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Chinese Physics Letters

Quantum Effects of Many Atoms in Spinor Bose–Einstein Condensates

Zhao-Xian Yu, Liang Jiu-Qing, Jiao Zhi-Yong

Published Jul 21, 2006• 1 citation
Publisher

Abstract

We have studied the evolutions of the population transfer, tunnelling current and antibunching effects between spin-(+1) and spin-(-1) in the case of the strong laser pulses. It is found that the population transfer and tunnelling current exhibit periodical oscillation. For the same Rabi frequency, the larger the atom number, the longer the oscillation period is. For the spin-(-1) component, when the atomic numbers are N = 4 and 10, the antibunching effect can appear. For different atomic numbers, the appearing regions are very different. For spin component +1, the antibunching effect can always appear for different atomic numbers.

DOI
10.1088/0256-307x/23/8/012

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We have studied the evolutions of the population transfer, tunnelling current and antibunching effects between spin-(+1) and spin-(-1) in the case of the strong laser pulses. It is found that the population transfer and tunnelling current exhibit periodical oscillation. For the same Rabi frequency, the larger the atom number, the longer the oscillation period is. For the spin-(-1) component, when the atomic numbers are N = 4 and 10, the antibunching effect can appear. For different atomic numbers, the appearing regions are very different. For spin component +1, the antibunching effect can always appear for different atomic numbers.
In this paper, we have studied the atomic population difference and the atomic tunneling current of two-component Bose-Einstein condensates with a coupling drive. It is found that when the two-component Bose-Einstein condensates are initially in the coherent states, the atomic population difference may exhibit the step structure, in which the numbers of the step increase with the decrease of the Rabi frequency and with the increment of the initial phase difference. The atomic population difference may exhibit collapses, and revivals, in which their periods are affected dramatically by the Rabi frequency and the initial phase difference. The atomic tunneling current may exhibit damping oscillation behaviors, and exist the step structure for the time range of second.
In this paper, we have studied the atomic population difference and the atomic tunneling current of twocomponent Bose-Einstein condensates with a coupling drive. It is found that when the two-component Bose-Einstein condensates are initially in the coherent states, the atomic population difference may exhibit the step structure, in which the numbers of the step increase with the decrease of the Rabi frequency and with the increment of the initial phase difference. The atomic population difference may exhibit collapses, and revivals, in which their periods are affected dramatically by the Rabi frequency and the initial phase difference. The atomic tunneling current may exhibit damping oscillation behaviors, and exist the step structure for the time range of 10-10 ～ 10-9 second.
In this letter, we have studied sub-Poissonian distributions and quantum correlation of atoms in spinor Bose–Einstein condensates. It is found that there exists the sub-Poissonian distributions for spin-1 and spin-(-1) components, respectively. There may exist the violation of the Cauchy–Schwartz inequality. For the same atomic numbers, the regions that include violation of the Cauchy–Schwartz inequality will shift rightwards with the increment of the Rabi frequency, whereas for the same Rabi frequency, the regions will shift leftwards with the increment of the atomic numbers.
We present a theoretical treatment of dynamics of an atomic Bose–Einstein condensation interacting with a single-mode quantized travelling-wave laser field in a double-well potential. When the atom-field system is initially in a coherent state, expressions for the energy exchange between atoms and photons are derived. It is revealed that atoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions, in which the resonant and far off-resonant cases are included. It is found that there is an alternating current with two different sinusoidal oscillations between the two wells, but no dc characteristic of the atomic tunnelling current occurs. It should be emphasized that when without the laser field, both the population difference and the atomic tunnelling current are only a single oscillation. But they will respectively become a superposition of two oscillations with different oscillatory frequencies in the presence of the laser field. For the two oscillations of the population difference, one always has an increment in the oscillatory frequency, the other can have an increment or a decrease under different cases. These conclusions are also suitable to those of the atomic tunnelling current. As a possible application, by measurement of the atomic tunnelling current between the two wells, the number of Bose-condensed atoms can be evaluated. By properly selecting the laser field, the expected atomic tunnelling current can be obtained too.
The dynamics of an F=1F=1F=1 spinor condensate in a two-well potential is studied within the framework of the Gross-Pitaevskii equation. We derive two-mode equations relating the population imbalances, the phase differences among the condensates at each side of the barrier and the time evolution of the different Zeeman populations for the case of small population imbalances. The case of zero total magnetization is scrutinized in this limit demonstrating the ability of a two-mode analysis to describe to a large extent the dynamics observed in the Gross-Pitaevskii equations. It is also demonstrated that the time evolution of the different total populations fully decouples from the Josephson tunneling phenomena. All the relevant time scales are clearly identified with microscopic properties of the atom-atom interactions.
We present a theoretical treatment of dynamics of an atomic Bose-Einstein condensation interacting witha single-mode quantized travelling-wave laser field in a double-well potential. When the atom-field system is initiallyin a coherent state, expressions for the energy exchange between atoms and photons are derived. It is revealed thatatoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions,in which the resonant and far off-resonant cases are included. It is found that there is an alternating current with twodifferent sinusoidal oscillations between the two wells, but no dc characteristic of the atomic tunnelling current occurs.It should be emphasized that when without the laser field, both the population difference and the atomic tunnellingcurrent are only a single oscillation. But they will respectively become a superposition of two oscillations with differentoscillatory frequencies in the presence of the laser field. For the two oscillations of the population difference, one alwayshas an increment in the oscillatory frequency, the other can have an increment or a decrease under different cases. Theseconclusions are also suitable to those of the atomic tunnelling current. As a possible application, by measurement of theatomic tunnelling current between the two wells, the number of Bose-condensed atoms can be evaluated. lBy properlyselecting the laser field, the expected atomic tunnelling current can be obtained too.