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理论物理通讯：英文版

Dynamic Analysis for Bose-Einstein Condensation in Quantum Cavity

ZHANGLi, WANGCheng, LIYan-Min, WANGJin-Fang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

For the two-level atoms system interacting with single-mode active field in a quantum cavity, the dynamics of the Bose-Einstein Condensation (BEC) is analyzed using an ordinary method suggested by authors to solve the system of Schrodinger representation in the Heisenberg representation. The wave function of the atoms is given. The stability factor determining the BEC and the selection rules of the quantum transition are solved.

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For the two-level atoms system interacting with single-mode active field in a quantum cavity, the dynamics of the Bose-Einstein Condensation (BEC) is analyzed using an ordinary method suggested by authors to solve the system of Schrodinger representation in the Heisenberg representation. The wave function of the atoms is given. The stability factor determining the BEC and the selection rules of the quantum transition are solved.
The dynamics in the Bose-Einstein Condensation(BEC) process with interaction between two energy-level Bose atoms and single-mode active cavity field in the quantum cavity is analyzed using the ordinary method suggested by the authors for solving the wave function in the Schrodinger ideal from the Heisenberg idea. A wave function has been established for the atoms under the BEC conditions in the quantum cavity. Then the stability factor determining the BEC and the selection rules of the quantum transition can be solved.
The dynamics in the Bose-Einstein Condensation(BEC) process with interaction between two energy-level Bose atoms and single-mode active cavity field in the quantum cavity is analyzed using the ordinary method suggested by the authors for solving the wave function in the Schrodinger ideal from the Heisenberg idea. A wave function has been established for the atoms under the BEC conditions in the quantum cavity. Then the stability factor determining the BEC and the selection rules of the quantum transition can be solved.
The dynamics in the Bose-Einstein Condensation (BEC) process with interaction between three energy-level Bose atoms and Single-Mode active cavity field and between three Energy-Level Bose atoms in the quantum cavity is analyzed using the ordinary method for solving the wave function in the Schrödinger idea from the Heisenberg idea. A wave function has been established for the atoms under the BEC conditions in the quantum cavity, and the factors having effect on the BEC stability in the quantum cavity and the rules for selecting quantum leaps are analyzed.
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.
Summary form only given. We perform a theoretical and numerical analysis of a system comprising a Bose-Einstein condensate (BEC) interacting with a laser beam in an optical cavity. Recent studies have modelled this system with two motional modes coupled with a light mode and have shown nonlinear behaviour, e.g. bistability [1,2]. Our approach tackles the full Gross-Pitaevskii equation coupled to the cavity field as well as expansions in a number of motional modes.We consider a fixed value of the cavity-pump detuning and increase the pump intensity to cross the region of bistability (see Fig. 1 left panel). The system then displays a variety of behaviours, including regular oscillations, chaotic dynamics, and quasi-periodic behaviour, as displayed in the right panel of Fig. 1. In Fig. 1 we have used a coupled-equation system comprising the Schrödinger wave equation and a cavity-field evolution [3], where we have adiabatically eliminated the latter leading to a conservative dynamics. The chaotic dynamics here is not induced by the detector noise and is an intrinsic property of the light-BEC interaction.Our second model considers a multiple-modes expansion. By using just three modes, the chaotic dynamics observed in the full simulation is recovered. The bifurcation structure, typical of conservative dynamics in the vicinity of a separatrix, is identified through the use of projections and power spectra. Our results suggest that chaotic oscillations in this system are deterministic in nature and arise purely from nonlinear effects. In more general terms, the model is a novel example of quantum matter exhibiting chaotic behaviour and invites further research.