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arXiv:cond-mat/0309164 · Physical Review Letters

Observation of Spinor Dynamics in Optically Trapped Rb87 Bose-Einstein Condensates

M.-S. Chang, Christopher D. Hamley, M. D. Barrett, J. A. Sauer, Kevin Fortier, W. Zhang, Li You, Michael Chapman

Published Apr 7, 2004• 432 citations
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Abstract

We measure spin mixing of F=1 and F=2 spinor condensates of 87Rb atoms confined in an optical trap. We determine the spin mixing time to be typically less than 600 ms and observe spin population oscillations. The equilibrium spin configuration in the F=1 manifold is measured for different magnetic fields and found to show ferromagnetic behavior for low field gradients. An F=2 condensate is created by microwave excitation from the F=1 manifold, and this spin-2 condensate is observed to decay exponentially with time constant 250 ms. Despite the short lifetime in the F=2 manifold, spin mixing of the condensate is observed within 50 ms.

DOI
10.1103/physrevlett.92.140403

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We measure spin mixing of F=1 and F=2 spinor condensates of 87Rb atoms confined in an optical trap. We determine the spin mixing time to be typically less than 600 ms and observe spin population oscillations. The equilibrium spin configuration in the F=1 manifold is measured for different magnetic fields and found to show ferromagnetic behavior for low field gradients. An F=2 condensate is created by microwave excitation from the F=1 manifold, and this spin-2 condensate is observed to decay exponentially with time constant 250 ms. Despite the short lifetime in the F=2 manifold, spin mixing of the condensate is observed within 50 ms.
We experimentally studied the spin-dependent collision dynamics of 87Rb^{87}\mathrm{Rb}87Rb spin-2 Bose-Einstein condensates confined in an optical trap. The condensed atoms were initially populated in the $\ensuremath{\mid}F=2,{m}_{F}=0⟩$ state, and their time evolutions in the trap were measured in the presence of external magnetic field strengths ranging from 0.1 to 3.0G3.0\phantom{\rule{0.3em}{0ex}}\mathrm{G}3.0G. The atom loss rate due to inelastic two-body collisions was found to be $1.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{3}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Spin mixing in the F=2F=2F=2 manifold developed dramatically for the first few tens of milliseconds, and the oscillations in the population distribution between different magnetic components were observed over a limited range of magnetic field strengths. The antiferromagnetic property of this system was deduced from the magnetic field dependence on the evolution of relative populations for each mF{m}_{F}mF​ component.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.
We investigate the dynamics of a F=1F=1F=1 spinor Bose-Einstein condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms confined in a quasi-one-dimensional trap both at zero and at finite temperature. At zero temperature, we observe coherent oscillations between populations of the various spin components and the formation of multiple domains in the condensate. We study also finite temperature effects in the spin dynamics taking into account the phase fluctuations in the Bogoliubov-de Gennes framework. At finite TTT, despite complex multidomain formation in the condensate, population equipartition occurs. The length scale of these spin domains seems to be determined intrinsically by nonlinear interactions.
We studied the dynamics of quadruply quantized vortices in 87 Rb Bose–Einstein condensates. Vortices were created in magnetically trapped condensates with hyperfine spin F = 2 by employing topological phase imprinting technique, wherein the direction of atomic spin is adiabatically reversed by applying a bias magnetic field. Vortices were observed for a holding time of up to 10 ms. Disappearance of the vortices was attributed to considerable expansion and excitation of the condensates, which were caused by the distortion of the magnetic potential. In order to observe the long-term behavior of the vortices, we transferred the condensates to a crossed-type optical dipole force trap after creating the vortices. In this case, the vortices were observed for a holding time of up to 22 ms. We also observed density profiles, which indicated the presence of split vortices.
We study the nonequilibrium coherent spin-mixing dynamics in ferromagnetic spin-1 and antiferromagnetic spin-2 thermal gases of ultracold 87Rb^{87}\mathrm{Rb}87Rb atoms. Long-lasting spin population oscillations with magnetic-field-dependent resonances are observed in both cases. Our observations are well reproduced by Boltzmann equations of the Wigner distribution function. Compared to the equation of motion of spinor Bose-Einstein condensates, the only difference here is a factor-of-2 increase in the spin-dependent interaction, which is confirmed directly in the spin-2 case by measuring the relation between the oscillation amplitude and the sample's density.
We report the observation of strongly ferromagnetic F = 1 spinor Bose-Einstein condensates of 7 Li atoms.The condensates are generated in an optical dipole trap without using magnetic Feshbach resonances, so that the condensates have internal spin degrees of freedom.Studying the nonequilibrium spin dynamics, we have measured the ferromagnetic spin interaction energy and determined the s-wave scattering length difference among total spin f channels to be a f =2a f =0 = -18(3) Bohr radius.This strong collision-channel dependence leads to a large variation in the condensate size with different spin composition.We were able to excite a radial monopole mode after a spin-flip transition between the |m F = 0 and |m F = 1 spin states.From the experiments, we estimated the scattering length ratio a f =2 /a f =0 = 0.27(6), and determined a f =2 = 7(2) and a f =0 = 25(5) Bohr radii, respectively.The results indicate the spin-dependent interaction energy of our system is as large as 46% of the condensate chemical potential.