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Journal of Lanzhou University

Evolution of the average spin of spinor Bose-Einstein condensates in external fields

Lei Tan

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Within the mean field approximation and the single mode approximation,the evolution of the average spin of the F=1 spinor condensate in an external magnetic field was studies and the evolution was independent of the density-density collisional interaction.When the population in each quantum state was constant,the average spin was determined by the external magnetic field and the spin-spin collisional interaction.

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Within the mean field approximation and the single mode approximation,the evolution of the average spin of the F=1 spinor condensate in an external magnetic field was studies and the evolution was independent of the density-density collisional interaction.When the population in each quantum state was constant,the average spin was determined by the external magnetic field and the spin-spin collisional interaction.
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 show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor F=1F=1F=1 Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicate the absence of metastability.
We show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor F=1 Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicates the absence of metastability.
The spin mixing dynamics of spin-1 Bose-Einstein condensates with zero magnetization and under an external magnetic field is investigated. The time-dependent solutions are obtained via a diagonalization of the Hamiltonian, which has a simple form under the single mode approximation. The features of evolution are compared in detail with those with the field removed so as to emphasize the effect of the field, which can induce strong oscillation in population of atoms in spin component 0 . A new mode of oscillation characterized by a high frequency and a low frequency, is found when the field is sufficiently strong.
With full consideration given to symmetry, we derive an exact analytical formula governing the evolution of the average populations of the spin components for spin-1 condensates. Based on the formula, a number of peculiarities of the evolution can be better understood. Our numerical results are consistent with existing experimental data. A special initial state is found; starting from this state, the average populations remain constant during a very long time, much longer than the duration observed during experiments.
Decoherence and Recurrences in a Large Ferromagnetic F=1F = 1F=1 Spinor Bose-Einstein Condensate
Decoherence with recurrences appear in the dynamics of the one-body density matrix of an F=1F = 1F=1 spinor Bose-Einstein condensate, initially prepared in coherent states, in the presence of an external uniform magnetic field and within the single mode approximation. The phenomenon emerges as a many-body effect of the interplay of the quadratic Zeeman effect, that breaks the rotational symmetry, and the spin-spin interactions. By performing full quantum diagonalizations very accurate time evolution of large condensates are analyzed, leading to heuristic analytic expressions for the time dependence of the density matrix, in the weak and strong interacting regimes. We are able to find accurate analytical expressions for both the decoherence and the recurrence times, in terms of the number of atoms and strength parameters, that show remarkable differences depending on the strength of the spin-spin interactions. We discuss the nature of these limits in the light of the thermodynamic limit.