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Have left: B. Pasquiou (PhD), G. Bismut (PhD ), M. Efremov, Q. B eaufils (PhD),

This research delves into the properties and dynamics of Chromium Bose-Einstein Condensates (BECs) influenced by dipole-dipole interactions. The interactions in Chromium (S=3) with aligned spins and long-range anisotropic properties lead to stable BECs despite attractive forces. The text discusses the manipulation of contact interactions using Feshbach resonances and the manifestation of dipolar coupling in the expansion patterns. Furthermore, it addresses the magnetic and hydrodynamic aspects, including collective excitations and phase transitions, providing insights into the behavior of dipolar BECs. The work explores the influence of dipole-dipole interactions on BEC expansion, collective excitation frequencies, and quasi-particle properties. Notably, the study reveals the sensitivity of dipolar shifts to trap geometry and offers a comprehensive understanding of the anisotropic behavior in the system. The research highlights the importance of controlling magnetic fields in studying phenomena like vortices and angular momentum conservation in dipolar BECs.

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Have left: B. Pasquiou (PhD), G. Bismut (PhD ), M. Efremov, Q. B eaufils (PhD),

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  1. DipolarchromiumBECs • 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 (PhD), J.C. Keller, T. Zanon, R. Barbé, A. Pouderous (PhD), R. Chicireanu (PhD) Collaborator:Anne Crubellier (Laboratoire Aimé Cotton)

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

  3. BEC stable despite attractive part of dipole-dipole interactions BEC collapses R Relative strength of dipole-dipole and Van-der-Waals interactions Stuttgart: Tune contact interactions using Feshbach resonances (Nature. 448, 672 (2007)) Anisotropic explosion pattern reveals dipolar coupling. Stuttgart: d-wave collapse, PRL 101, 080401 (2008) See also Er PRL, 108, 210401 (2012) See also Dy, PRL, 107, 190401 (2012) … and Dy Fermi sea PRL, 108, 215301 (2012) Also coming up: heteronuclear molecules (e.g. K-Rb) Cr:

  4. 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

  5. 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

  6. 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) TF radii after expansion related to interactions Cs BEC with tunable interactions (from Innsbruck))

  7. Modification of BEC expansion due to dipole-dipole interactions TF profile Striction of BEC (non local effect) Eberlein, PRL 92, 250401 (2004) (similar results in our group) Pfau,PRL 95, 150406 (2005)

  8. Frequency of collective excitations (Castin-Dum) 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)

  9. Collective excitations of a dipolar BEC Parametric excitations 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 Repeat the experiment for two directions of the magnetic field (differential measurement) Phys. Rev. Lett. 105, 040404 (2010) A small, but qualitative, difference (geometry is not all) Note : dipolar shift very sensitive to trap geometry : a consequence of the anisotropy of dipolar interactions

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

  11. 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

  12. Anisotropic speed of sound A 20% effect, much larger than the (~2%) modification of the mean-field due to DDI An effect of the momentum-sensitivity of DDI Good agreement between theory and experiment; Finite size effects at low q (See also prediction of anisotropic superfluidity of 2D dipolar gases : Phys. Rev. Lett. 106, 065301 (2011))

  13. Hydrodynamic properties of a BEC with weak dipole-dipole interactions Striction Stuttgart, PRL 95, 150406 (2005) Collective excitations Villetaneuse, PRL 105, 040404 (2010) Anisotropic speed of sound Bragg spectroscopy Villetaneuse arXiv: 1205.6305 (2012) Interesting but weak effects in a scalar Cr BEC

  14. 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

  15. R Dipolar interactions introduce magnetization-changing collisions without with 1 0 Dipole-dipole interactions -1 3 2 1 0 -1 -2 -3

  16. 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 (losses) (x1000 compared to alkalis)

  17. 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)

  18. 3 2 1 0 • B=1G • Particleleaves the trap -1 -2 -3 • B=10 mG • Energy gain matches band excitation in a lattice • B=.1 mG • Energy gain equals to chemicalpotential in BEC

  19. Energy Interpartice distance From the molecular physics point of view: a delocalized probe PRA 81, 042716 (2010) B = 3 G 2-body physics B = .3 mG many-body physics

  20. S=3 Spinor physics with free magnetization • New featureswith Cr: • S=3 spinor (7 Zeeman states, four scatteringlengths, a6, a4, a2, a0) • No hyperfine structure • Free magnetization • Magneticfieldmatters ! • Alkalis : • - S=1 and S=2 only • - Constant magnetization • (exchange interactions) • Linear Zeeman effectirrelevant Technical challenges : Good control of magnetic field needed (down to 100 mG) Active feedback with fluxgate sensors Low atom number – 10 000 atoms in 7 Zeeman states

  21. S=3 Spinor physics with free magnetization • New featureswith Cr: • S=3 spinor (7 Zeeman states, four scatteringlengths, a6, a4, a2, a0) • No hyperfine structure • Free magnetization • Magneticfieldmatters ! • Alkalis : • - S=1 and S=2 only • - Constant magnetization • (exchange interactions) • Linear Zeeman effectirrelevant • 1 Spinorphysics of a Bose gaswith free magnetization • Thermodynamics: how magnetizationdepends on temperature • Spontaneousdepolarization of the BEC due to spin-dependent interactions • 2 Magnetism in opicallattices • Depolarizedground state atlowmagneticfield • Spin and magnetizationdynamics

  22. 3 2 1 0 -1 -2 -3 Spin temperature equilibriates with mechanical degrees of freedom At low magnetic field: spin thermally activated -3 -2 -1 0 1 2 3 We measure spin-temperature by fitting the mS population (separated by Stern-Gerlach technique)

  23. Spontaneous magnetization due to BEC T>Tc T<Tc -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 a bi-modal spin distribution Thermal population in Zeeman excited states BEC only in mS=-3 (lowest energy state) Cloud spontaneously polarizes ! Non-interacting multicomponent Bose thermodynamics: a BEC is ferromagnetic Phys. Rev. Lett. 108, 045307 (2012)

  24. Below a critical magnetic field: the BEC ceases to be ferromagnetic ! B=100 µG B=900 µG • Magnetization remains small even when the condensate fraction approaches 1 • !! Observation of a depolarized condensate !! Necessarily an interaction effect Phys. Rev. Lett. 108, 045307 (2012)

  25. Cr spinor properties at low field -1 3 3 2 2 1 1 -2 0 0 -1 -1 -2 -2 -3 -3 -3 Large magnetic field : ferromagnetic Low magnetic field : polar/cyclic Santos PRL 96, 190404 (2006) Ho PRL. 96, 190405 (2006) -2 -3 Phys. Rev. Lett. 106, 255303 (2011)

  26. Density dependent threshold Phys. Rev. Lett. 106, 255303 (2011) Load into deep 2D 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, 065012 (2011)

  27. Produce BEC m=-3 Rapidly lower magnetic field Dynamics analysis PRL 106, 255303 (2011) Meanfield picture : Spin(or) precession Ueda, PRL 96, 080405 (2006) Natural timescale for depolarization:

  28. Open questions about equilibrium state Phases set by contact interactions, magnetizationdynamics set by dipole-dipole interactions Santos and Pfau PRL 96, 190404 (2006) Diener and Ho PRL. 96, 190405 (2006) Magnetic field Demler et al., PRL 97, 180412 (2006) • - 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 ? Cyclic Polar !! Depolarized BEC likely in metastable state !!

  29. 1 Spinorphysics of a Bose gaswith free magnetization • Thermodynamics: Spontaneousmagnetization of the gas due to ferromagnetic nature of BEC • Spontaneousdepolarization of the BEC due to spin-dependent interactions • 2 Magnetism in 3D opicallattices • Depolarizedground state atlowmagneticfield • Spin and magnetizationdynamics

  30. 2D 3D Loading an optical lattice Optical lattice = periodic (sinusoidal) potential due to AC Stark Shift of a standing wave (from I. Bloch) We load in the Mott regime U=10kHz, J=100 Hz J U In practice, 2 per site in the center (Mott plateau) (in our case (1 , 1 , 2.6)* l/2 periodicity)

  31. Spontaneous demagnetization of atoms in a 3D lattice -2 -3

  32. Control the ground state by a light-induced effective Quadratic Zeeman effect 1 0 -3 -2 -1 0 1 2 3 Energy A s- polarized laser Close to a JJ transition (100 mW 427.8 nm) -1 -2 D=a mS2 -3 In practice, a p component couples mS states Note : The effective Zeeman effect is crucial for good state preparation Typical groundstate at 60 kHz -3 -2 -1 0 1 2 3

  33. Adiabatic (reversible) change in magnetic state (unrelated to dipolar interactions) quadratic effect t -3 -2 3D lattice (1 atom per site) Note: the spin state reached without a 3D lattice is completely different ! Large spin-dependent (contact) interactions in the BEC have a very large effect on the final state -1 -2 1 0 -1 -2 -3 -3 BEC (no lattice)

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

  35. Magnetization dynamics resonance for two atoms per site 3 2 1 0 -1 -2 -3 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

  36. Measuring population in higher bands (1D) (band mapping procedure): 3 2 1 0 -1 m=3 -2 -3 m=2 Population in different bands due to dipolar relaxation PRL 106, 015301 (2011)

  37. Strong anisotropy of dipolar resonances Anisotropic lattice sites At resonance May produce vortices in each lattice site (EdH effect) (problem of tunneling) See also PRL 106, 015301 (2011)

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

  39. Conclusions Magnetization changing dipolar collisions introduce the spinor physics with free magnetization New spinor phases at extremely low magnetic fields Tensor light-shift allow to reach new quantum phases 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)

  40. 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

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