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Physical Review A

Stark effect in nonlinear Jaynes-Cummings models

David A. Cardimona, Vassilios I. Kovanis, M. P. Sharma

Published Feb 1, 1993• 15 citations
Publisher

Abstract

We investigate the effect of the Stark shifts on the atomic-inversion dynamics when a multilevel atom interacts with a two-mode quantized radiation field. We utilize Hamiltonians obtained by adiabatically eliminating all but two of the atomic levels and including terms that give rise to the Stark shifts for a Raman-type process as well as for equal- and unequal-frequency two-photon absorption. We find that the Stark effect is relatively unimportant for Raman scattering but should not be ignored in equal- or unequal-frequency absorption. In equal-frequency absorption, the atomic dynamics can be made exactly periodic through an appropriate choice of detuning.

DOI
10.1103/physreva.47.1227

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We investigate the effect of the Stark shifts on the atomic-inversion dynamics when a multilevel atom interacts with a two-mode quantized radiation field. We utilize Hamiltonians obtained by adiabatically eliminating all but two of the atomic levels and including terms that give rise to the Stark shifts for a Raman-type process as well as for equal- and unequal-frequency two-photon absorption. We find that the Stark effect is relatively unimportant for Raman scattering but should not be ignored in equal- or unequal-frequency absorption. In equal-frequency absorption, the atomic dynamics can be made exactly periodic through an appropriate choice of detuning.
We investigate the atomic inversion dynamics when a multilevel atom interacts with a two-mode quantized radiation field in a Raman-type process. By utilizing the rotating-wave approximation and adiabatically eliminating all but two of the atomic levels, we derive a nonlinear-interaction Hamiltonian for this system. Working in the Schr\"odinger picture, we obtain numerical results that depend on the width and average photon number of the field statistics. Varying these photon statistics allows us to uncover secondary revivals that arise due to the complicated double sum over the two field modes that appear in the solutions. The origin of this phenomenon is described analytically.
We consider a two-mode quantized field described in a coherent state interacting with a four-level atom. An effective Hamiltonian is obtained by adiabatically eliminating the intermediate two levels in a cascade process. The influence of the Stark shifts on the atomic inversion is examined, as well as on the second order auto-correlation function and on the cross-correlation between the field modes. The results of the calculations are illustrated numerically.   Key word: Adiabatic elimination, Stark-shift, second order auto-correlation function, cross-correlation between the field modes.
In this contribution, a three level atom in interaction with a two-mode quantized electromagnetic field, initially prepared in an entangled two-mode coherent state, is considered. Through the elimination of an intermediate level using the adiabatic elimination method, a nonlinear Stark shift is introduced. The exact solution of the wave function in the Schrödinger picture is obtained. Some statistical aspects through the effective two-level atom interacting with the two-mode and multiphotons processess with the nonlinear Stark shift are presented. The results are employed to perform a careful investigation of the temporal evolution of the atomic inversion, entropy squeezing and variance squeezing. It has been shown that the system is sensitive to any change in the parameter representation of the Stark shift. General conclusions reached are illustrated by numerical results.
In this thesis, we investigate the effect of the dynamical Stark shift on the quantum electrodynamics of an atom undergoing two-photon transitions, interacting with a quantized radiation field in an ideal cavity. To begin with, we discuss the dynamics of the electromagnetic field and the atom in the presence of the Stark shift. We derive closed expressions for the second-order coherence function, quadrature variances, atomic population inversion and dipole squeezing under the approximation of a large initial photon number and coherent or squeezed field input. We show that for an atom initially in the ground state, the inclusion of Stark shift reduces the field squeezing as well as the antibunching. Both the population inversion and the dipole squeezing exhibit phase sensitivity in the presence of Stark shift and for a particular choice of the relative phase of the two atomic levels "trapping" occurs in a two-level atom and the dipole is modified in such a way that it is permanently squeezed. We then discuss the effect of the stark shift on the emission spectrum of an atom and the cavity field spectrum. The inclusion of Stark shift results in asymmetric vacuum field Rabi splitting. We also study the dynamics of the combined atom-field wave function in the presence of the Stark shift and show that both the electromagnetic field and the atom periodically evolve to pure states which are radically different from those in the absence of the Stark shift. Finally, we study the nondegenerate two-photon Jaynes-Cummings model (NTPJCM) in the presence of the Stark shift and show that the dynamics of the NTPJCM in the presence of Stark shift is qualitatively different from the case of the absence of the Stark shift and radically different from the case of degenerate two-photon JCM in the presence of Stark shift.