnetic field control below .5 mG (dynamic lock, fluxgate**sensors) (.1mG stability) (no magnetic shield…) 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**Mean-field effect**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:**3**2 1 0 -1 3 -2 -3 2 1 0 -1 -2 -3 A quench through a zero temperature (quantum) phase transition Santos and Pfau PRL 96, 190404 (2006) Diener and Ho PRL. 96, 190405 (2006) 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, magnetizationdynamics set by dipole-dipole interactions « quantum magnetism » Also new physics in 1D: Polar phase is a singlet-paired phase arXiv:1103.5534 (Shlyapnikov-Tsvelik)**3**2 1 0 -1 -2 -3 Prospect : new cooling method using the spin degrees of freedom 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-localcorrelations 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)**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…**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**3**2 1 0 -1 -2 -3 Multi-component Bose thermodynamics 3 2 7 Zeeman states; all trapped 1 0 -1 PRA, 59, 1528 (1999) J. Phys. Soc. Jpn, 69, 12, 3864 (2000) -2 -3 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 ChromiumBEC**7P4 7P3 650 nm 600 425 nm 550 5S,D (2) (1) 500 427 nm Z 450 500 550 600 650 700 750 7S3 • An atom: 52Cr • An oven • A Zeeman slower • A small MOT Oven at 1425 °C N = 4.106 T=120 μK • A dipole trap • All optical evaporation • A BEC • A crossed dipole trap**BEC with Cr atoms in an optical trap**PRA 73, 053406 (2006) PRA 77, 053413 (2008) PRA 77, 061601(R) (2008)**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**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)

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