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Institute of Physics eBooks

Time evolution of the single-wave?particle system

Published Nov 26, 2004• 0 citations
Publisher
DOI
10.1887/0750306122/b1104c8

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The wave-function of the system of single-mode field interacting with N-type four-level atom is solved exactly, and the time-evolution of atomic particle's occupancy is analyzed by means of numerical method. The N-type four-level atom is about equal to the two-level atom whose every level has double-skin fine structure, it could degenerate into V-type or Λ-type three-level atom even into simple two-level atom under some conditions. The results of the studies indicate that the time-evolution of atomic particle's occupancy of the four-level system is nonperiodic.
Under certain conditions it is possible to describe time evolution using different times for different particles. Use of multiple times is optional in the independent particle approximation, where interparticle interactions are removed, and the N-particle evolution operator factors into N single-particle evolution operators. In this limit one may use either a single time, with a single energy-time Fourier transform, or N different times with a different energy-time transform for each particle. The use of different times for different particles is fully justified when coherence between single-particle amplitudes is lost, e.g., if relatively strong randomly fluctuating residual fields influence each particle independently. However, when spatial correlation is present the use of multiple times is not feasible, even when the evolution of the particles is uncorrelated in time. Some calculations in simple atomic systems with and without spatial and temporal correlation between different electrons are included.
The Heisenberg spin cluster with two particles controlled by a time-dependent magnetic field is investigated. Since the system possesses an SU（2） algebraic structure, the exact analytical solution to time evolution operator can be obtained by using algebraic dynamical method. Based on the analytical solution, the time evolution of wave function of the two-particle system can be obtained, then the entanglement can be calculated easily. The time evolution of the entanglement for different initial states is studied, and the effect of external field on the entanglement is discussed as well.