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Time-evolution of a trapped Bose-Einstein Condensation in a quantum cavity - art. no. 60282E

L Zhang, C. Wang, Jinghang Wang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

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.

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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.
We discuss Bose-Einstein condensation in a trapped atomic gas and analyze how the sign of the scattering length a and the ratio \ensuremath{\eta} of the interaction between particles to the level spacing in the trap influence the behavior of the condensate wave function ${\ensuremath{\psi}}_{0}$. We find that for a<0a<0a<0 and $\ensuremath{\eta}\ensuremath{\ll}1$ it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For $\ensuremath{\eta}\ensuremath{\gg}1$ a negative scattering length prevents the formation of the condensate. If a>0a>0a>0, then an increase of density is accompanied by the evolution of ${\ensuremath{\psi}}_{0}$ to a comparatively wide quasihomogeneous distribution.
We study the dynamics of weakly interacting Bose-Einstein condensates consisting of alkali atoms with two or more internal eigenstates. Three separate problems are examined in this thesis, which look at the behavior of the condensates in the presence of electromagnetic fields, which couple the internal states of the atoms. First, we examine the ground state and quasiparticle excitations for a condensate with a spatially uniform and time independent field, which couples two of the internal states. In particular, we address the nature of the instabilities that have been predicted in these systems. Second, we look at the time evolution of small condensates with a time dependent field, which couples two states. It is shown that the atomic population in the two components, as a function of time, is very different for a condensate with a precisely defined number of atoms and one that exhibits spontaneous symmetry breaking. Finally, we propose two methods for mapping information about the quantum state of the condensate to a mode of an electromagnetic cavity. The first method, which is irreversible, is only able to transfer the population statistics of the condensate to the cavity field. The second method involves the adiabatic transfer of the quantum state of the condensate to the cavity field.