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理论物理通讯：英文版

Self—Trapping State and Atomic Tunnelling Current of an Atomic Bose—Einstein Condensate Interacting with a Laser Field in a Double—Well Potential

YUZhao-Xian, JIAOZhi-Yong

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

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.

Related papers

Self-Trapping State and Atomic Tunnelling Current of an Atomic Bose–Einstein Condensate Interacting with a Laser Field in a Double-Well Potential

Zhao-Xian Yu, Jiao Zhi-Yong

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.

Communications in Theoretical Physics•May 15, 2002•1 citation

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

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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.

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We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the $n\mathrm{th}$ LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.

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In this paper, we study the influence of the interatomic linear and nonlinear interactions on tunneling dynamics in two zerotemperature BoseEinstein condensates (BECs) when the two BECs are in coherent states. The shorttime behaviors of the tunneling dynamics are investigated in detail. It is found that the population difference between two BECs exhibits periodic Rabbi oscillations with a period, which depends upon not only interatomic linear and nonlinear interactions but also the initial state of two BECs. We show that the twoBEC system may reach a selftrapping stationary state through adjusting interatomic interactions and the initial state of the system under our consideration. We also investigate the coherent atomic tunneling current between BECs, and find that under certain conditions coherent atomic tunneling current may be a pure DC atom current.

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One-BEC-species coherent oscillations with frequency controlled by a second species atom number

L. Morales-Molina, E Arévalo

Abstract Controlling the tunneling of atoms of one species using a different atom species is a fundamental step in the development of a new class of atom quantum devices, where detection, motion control, and other functions over the atoms, can be achieved by exploiting the interaction between two different atomic species. Here, we theoretically study coherent oscillations of a non-self-interacting Bose–Einstein condensate (BEC) species in a triple-well potential controlled by a self-interacting species self-trapped in the central well of the potential. In this system, a blockade, due to the interspecies interaction, prevents atoms of the non-self-interacting species from populating the central well. Thus, for an initial population imbalance between the left- and right-hand wells of the non-self-interacting species, coherent BEC oscillations are induced between these two wells, resembling those of Rabi-like BEC oscillations in a double-well potential. The oscillation period is found to scale linearly with the number of self-trapped atoms as well as with the interspecies interaction strength. This behavior is corroborated by the quantum many-particle and the mean-field models of the system. We show that BEC oscillations can be described by using an effective bosonic Josephson junction with a tunneling amplitude that depends on the number of the self-trapped atoms in the central well. We also consider the effect of the self-trapped atom losses on the coherent oscillations. We show, by using quantum trajectories, that this type of losses leads to a dynamical change in the oscillation period of the non-self-interacting species, which in turn allows the number of self-trapped atoms lost from the system to be estimated.

New Journal of Physics•Dec 7, 2021•3 citations
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.
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.
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 describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the nthn\mathrm{th}nth LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.
Summary form only given. Dynamical control of the atomic tunneling between two Bose-Einstein condensates (BEC's) confined in a double-well potential is predicted to occur when laser pulses induce transition between one of the condensate state and the excited state which brings about phase shifts for the condensate wave function, leading to transition between macroscopic quantum self-trapping, which is a self-maintained population imbalance between two BEC's due to interatomic interaction, and large amplitude oscillations. We investigate this phenomenon for the case of a three-level system with two condensate states and an excited state.
In this paper, we study the influence of the interatomic linear and nonlinear interactions on tunneling dynamics in two zerotemperature BoseEinstein condensates (BECs) when the two BECs are in coherent states. The shorttime behaviors of the tunneling dynamics are investigated in detail. It is found that the population difference between two BECs exhibits periodic Rabbi oscillations with a period, which depends upon not only interatomic linear and nonlinear interactions but also the initial state of two BECs. We show that the twoBEC system may reach a selftrapping stationary state through adjusting interatomic interactions and the initial state of the system under our consideration. We also investigate the coherent atomic tunneling current between BECs, and find that under certain conditions coherent atomic tunneling current may be a pure DC atom current.
Abstract Controlling the tunneling of atoms of one species using a different atom species is a fundamental step in the development of a new class of atom quantum devices, where detection, motion control, and other functions over the atoms, can be achieved by exploiting the interaction between two different atomic species. Here, we theoretically study coherent oscillations of a non-self-interacting Bose–Einstein condensate (BEC) species in a triple-well potential controlled by a self-interacting species self-trapped in the central well of the potential. In this system, a blockade, due to the interspecies interaction, prevents atoms of the non-self-interacting species from populating the central well. Thus, for an initial population imbalance between the left- and right-hand wells of the non-self-interacting species, coherent BEC oscillations are induced between these two wells, resembling those of Rabi-like BEC oscillations in a double-well potential. The oscillation period is found to scale linearly with the number of self-trapped atoms as well as with the interspecies interaction strength. This behavior is corroborated by the quantum many-particle and the mean-field models of the system. We show that BEC oscillations can be described by using an effective bosonic Josephson junction with a tunneling amplitude that depends on the number of the self-trapped atoms in the central well. We also consider the effect of the self-trapped atom losses on the coherent oscillations. We show, by using quantum trajectories, that this type of losses leads to a dynamical change in the oscillation period of the non-self-interacting species, which in turn allows the number of self-trapped atoms lost from the system to be estimated.