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arXiv:1105.0280 · Physical Review A

Magnetization oscillation of a spinor condensate induced by a magnetic field gradient

Jie Zhang, Baoguo Yang, Yunbo Zhang

Published May 27, 2011• 4 citations
arXivHTMLPDF

Abstract

We study the spin-mixing dynamics of ultracold spin-1 atoms in a weak nonuniform magnetic field with field gradient $G$, which can flip the spin from $+1$ to $\ensuremath{-}1$ so that the magnetization $m={\ensuremath{\rho}}_{+}\ensuremath{-}{\ensuremath{\rho}}_{\ensuremath{-}}$ is not a constant anymore. The dynamics of ${m}_{F}=0$ Zeeman component ${\ensuremath{\rho}}_{0}$, as well as the system magnetization $m$, 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.

DOI
10.1103/physreva.83.053634

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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\ensuremath{-}1\ensuremath−1 so that the magnetization m=\ensuremathρ+\ensuremath−\ensuremathρ\ensuremath−m={\ensuremath{\rho}}_{+}\ensuremath{-}{\ensuremath{\rho}}_{\ensuremath{-}}m=\ensuremathρ+​\ensuremath−\ensuremathρ\ensuremath−​ is not a constant anymore. The dynamics of mF=0{m}_{F}=0mF​=0 Zeeman component \ensuremathρ0{\ensuremath{\rho}}_{0}\ensuremathρ0​, 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 \ensuremathρ0{\ensuremath{\rho}}_{0}\ensuremathρ0​ 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.
We study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective spin variables other than the magnetization. Our study points to an alternative approach to observe coherent tunnelling of a condensate through a (spatial) potential barrier.
We study spin mixing dynamics in a chromium dipolar Bose-Einstein condensate, after tilting the atomic spins by an angle $\ensuremath{\theta}$ with respect to the magnetic field. Spin mixing is triggered by dipolar coupling, but, once dynamics has started, it is mostly driven by contact interactions. For the particular case $\ensuremath{\theta}=\ensuremath{\pi}/2$, an external spin-orbit coupling term induced by a magnetic gradient is required to enable the dynamics. Then the initial ferromagnetic character of the gas is locally preserved, an unexpected feature that we attribute to large spin-dependent contact interactions.
We experimentally study spin dynamics in a sodium antiferromagnetic spinor condensate as a result of spin-dependent interactions ccc and microwave dressing field interactions characterized by the net quadratic Zeeman effect qnet{q}_{\mathrm{net}}qnet​. In contrast to magnetic fields, microwave dressing fields enable us to access both negative and positive values of qnet{q}_{\mathrm{net}}qnet​. We find an experimental signature to determine the sign of qnet{q}_{\mathrm{net}}qnet​ and observe harmonic spin population oscillations at every qnet{q}_{\mathrm{net}}qnet​ except near each separatrix in phase space where spin oscillation period diverges. No spin domains and spatial modes are observed in our system. Our data in the negative qnet{q}_{\mathrm{net}}qnet​ region exactly resembles what is predicted to occur in a ferromagnetic spinor condensate in the positive qnet{q}_{\mathrm{net}}qnet​ region. This observation agrees with an important prediction derived from the mean-field theory: spin dynamics in spin-1 condensates substantially depends on the sign of qnet/c{q}_{\mathrm{net}}/cqnet​/c. This work uses only one atomic species to reveal mean-field spin dynamics, especially the remarkably different relationship between each separatrix and the magnetization, of spin-1 antiferromagnetic and ferromagnetic spinor condensates.
The spin mixing dynamics of spin-1 Bose–Einstein condensates with zero magnetization and under an external magnetic field is investigated in a systematic way. Beyond the mean field theory, the time-dependent solutions of the Hamiltonian under the single mode approximation are obtained via a procedure of diagonalization. Thereby the time-dependent populations of spin-0 component starting from various initial states are obtained and analyzed. The features of evolution are compared in detail with those with the field removed so as to emphasize the effect of the field. Since the solutions are exact for the Hamiltonian, we can study the long-term behavior of the evolution, where periodicity and inherent symmetry emerge. In particular, some special cases are found in which the evolution is highly sensitive to the field, very strong oscillation in population can be thereby induced. A new mode of oscillation of the population characterized by having two frequencies, one is high and one is low, is found when the field is sufficiently strong.
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.