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Journal of the Optical Society of America B

Atomic emission and cavity field spectra for a two-photon Jaynes–Cummings model in the presence of the Stark shift

Tahira Nasreen, M. S. K. Razmi

Published Jul 1, 1993• 40 citations
Publisher

Abstract

The emission spectrum of the atom and the cavity field spectrum of the two-photon Jaynes–Cummings model are studied, with the input field assumed to be in a number state, a thermal state, a squeezed vacuum state, and a coherent state. The effects of the Stark shift are highlighted. Both the emission and the cavity field spectra show central two-peak structures and no sidebands. A comparison with the one-photon Jaynes–Cummings model is carried out.

DOI
10.1364/josab.10.001292

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The emission spectrum of the atom and the cavity field spectrum of the two-photon Jaynes–Cummings model are studied, with the input field assumed to be in a number state, a thermal state, a squeezed vacuum state, and a coherent state. The effects of the Stark shift are highlighted. Both the emission and the cavity field spectra show central two-peak structures and no sidebands. A comparison with the one-photon Jaynes–Cummings model is carried out.
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.
The field spectra in an ideal cavity for the multiphoton Jaynes-Cummings model are studied. The analytical expression for the spectrum is obtained from the finite double-Fourier transform of the two-time field correlation function. The spectral differences between the initial coherent and initial thermal states are discussed, and the comparisons between the field spectra and atomic emission spectra for k = 2, 3 and 4 are presented. It is shown that the kth power of the photon annihilation operator and atomic lowering operator are subjected to identical forms of a second-order differential equation, in which the coefficients consist of the constants of motion. The field spectrum in the cavity and the emission spectrum of the atom for the initial vacuum state are compared.
The cavity field spectra for various initial fields of a nondegenerate two-photon Jaynes-Cummings Model are investigated. It is shown that the two-peak structure due to the resonant interaction between a single two-level atom and two different mode fields inside a high-Q cavity persists for coherent and thermal cases. Moreover, coherent sidebands appear for a coherent field whose widths are governed by the field statistics. However, squeezed vacuum fields exhibit rather different features showing the classical resonance fluorescence spectra at large n\ifmmode\bar\else\textasciimacron\fi{} (even in two-photon transitions).
A nondegenerate two-photon Jaynes-Cummings model is analyzed for its atomic-dipole squeezing and emission spectra. The input fields are assumed to be coherent or squeezed. The atomic dipole squeezes both for the on- and off-resonance excitations, showing a greater amount of squeezing for the former. The emission spectrum shows a central-two-peak structure for a variety of field inputs. When the fields are initially in coherent or squeezed states, sidebands appear whose widths are governed by the input-field statistics.
The emission spectra of an atom in a cavity for the multiphoton Jaynes–Cummings model are investigated. Using Eberly's formula for the time-dependent physical spectrum, the analytical expression for the atomic emission spectrum is obtained from the two-time dipole-moment correlation function of the atom. The appearance of two strong peaks in the spectrum is explained in detail, and the relationship between the initial photon distributions and the shapes of the spectra are examined. The fundamental differences in the atomic emission spectra for the two-photon and multiphoton models are specified. Furthermore, the role of the detector filter is thoroughly studied. It is explicitly shown that the atomic emission spectra can be obtained by averaging over the convolution integrals between the Fourier transform of the atomic dipole-moment correlation function associated with a pure number state and the detector filter function on frequency domain. The comparisons of the spectra for a coherent initial field to those for a thermal initial field are presented.