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Advanced materials research

The Dynamics in the Bose-Einstein Condensation Process with Interaction between Three Energy-Level Bose Atoms

Yan Min Li, Li Zhang, Chen Di Li

Published Nov 1, 2011• 0 citations
Publisher

Abstract

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.

DOI
10.4028/www.scientific.net/amr.403-408.2152

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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 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.
We investigate the energy structures and the dynamics of a Bose-Einstein condensates (BEC) in a triple-well potential coupled a high finesse optical cavity within a mean field approach. Due to the intrinsic atom-cavity field nonlinearity, several interesting phenomena arise which are the focuses of this work. For the energy structure, the bistability appears in the energy levels due to this atoms-cavity field nonlinearity, and the same phenomena can be found in the intra-cavity photons number. With an increase of the pump-cavity detunings, the higher and lower energy levels show a loop structure due to this cavity-mediated effects. In the dynamical process, an extensive numerical simulation of localization of the BECs for atoms initially trapped in one-, two-, and three-wells are performed for the symmetric and asymmetric cases in detail. It is shown that the the transition from oscillation to the localization can be modified by the cavity-mediated potential, which will enlarge the regions of oscillation. With the increasing of the atomic interaction, the oscillation is blocked and the localization emerges. The condensates atoms can be trapped either in one-, two-, or in three wells eventually where they are initially uploaded for certain parameters. In particular, we find that the transition from the oscillation to the localization is accompanied with some irregular regime where tunneling dynamics is dominated by chaos for this cavity-mediated system.
The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schrödinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s-wave. The lowest collective mode excitations are determined and their dependences on the number of atoms and on the strength of the three-body force are studied. The addition of three-body dynamics can allow the number of condensed atoms to increase considerably, even when the strength of the three-body force is very small compared with the strength of the two-body force. We study in detail the first-order liquid-gas phase transition for the condensed state, which can happen in a critical range of the effective three-body force parameter.