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Journal of Yangtze University

Dynamic Behavior of Atoms in Time-dependent Nonlinear Jayres-Cummings(J-C)Model

Pei Qi-ming

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The dynamic behavior of atoms in time-dependent nonlinear J-C model is studied. The influ- ence of pulse width and average photon number on dynamic behavior of atoms as the atoms are cou- pled with photon field in the form of time pulse is discussed. The result shows that when the average photon number is fixed in the field,with the increase of pulse width,the collapse and revival number are enhanced,while the time of collapse and period of revival are reduced. When the pulse width is fixed,the time of collapse and revival period are reduced gradually with the increase of pulse width in the field.

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The dynamic behavior of atoms in time-dependent nonlinear J-C model is studied. The influ- ence of pulse width and average photon number on dynamic behavior of atoms as the atoms are cou- pled with photon field in the form of time pulse is discussed. The result shows that when the average photon number is fixed in the field,with the increase of pulse width,the collapse and revival number are enhanced,while the time of collapse and period of revival are reduced. When the pulse width is fixed,the time of collapse and revival period are reduced gradually with the increase of pulse width in the field.
When the light field was initially in the coherent state and the atom was in the excited state,the effect of amplitude-squared squeezing of light field in the nonliner model containing time was discussed.It was found that average photon numbers and the pulse width had greatly influence on the depth and the time of squeezing.When the pulse width is certain value,the squeezing depth increases with average photon numbers increasing.When the average photon numbers is certain value,the times and time of squeezing gradually increase with the pulse width increasing.
The time evolution of atomic occupancy for the system of squeezed vacuum field interacting with two coupling atoms via intensity-dependent coupling in two-photon transition are investigated. The influences of the atomic initial state, the interaction between atoms and the initial squeezed parameter of field on the atomic occupancy are discussed. The results show that periodical collapse-revival phenomenon of the time evolution of atomic occupancy appears, which is caused by the influence of the dipole-dipole interaction between atoms. The periods of the collapse-revival shortens till the collapse-revival disappears while increasing the interaction between atoms. The amplitude of oscillations decreases in increasing the initial squeezed parameter of field.
With the help of a two-photon Jaynes-Cummings model, which is an exactly solvable model, we have dealt analytically with the dynamical behavior of the atom and the field for a two-photon process in squeezed and coherent fields under the appropriate approximation. The features of collapses and revivals of Rabi oscillations for the atom and the field in a two-photon process represent strict periodicity. The phase jump and the large and negative frequency for the combination Rabi oscillation are exhibited in the case of a squeezed field. The results show that squeezing in a field strikingly affects the evolution behavior of the atom and the field.
By means of simple mathematical methods, typical properties of the quantum dynamics in the Jaynes-Cummings model are discussed. The methods used allow a clear physical interpretation in the sense of an ensemble average and permit an investigation of the influence of the initial photon distribution width on collapse and revivals. Results obtained by a more sophisticated treatment provide corrections which are on the order 1/ square root N/sub 0/ for N/sub 0/>>1 where N/sub 0/ is the average photon number. The time evolution of the electric field strength and the photon distribution are also studied.>
The driven two-photon Jaynes-Cummings model (JCM) exhibits a collapse and revival phenomenon in its mean photon number on a time scale much larger than the periodic revival time for two-state inversion in the usual two-photon JCM. The time scale of revivals for these oscillations is much larger than the corresponding time scale for the driven one-photon JCM and can be explained with the Hamiltonian of type ${H}_{\ensuremath{\eta}}=\ifmmode\pm\else\textpm\fi{}\sqrt{{(J}_{\ensuremath{\eta}}^{\ifmmode\dagger\else\textdagger\fi{}}+\ensuremath{\alpha}{P}_{\ensuremath{\eta}}{)}^{2}{(J}_{\ensuremath{\eta}}+\ensuremath{\alpha}{P}_{\ensuremath{\eta}}{)}^{2}}$ constructed explicitly for this purpose. The effect of Stark shifts is also studied and it is observed that the dynamics is strongly influenced by such Stark shifts both at early stages as well as at late stages of the evolution but in different ways, and thus Stark shifts play a significant role in determining the dynamical evolution of the system.