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Physical Review A

Dynamics of an atomic Bose-Einstein condensation interacting with a laser field in a double-well potential

Haijun Wang, Yi Xue-Xi, Xinwu Ba

Published Jun 23, 2000• 13 citations
Publisher

Abstract

For the case of an atomic Bose-Einstein condensate formed in a symmetrical double-well potential with well-separated minima, the dynamics of Bose-condensed atoms interacting with a single-mode quantized traveling-wave laser field are investigated in detail. By considering the system consisting of the Bose-condensed atoms and laser field with and without dissipation, the eigenstates and eigenvalues of the corresponding Hamiltonian for both cases are obtained. The time development of the Bose-condensed state plays a major role in the discussion. It is shown that the probability of finding all atoms in the Bose-condensed state displays an undamped oscillatory behavior in the absence of dissipation and a damped oscillatory behavior in the presence of dissipation. Moreover, it is found that the tunneling effect can increase the oscillatory frequency among the dressed bosonic states and affect the dynamics of the system. As an application of these results, a characteristic time that may be used to evaluate the number of condensed atoms is introduced.

DOI
10.1103/physreva.62.023601

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For the case of an atomic Bose-Einstein condensate formed in a symmetrical double-well potential with well-separated minima, the dynamics of Bose-condensed atoms interacting with a single-mode quantized traveling-wave laser field are investigated in detail. By considering the system consisting of the Bose-condensed atoms and laser field with and without dissipation, the eigenstates and eigenvalues of the corresponding Hamiltonian for both cases are obtained. The time development of the Bose-condensed state plays a major role in the discussion. It is shown that the probability of finding all atoms in the Bose-condensed state displays an undamped oscillatory behavior in the absence of dissipation and a damped oscillatory behavior in the presence of dissipation. Moreover, it is found that the tunneling effect can increase the oscillatory frequency among the dressed bosonic states and affect the dynamics of the system. As an application of these results, a characteristic time that may be used to evaluate the number of condensed atoms is introduced.
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.
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.
Josephson effect of Bose-Einstein condensate in double-well potential is an obvious manifestation of macroscopic quantum coherence. Most of researches focus on the symmetric double-well potential. In this work, we investigate the dynamic of Bose-Einstein condensates in an asymmetric double-well potential by using two-mode theory and computer simulation. In the absence of the interaction between atoms, the dynamic equation of condensate can be solved analytically. The amplitude as a function of energy difference of two wells is obtained. We can find that the change of energy difference will lead to the different dynamic behaviors of condensate. If the energy difference is relatively large, the condensate will primarily occupy the well that is occupied more than the other well at the beginning time. It is interesting that such a trap phenomenon is not dependent on the position of the high energy potential well nor the position of low energy potential well. If the energy difference becomes small, the tunneling and oscillation of condensate will be enhanced. When the interaction between atoms is present, our numerical calculations show that as the nonlinear interaction increases, the dynamic behavior of condensate exhibits different characteristics, such as trapping in a well, enhancing the tunneling and oscillation between two wells, and enhancing the trapping in a well at large nonlinear interaction, which is similar to the dynamic change caused by the energy difference in the case of ideal condensate. That is to say, on the one hand, the nonlinear interaction can lead to the trap of condensate as well as the dynamic trap to happen in symmetric double-well potential. On the other hand, the nonlinearity can promote the tunneling of condensate, counteracting the effect of the asymmetry of potential. And, this counteracting effect is related to the difference in energy between asymmetric potential wells. To understand the underlying mechanism, the full dynamic behavior of two-mode model is illustrated and the dynamic transition can be seen clearly. Combining the results obtained with and without interaction, regarding nonlinear interaction as effective potential provides a clear way to explain dynamic transition of condensate in an asymmetric double-well potential. In addition, we also perform the numerical simulations of the Gross-Pitaevskii equation, and the results are consistent with the conclusions obtained by using the two-mode theory.
Abstract In this paper we consider a system consisting of a number of two-level atoms in a Bose–Einstein condensate (BEC) and a single-mode quantized field, which interact with each other in the presence of two different damping sources, i.e. cavity and atomic reservoirs. The reservoirs which we consider here are thermal and squeezed vacuum ones corresponding to field and atom modes. Strictly speaking, by considering both types of reservoirs for each of the atom and field modes, we investigate the quantum dynamics of the interacting bosons in the system. Then, via solving the quantum Langevin equations for such a dissipative BEC system, we obtain analytical expressions for the time dependence of atomic population inversion, mean atom as well as photon number and quadrature squeezing in the field and atom modes. Our investigations demonstrate that for modeling the real physical systems, considering the dissipation effects is essential. Also, numerical calculations which are presented show that the atomic population inversion, the mean number of atoms in the BEC and the photons in the cavity possess damped oscillatory behavior due to the presence of reservoirs. In addition, non-classical squeezing effects in the field quadrature can be observed especially when squeezed vacuum reservoirs are taken into account. As an outstanding property of this model, we may refer to the fact that one can extract the atom–field coupling constant from the frequency of oscillations in the mentioned quantities such as atomic population inversion.
The quantum nonlinear dynamics of an atomic Bose-Einstein condensate (BEC) in a double-well potential is studied. Using a double-well single-particle potential model system and a two-mode approximation, results showed that the coherent oscillations resulting from tunneling are suppressed when the number of atoms is greater than a critical value. The spectrum if nonresonant light scattered by the condensate to include an asymmetric double peak structure with peak separation and relative heights determined by the number of atoms in the condensate and the interaction strength for hard sphere collisions.