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arXiv:0808.4018

Interference of the evolutions of Rb and Na Bose-Einstein condensates

Ma Luo, Bao Cheng-guang, Zhibing Li

Published Aug 29, 2008• 0 citations
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Abstract

Spin evolution of a mixture of two species of spin-1 Bose-Einstein condensates (Rb and Na) has been investigated beyond the mean field theory. Both analytical expression and numerical results on the populations of spin-components are obtained. The interference is found to depend on the initial states and the inter-species interaction sensitively. A number of phenomena arising from the interference have been predicted. In particular, periodic behavior and the alternate appearances of a zone of oscillation and a long quiet zone are found.

DOI
10.48550/arxiv.0808.4018

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Spin evolution of a mixture of two species of spin-1 Bose-Einstein condensates (Rb and Na) has been investigated beyond the mean field theory. Both analytical expression and numerical results on the populations of spin-components are obtained. The interference is found to depend on the initial states and the inter-species interaction sensitively. A number of phenomena arising from the interference have been predicted. In particular, periodic behavior and the alternate appearances of a zone of oscillation and a long quiet zone are found.
Spin evolution of a mixture of two species of spin-1 Bose–Einstein condensates (Rb and Na) has been investigated rigorously. The Hamiltonian under the single-mode approximation (which is the only approximation in the present theory) has been solved exactly. Both analytical expressions and numerical results on the populations of spin components are obtained. Interference between the two species is found to depend sensitively on the initial states and the inter-species interaction. A number of phenomena arising from the interference have been predicted. In particular, periodic behaviour and the alternate appearances of a zone of oscillation and a long quiet zone are found.
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.
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.
In terms of exact solutions of the time-dependent Schr\"odinger equation for an effective giant spin modeled from a coupled two-mode Bose-Einstein condensate (BEC) with adiabatic and cyclic time-varying Raman coupling between two hyperfine states of the BEC, we obtain analytic time-evolution formulas of the population imbalance and relative phase between two components with various initial states, especially the SU(2) coherent state. We find the Berry phase depending on the number parity of atoms, and particle number dependence of the collapse revival of population-imbalance oscillation. It is shown that self-trapping and phase locking can be achieved from initial SU(2) coherent states with proper parameters.
Atomic interactions play an important role in the properties of ultracold atomic gases. In single-component bosonic systems, its effect is already present at the critical point for the Bose-Einstein condensate phase transition by shifting it to lower temperatures as a consequence of effective repulsion between the atoms. When considering atomic bosonic mixtures, interesting effects arise from the competition between intra- and interspecies interactions such as the miscible-immiscible phase transition and the particular case of self-bounded quantum droplets. In such a scenario, it is natural to expect that these interactions will also affect the critical point of each species composing the mixture. In this paper, we obtain semianalytical expressions for the critical temperature shift of the phase transition to a Bose-Einstein condensate in the presence of a second species considering the mean-field framework. We treat differently the cases in which the second species is above or below its own critical temperature and apply the obtained relations to the case of a Na 23 − K 39 bosonic mixture that can be realized in current running experimental setups. Our findings can be easily extended to other atomic mixtures.