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EFFECT OF THE DYNAMIC SHIFT ON THE QUANTUM ELECTRODYNAMICS OF AN ATOM MAKING TWO-PHOTONS IN AN IDEAL CAVITY

Tahira Nasreen

Published Jan 1, 1992• 0 citations
OpenAlex

Abstract

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.

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Journal of Atomic and Molecular Physics•Jan 1, 2007•0 citations
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.
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.
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.
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 atomic dipole squeezing and the emission spectra in a nondegenerate two-photon Jaynes–Cummings model in the presence of Stark shift for various field inputs are studied. The percentage duration of the atomic dipole squeezing is greatly enhanced by the inclusion of the Stark shift. The emission spectra show an asymmetric central two-peak structure that is quite different from that in the absence of the Stark shift. When the fields are initially in the coherent state, asymmetric coherent sidebands emerge. The effect of atomic coherence on dipole squeezing and the emission spectrum have also been incorporated
The cavity field spectrum of an atom interacting with a field in the presence of Stark shift is investigated. By solving the eigen equation, The expression of the cavity field spectrum is given out. Some numerical results for the initial field in pear number state are presented. The effects of Stark shift and initial photon number on the spectral structure are discussed. It is found that two Rabi peaks with equal height appear when the initial field is vacuum. Along with the accretion of Stark shift, the both peaks shift to lower frequency and the peak-space increases. In the case of strong input field, the heights of the two peaks are no longer equal. The Stark shift coefficient can be detected by measuring the relative height of the two peaks. With increasing of the Stark shift coefficient, the two peaks shift also to lower frequency but the peak-space decrease. In the case of weak input field, one of the two Stark shift coefficient affects one peak's height respectively. The spectral structure can be affected by the photon number and by one or two of the Stark sift coefficient sensitively.