Magnetic properties of a dipolar BEC loaded into
Magnetic properties of a dipolar BEC loaded into a 3 D optical lattice Quantum magnetism with atomic quantum magnets A. Chotia, A. de Paz, A. Sharma, E. Maréchal, P. Pedri, L. Vernac, O. Gorceix and B. Laburthe-Tolra Laboratoire de Physique des Lasers, UMR 7538 CNRS, Université Paris Nord, Villetaneuse, France The basics Interplay between contact and long range interactions Dipole-dipole interactions: detailed contributions Chromium (S=3) Permanent magnetic moment of 6 µB 7 Zeeman states, linear Zeeman structure 4 Scattering lengths, a 6=103 a. u, a 4=64 a. u, a 2, a 0 Relative strength of dipole-dipole and Van-der-Waals interactions Spin operators Zeeman state Elastic collisions. Spin exchange. Magnetization is conserved. 52 Cr ∆ms=1 1 0 -1 ∆ms=0 +3 or +2 Inelastic collisions. Magnetization is free. 87 Rb ∆ms=2 +1 Spinor physics Dipolar Relaxation Opening new relaxation channels with the quadratic Zeeman effect Relaxation rates depend on the confining geometry Relaxation time ∆t Rf puls e Linear Zeeman effect E = msgsµBB lattice Stern Rf pulse and Gerlach analysis 1 1 0 -1 -2 -3 -1 -2 ms=+3, +2. . ms=-3, -2. . ms=+3 ms=-3 Linear+Quadratic Zeeman effect E= msgsµBB + Lms + Qms 2 Energy optical Energy 3 D -3 Magnetic field What happens? -3 -2 -1 0 1 2 3 Magnetic field A s- polarized laser close to a J J transition (100 m. W 427. 8 nm). Some p component remains. Below a critical magnetic • Dipolar relaxation channels are ∆ms=1, 2. • Resonant process: the Zeeman energy is equal to the band gap. • The band gap depends on the lattice depth and on contact interactions. Adiabatic state preparation field ms=-2 is the ground state Changing the ground state Laser intensity v=2 v=1 ∆ms=2 ∆ms=1 -3 U 4 U 6 v=0 -3 -2 -1 0 -2 -3 1 2 3 -3 Unresolved splitting New phases appear at extremely low field Depolarization in a 3 D lattice Spontaneous depolarization in a dipole trap. B-field Probing dipolar relaxation resonances along two axis of the non degenerate 3 D lattice. λ=532 nm ω1=170 k. Hz, ω2=45 k. Hz, ω3=110 k. Hz Away from resonances the excited state is metastable. ~k. Hz resonance In agreement with the calculated 2 atoms resonance width. Squeezed states: Mott plateau with 2 atoms per lattice site. Magnetic field Sensitivity to sites occupation +3 Coherent Spin dynamics in a 3 D lattice Preliminary data 3 D Short time scale ∆t <1 ms: Spin exchange driven by contact interactions optical Dynamics ∆t Quadratic lattice Stern and analysis field +2 In 2 D: dipolar relaxation shows a threshold. Σ ms Constant population Measuring doublons at high field through loss ms=+3 t(ms) Q=0 Bc~1. 5 m. G B. Pasquiou et al. , Phys. Rev. Lett 106, 255303 (2011). Relaxation Dynamics t(ms) Population in ms=+3 Increasing the occupation number Magnetic field Relative population No contribution from triplons Q=10 k. Hz Bc>10 m. G B. Pasquiou et al. PRL 106, 015301 (2011) Long time scale ∆t >10 ms: Spin exchange driven by dipole-dipole interactions ? Correlations between the lattice depth and the amplitude of the coherent dynamics Ge
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