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Laser Physics

Spin mixing in colliding spinor condensates

M. Guilleumas, Bruno Juliá-Díaz, Jordi Mur-Petit, A. Polls

Published Apr 1, 2009• 0 citations
Publisher

Abstract

F = 1 spinor condensates initially prepared in a double-well potential are studied in the mean field approach. First, the decoupling of the dipolar oscillation and the internal dynamics is presented. Second, the dynamical consequences of a small seed of m = 0 atoms on a system with initially well separated m = 1 and −1 condensates is explored. It is found that such a seed drives the dynamics of the m = ±1 condensates, thus departing dramatically from the behavior of binary mixtures.

DOI
10.1134/s1054660x09040070

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F = 1 spinor condensates initially prepared in a double-well potential are studied in the mean field approach. First, the decoupling of the dipolar oscillation and the internal dynamics is presented. Second, the dynamical consequences of a small seed of m = 0 atoms on a system with initially well separated m = 1 and −1 condensates is explored. It is found that such a seed drives the dynamics of the m = ±1 condensates, thus departing dramatically from the behavior of binary mixtures.
The dynamics of F =1 spinor condensates initially prepared in a double-well potential is studied in the mean-field approach. It is shown that a small seed of m =0 atoms on a system with initially well-separated m =1 and m =-1 condensates has a dramatic effect on their mixing dynamics, acting as an effective barrier for a remarkably long time. We show that this effect is due to the spinor character of the system, and provides an observable example of the interplay between the internal spin dynamics and the macroscopic evolution of the magnetization in a spinor Bose-Einstein condensate.
We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.
We analyze theoretically Josephson oscillations in a mixture of two Zeeman states of a spinor Bose-Einstein condensate in a double-well potential. We find that in the strongly polarized case, the less populated component exhibits a complex dynamics with an anti-Josephson behavior, i.e., oscillates in phase with the more populated one. In the balanced population case, the Josephson oscillations unveil a dependence with the different spin collision channels. This effect could be used to experimentally measure the distinct scattering lengths entering in the description of a spinor condensate. Our numerical results are in close agreement with an analytical description of the binary mixture using a two-mode model.
We study the dynamics of Josephson oscillations in a mixture of two Zeeman states of a spinor Bose-Einstein condensate in a double well potential. Two interesting mixture genuine effects are identified. First, we find that in the strongly polarized case, the less populated component exhibits a complex dynamics with an anti-Josephson behavior, i.e., oscillates in phase with the more populated one. Secondly, in the balanced population case, the Josephson oscillations behave as if the interatomic interactions have been partially cancelled. This effect could be used as a new procedure to measure the distinct scattering lengths entering in the description of a spinor condensate. Our numerical results are physically interpreted in terms of an analytical description of the binary mixture using a two-mode model.
The collisional and magnetic field quench dynamics of a coupled spin-vortex pair in dipolar spinor Bose-Einstein condensates in a double-well potential are numerically investigated in the mean-field theory. Upon a sudden release of the potential barrier the two layers of condensates collide with each other in the trap center with the chirality of the vortex pair exchanged after each collision, showing the typical signature of in-phase collision for the parallel spin-vortex phase, and out-of-phase collision for the antiparallel phase. When quenching the transverse magnetic field, the vortex center in the single-layered condensate starts to make a helical motion with oval-shaped trajectories and the displacement of the center position is found to exhibit a damped simple harmonic oscillation with an intrinsic frequency and damping rate. The oscillation mode of the spin-vortex pair may be tuned by the initial magnetic field and the height of the Gaussian barrier; e.g., the gyrotropic motions for a parallel spin-vortex pair are out of sync with each other in the two layers, while those for the antiparallel pair exhibit a double-helix structure with the vortex centers moving opposite to each other with the same amplitude.
We study the spin-mixing dynamics of ultracold spin-1 atoms in a weak nonuniform magnetic field with field gradient GGG, which can flip the spin from +1+1+1 to $\ensuremath{-}1$ so that the magnetization $m={\ensuremath{\rho}}_{+}\ensuremath{-}{\ensuremath{\rho}}_{\ensuremath{-}}$ is not a constant anymore. The dynamics of mF=0{m}_{F}=0mF​=0 Zeeman component ${\ensuremath{\rho}}_{0}$, as well as the system magnetization mmm, are illustrated for both ferromagnetic and polar interaction cases in the mean-field theory. We find that the dynamics of system magnetization can be tuned between the Josephson-like oscillation similar to the case of double well and the interesting self-trapping regimes, i.e., the spin-mixing dynamics sustains a spontaneous magnetization. Meanwhile, the dynamics of ${\ensuremath{\rho}}_{0}$ may be sufficiently suppressed for initially imbalanced number distribution in the case of polar interaction. A ``beat-frequency''oscillation of the magnetization emerges in the case of balanced initial distribution for polar interaction, which vanishes for ferromagnetic interaction.