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Journal of the Optical Society of America B

Two-photon atomic transitions with a squeezed cavity field and Stark shift

Tahira Nasreen, M. S. K. Razmi

Published Nov 1, 1991• 13 citations
Publisher

Abstract

The problem of a single atom making two-photon transitions in the presence of a cavity field that is initially in the general squeezed state or squeezed vacuum state is studied. Closed expressions for the atomic inversion, the second-order coherence function, and the quadrature variances are derived under the assumption of a large initial average photon number and a squeezed field input. The effects of Stark shift on these quantities are analyzed and discussed. We see collapses and revivals of atomic inversion and the second-order coherence function with a general squeezed input, but none are apparent when the input is in the squeezed vacuum state. Perodic revivals of squeezing are seen.

DOI
10.1364/josab.8.002303

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The problem of a single atom making two-photon transitions in the presence of a cavity field that is initially in the general squeezed state or squeezed vacuum state is studied. Closed expressions for the atomic inversion, the second-order coherence function, and the quadrature variances are derived under the assumption of a large initial average photon number and a squeezed field input. The effects of Stark shift on these quantities are analyzed and discussed. We see collapses and revivals of atomic inversion and the second-order coherence function with a general squeezed input, but none are apparent when the input is in the squeezed vacuum state. Perodic revivals of squeezing are seen.
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.
It is shown that a single atom making two-photon transitions in an ideal cavity (Q = ∞) in the presence of an initial coherent state field will, as expected, continue to show the collapses and revivals of atomic inversion and the intensity–intensity correlation of the field; however, these collapses and revivals are both compact and regular, in contrast to the one-photon case. This is because, although the several Rabi frequencies involved are incommensurate, for the two-photon case, unlike for the one-photon problem, they become commensurate in the limit of intense field. We derive analytic expressions for the atomic inversion and the intensity–intensity correlation in the case of direct, as well as homodyned, detection of the intracavity field. The effects of the Stark shift are discussed.
Atomic-dipole squeezing in the presence of the Stark shift in two-photon Jaynes-Cummings model for an atom initially prepared in a coherent superposition of states, interacting with the coherent- or squeezed-vacuum-state field, is studied. Closed expressions for dispersive and absorptive components of the dipole for the coherent-field input under the large-n\ifmmode\bar\else\textasciimacron\fi{} approximation are derived. It is shown that atomic-dipole squeezing is sensitive to both the phase of the initial field and the relative phase between the two atomic levels. Our results show that, for certain choices of these phases, permanent dipole squeezing can be obtained.
A generalized Jaynes–Cummings model including the Stark shifts is investigated where the transition is mediated by two different modes of photons. For two different types of correlated field states, the pair coherent states and two-mode SU(1, 1) coherent states, the effect of including the Stark shift on the dynamical behavior of atomic inversion, atomic squeezing parameters, second order coherence function, and photon number distribution is investigated. Our results indicate significant changes in the behavior of these quantities for large and small average photon number <n> in the presence and absence of Stark shift and depending on the type of correlated field involved.
The cavity field spectrum of an atom interacting with two-mode squeezed vacuum fields in the presence of Stark shift is investigated.The expression of cavity field spectrum and some numerical results are presented.The effects of Stark shift and initial field intensity on the spectrum structure are discussed.It is found that the peak positions are sensitive to the Stark-shift while the peak heights are not under the condition of weak initial fields.Whenn1=n2≥2,the central peak of each mode rises and the other peaks reduce along with the accretion of the Stark-shift coefficients.Various spectral structures may be gained by changing of the Stark-shift coefficients or initial fields.