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arXiv:cond-mat/0603686 · Physical Review A

Nonadiabatic production of spinor condensates with a quadrupole-Ioffe-configuration trap

P. Zhang, Z. Xu, Li You

Published Jan 24, 2006• 1 citation
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Abstract

Motivated by the recent experimental observation of multicomponent spinor condensates via a time-dependent quadrupole-Ioffe-configuration trap, we provide a general framework for the investigation of nonadiabatic Landau-Zener dynamics of a hyperfine spin, e.g., from an atomic magnetic dipole moment coupled to a weak time-dependent magnetic $(B\text{\ensuremath{-}})$ field. The spin flipped population distribution, or the so-called Majorona formula, is expressed in terms of system parameters and experimental observables; thus, the distribution provides much needed insight into the underlying mechanism for the production of spinor condensates due to nonadiabatic level crossings.

DOI
10.1103/physreva.73.013623

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Motivated by the recent experimental observation of multicomponent spinor condensates via a time-dependent quadrupole-Ioffe-configuration trap, we provide a general framework for the investigation of nonadiabatic Landau-Zener dynamics of a hyperfine spin, e.g., from an atomic magnetic dipole moment coupled to a weak time-dependent magnetic (B\ensuremath-)(B\text{\ensuremath{-}})(B\ensuremath-) field. The spin flipped population distribution, or the so-called Majorona formula, is expressed in terms of system parameters and experimental observables; thus, the distribution provides much needed insight into the underlying mechanism for the production of spinor condensates due to nonadiabatic level crossings.
The generation of the population oscillation of the multicomponent spinor Bose-Einstein condensate is demonstrated in this paper. We observe and examine the nonsynchronous decreasing processes of the magnetic fields generated between quadrupole coils and Ioffe coils during the switch-off of the quadrupole-Ioffe-configuration trap, which is considered to induce a nonadiabatic transition. Starting from the two-level Schr\"odinger equation, we have done some numerical fitting and derived an analytical expression identical to the results of Majorana and Zener, of which both results well match the experimental data.
We investigate several mechanisms of vortex creation during splitting of a spinor Bose-Einstein condensate (BEC) in a magnetic double-well trap controlled by a pair of current carrying wires and bias magnetic fields. Our study is motivated by a recent MIT experiment on splitting BECs with a similar trap [Y. Shin et al., Phys. Rev. A 72, 021604 (2005)], where an unexpected fork-like structure appeared in the interference fringes indicating the presence of a singly quantized vortex in one of the interfering condensates. It is well known that in a spin-1 BEC in a quadrupole trap, a doubly quantized vortex is topologically produced by a ``slow'' reversal of bias magnetic field Bz{B}_{z}Bz​. Since in the experiment a doubly quantized vortex had never been seen, Shin et al. ruled out the topological mechanism and concentrated on the nonadiabatic mechanical mechanism for explanation of the vortex creation. We find, however, that in the magnetic trap considered both mechanisms are possible: singly quantized vortices can be formed in a spin-1 BEC topologically (for example, during the magnetic field switching-off process). We therefore provide a possible alternative explanation for the interference patterns observed in the experiment. We also present a numerical example of creation of singly quantized vortices due to ``fast'' splitting; i.e., by a dynamical (nonadiabatic) mechanism.
We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates in the homogeneous-local-spin-orientation approximation, that is, with unidirectional local magnetization. By analytically calculating the exact effective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbert equation for the dissipative condensate magnetization dynamics, and show how it leads to the Stoner-Wohlfarth model of a uniaxial ferromagnetic particle, where the latter model determines the stable magnetization patterns and hysteresis curves for switching between them. For an external magnetic field pointing along the axial, long direction, we analytically solve the Landau-Lifshitz-Gilbert equation. The solution explicitly demonstrates that the magnetic dipole-dipole interaction accelerates the dissipative dynamics of the magnetic moment distribution and the associated dephasing of the magnetic moment direction. Under suitable conditions, dephasing of the magnetization direction due to dipole-dipole interactions occurs within time scales up to two orders of magnitude smaller than the lifetime of currently experimentally realized dipolar spinor condensates, e.g., those produced with the large magnetic-dipole-moment atoms 166Er^{166}\mathrm{Er}166Er. This enables experimental access to the dissipation parameter $\mathrm{\ensuremath{\Gamma}}$ in the Gross-Pitaevskii mean-field equation, for a system currently lacking a complete quantum kinetic treatment of dissipative processes and, in particular, an experimental check of the commonly used assumption that $\mathrm{\ensuremath{\Gamma}}$ is a single scalar independent of spin indices.
Nonlinear Landau-Zener tunneling is an important nonlinear phenomenon. We propose to stimulate the nonlinear tunneling in a spin-orbit-coupled spinor Bose-Einstein condensate. The system provides an experimentally tunable nonlinearity as well as multiple avoided crossings with tunable gap size in nonlinear dispersion relations. The nonlinearity generates tilted cusp and loop structures around the avoided crossings, and the physical consequence of these nonlinear structures is the nonlinear Landau-Zener tunneling. The spin-momentum locking induced by the spin-orbit coupling leads to a time-resolved observation of the nonlinear tunneling by measuring atom populations.