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Effects of Dipolar Relaxation in Chromium BECs

Explore the specificities of chromium involving dipolar interactions, relative strengths, and non-local anisotropic mean-field effects on BECs. Learn about dipole-dipole interactions, collective excitations, and influence of trap geometry. Understand dipolar relaxation mechanisms, energy scales, and molecular binding in the experimental context.

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Effects of Dipolar Relaxation in Chromium BECs

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  1. Effects of dipolar relaxation in chromiumBECs 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)

  2. R Specificities of Chromium Chromium (S=3): Van-der-Waals + dipole-dipole interactions Long range Dipole-dipole interactions Anisotropic Relative strength of dipole-dipole and Van-der-Waals interactions Cr:

  3. Modification of BEC expansion due to dipole-dipole interactions Non local anisotropic mean-field Striction of BEC (non local effect) TF profile Parabolic ansatz is still a good ansatz Eberlein, PRL 92, 250401 (2004) (similar results in our group) Pfau,PRL 95, 150406 (2005)

  4. Collective excitations of a dipolar BEC Due to the anisotropy of dipole-dipole interactions, their effects on the BEC depend on the relative orientation of the magnetic field and the axis of the trap Repeat the experiment for two directions of the magnetic field Parametric excitations: Frequency shift(differential measurement) Bismut et al., PRL 105, 040404 (2010) Aspect ratio t (ms)

  5. Trap geometry dependence of the measured frequency shift BEC always stretches along B Shift of the quadrupole mode frequency (%) Shift of the aspect ratio (%) Sign of quadrupole shift depends on trap geometry Trap anisotropy Eberlein, PRL 92, 250401 (2004) Good agreement with Thomas-Fermi predictions Large sensitivity of the collective mode to trap geometry unlike the striction of the BEC

  6. Influence of the BEC atom number • In our experiment, MDDI is not much larger than the quantum kinetic energy Simulations with Gaussian anzatz It takes three times more atoms for the frequency shift of the collective mode to reach the TF predictions than for the striction of the BEC

  7. When dipolar mean field beats local contact meanfield Tune contact interactions using Feshbach resonances : dipolar interactions larger than contact interactions T.Lahaye et al, Nature. 448, 672 (2007) Anisotropic d-wave collapse of (spherical) BEC when scattering length is reduced (Feshbach resonance) => reveals dipolar coupling Pfau, PRL 101, 080401 (2008) And…, roton, vortices, Mott physics, 1D or 2D physics, breakdown of integrability in 1D… With… ? Cr ? Er ? Dy ? Dipolar molecules ?

  8. 1 0 -1 What is dipolar relaxation ? Dipole-dipole interaction potential: Induces several types of collision: Spin exchange Elastic collision Inelastic collisions with rotation

  9. What is dipolar relaxation ? 3 2 Only two channels for dipolar relaxation in mS = 3: 1 0 -1 -2 -3 - Dipolar relaxation associated with a change in kinetik energy: - Dependance with magnetic field and with a change in angular momentum: Change of magnetisation associated with rotation => (Einstein-de-Haas effect) Spontaneous creation of vortices ? Need of an extremely good control of B close to 0 Important to control magnetic field

  10. ( 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

  11. 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

  12. Static magnetic field Rf sweep 2 Rf sweep 1 Produce BEC m = -3 BEC m = +3, varying time detect BEC m = -3 Dipolar relaxation in a Cr BEC Experimental procedure : Typical results : Remains a BEC for ~30 ms Atom number Fit of decay gives b Time (ms) BEC lost

  13. Evolution of dipolar relaxation with the magnetic field Born approximation neglects molecular potentials : ok for B < 1G and B > 10 G… not in between. Pfau, Appl. Phys. B, 77, 765 (2003) Fermi golden rule Local character of dipolar relaxation, depending on B Node in the entrance wavefunction near a6 Determination of chromium scattering lengths a6 = 103 ± 4 a0 a4 = 64 ± 4 a0 See also Shlyapnikov PRL 73, 3247 (1994) Never observed up to now

  14. Interpretation from the molecular physics point of view Energy Interparticle distance Only valid for RC > a6 Better knowledge of the inner part of molecular potentials otherwise required In Out Node in the entrance wavefunction near a6, zero coupling, minimum in dipolar relaxation

  15. Dipolar relaxation: measuring non-local correlations Use of local character of dipolar relaxation Measure of two particule correlation function by varying the magnetic field Pair correlation function for hard-core potential 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

  16. New estimates of Cr scattering lengths Beaufils et al., PRA 79, 032706 (2009) Pasquiou et al., PRA 81, 042716 (2010) Collaboration Anne Crubellier (LAC, IFRAF)

  17. 100 7 6 5 4 3 2 Two-body loss param (10^(-19) m^3/s) 10 7 6 5 4 3 2 1 7 4 6 8 2 4 6 8 2 4 6 8 0.1 1 10 Magnetic field (G) Contribution of higher order partial waves DR in a BEC accounted for by a purely s-wave theory No surprise, as the pair wave-function in a BEC is purely l=0 What about DR in thermal gases ? Dipole-dipole interactions are long-range: all partial waves may contribute Temperature (µK) • The 2-body loss parameter is always twice smaller in the BEC than in thermal gases. • Probe for effect of thermal (HBT-like) correlations Dip still hold for thermal gases. At the dip, DR insensitive to temperature. Partial waves l>0 do not contribute to dipolar relaxation

  18. Contribution of higher order partial waves All partial waves contribute to elastic dipolar collisions… but … For large enough magnetic fields, only s-wave contributes to dipolar relaxation. (the input and output wave functions always oscillate at very different spatial frequencies) Overlap calculations Anne Crubellier (LAC, IFRAF) Red : l=0 Blue: l=2 Green : l=4 Magenta: l=6 Overlap Magnetic field Perspectives : - no DR in fermionic dipolar mixtures for sufficient B - use DR as a non-local probe for correlations

  19. 3 2 1 30 mGauss Spin relaxation and band excitation in optical lattices …spin-flipped atoms go from one band to another

  20. hn2 hn1 hn1 hn1 hn1 hn2 Reduction of dipolar relaxation in optical lattices Load the BEC in a 1D or 2D Lattice Experimental procedure: Static magnetic field Lattices height ~ 135 kHz 25 Er Loading in lattices Rf sweep 1 Rf sweep 2 Produce BEC m = -3 band mapping BEC m = +3, varying time detect BEC m = -3 One expects a reduction of dipolar relaxation, as a result of the reduction of the density of states in the lattice

  21. Reduction of dipolar relaxation in optical lattices Pasquiou et al., PRA 81, 042716 (2010) Pasquiou et al., PRL 106, 015301 (2011)

  22. What we measure in 1D: Non equilibrium velocity distribution along tubes Integrability Band mapping procedure Measure population in band v = 0 and v = 1, and heating from population created in v = 2 (collisional de-excitation) Population in different bands due to dipolar relaxation

  23. (almost) complete suppression of dipolar relaxation in 1D at low field 3 2 1 Fraction of atoms in v=1 0 -1 -2 -3 Energy released Magnetic field (kHz) 25 Er Band excitation Kinetic energy along tubes Temperature (µK) 12 Er Strong reduction of DR when Almost complete suppression below threshold at 1D Magnetic field (kHz)

  24. Importance of cylindrical symetry • Below threshold, suppression of DR is most efficient if : • Lattice sites are cylindrical (fully cylindrical ?) • - The magnetic field is parallel to the 1D gases Dipolar relaxation rate (a.u.) Dipolar relaxation rate (a.u.)

  25. (almost) complete suppression of dipolar relaxation in 1D at low field: 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…

  26. 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

  27. 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 irrelevant 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

  28. S=3 Spinor physics with free magnetization 7 Zeeman states; all trapped four scattering lengths, a6, a4, a2, a0 3 2 3 1 2 ferromagnetic i.e. polarized in lowest energy single particle state 0 1 0 -1 -1 -2 -2 -3 -3 Magnetic field Critical magnetic field Santos PRL 96, 190404 (2006) Ho PRL. 96, 190405 (2006) Phases are set by contact interactions (a6, a4, a2, a0) – differ by total magnetization a0/a6 (at Bc, it costs no energy to go from m=-3 to m=-2 : difference in interaction energy compensates for the loss in Zeeman energy) DDI ensure the coupling between states with different magnetization

  29. Magnetic field control below .5 mG (dynamic lock, fluxgate sensors) (50 Hz noise fluctuations, earth Magnetic field, …) (.1mG stability) (no magnetic shield…) (up to 1H stability) At VERY low magnetic fields, spontaneous depolarization of 3D and 1D quantum gases Experimental procedure 1 mG 0.5 mG 0.25 mG Produce BEC m=-3 « 0 mG » Stern Gerlach experiments Rapidly lower magnetic field

  30. Mean-field effect Field for depolarization depends on density Optical lattices : change only the density, not the symetry for DDI

  31. Mean-field effect In lattices, no changes for depolarisation with the orientation of B Optical lattices : change only the density, not the symetry for DDI Evidence for inter-sites dipolar coupling

  32. Dynamics analysis At short times, transfert between mS = -3 and mS = -2 ~ a two level system coupled by Vdd few atoms in mS = -2, so collision only in a6 Natural timescale for depolarization: (a few ms) But still unaccounted for B above dipolar meanfield Influence of the trap / temperature ??? Ueda, PRL 96, 080405 (2006) / Kudo Phys. Rev. A 82, 053614 (2010)

  33. Dynamics analysis In lattices (in our experimental configuration), the volume of the cloud is multiplied by 3 Mean field due to dipole-dipole interaction is reduced Slower dynamics, even with higher peak densities Bulk BEC Non local character of DDI 2D optical lattices

  34. Single component Bose thermodynamics

  35. 3 2 1 0 -1 -2 -3 Multi-component Bose thermodynamics 3 7 Zeeman states; all trapped in optical dipole trap 2 1 0 Phase diagram, non interacting case, cylindrical -1 -2 Simkin and Cohen, PRA, 59, 1528 (1999) Isoshima et al., J. Phys. Soc. Jpn,   69, 12, 3864 (2000) -3 Normal BEC in majoritary component+ Th temperature BEC in each component Double phase transition at constant magnetization magnetization

  36. Thermal effect: (Partial) Loss of BEC when demagnetization B=0 B=20 mG lower Tc: spin degree of freedom is released Dipolar interaction opens the way to spinor thermodynamics with free magnetization

  37. 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

  38. Spin population and thermometry (above Bc) BEC in m=-3 Depolarized thermal gas « bi-modal » spin distribution Above Bc: Only thermal gas depolarizes… get rid of it ? Cooling scheme? (Bragg excitations or field gradient) A new thermometry ? (limits to be checked)

  39. 3 2 1 0 -1 -2 -3 Summary: A quench through a zero temperature (quantum) phase transition Santos PRL 96, 190404 (2006) Ho PRL. 96, 190405 (2006) 3 3 2 2 1 1 0 • - Operate near B=0. Investigate absolute many-body ground-state • - We do not (cannot ?) reach those new ground state phases • Thermal excitations probably dominate -1 -2 -3 Pasquiou et al., accepted in PRL 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)

  40. Conclusion Dipolar relaxation in BEC: new measurement of Cr scattering lengths non-localcorrelations Dipolar relaxation in reduced dimensions: almost-suppression of DR 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 / cooling (Collective excitations – effect of non-local mean-field)

  41. Thank you for your attention …one open Post-doc position in our group…

  42. How to make a Chromium BEC 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 Pure BEC: 10 000 à 30 000 atomes • A dipole trap • All optical evaporation • A BEC • A crossed dipole trap

  43. 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)

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