We have studied the population trapping properties in the nondegenerate two - photon Jaynes-Cummings model in the presence of ac Stark shifts. The important influences of ac Stark shifts on the field inducing the atom to be trapped (called inducing trapping field) are pointed out and the properties of this field are analyzed.
By means of adiabatically eliminating the upper level or levels of a \ensuremath{\Lambda}-configuration atom coupling to a two-mode quantized field, we have studied the influences of ac Stark shifts on the atomic coherent population trapping in two important atom-field coupling systems via nondegenerate Raman two-photon processes. The states of the field that trap the atom in its two nondegenerate lower levels are obtained, and the important roles of ac Stark shifts and properties of the atomic upper level or levels in the states of the trapping field in two Raman-coupling systems are also analyzed.
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.
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.
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