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Physical Review A

Atomic-dipole squeezing and emission spectra of the nondegenerate two-photon Jaynes-Cummings model

M. M. Ashraf, M. S. K. Razmi

Published Jun 1, 1992• 56 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.45.8121

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arXiv:quant-ph/0504184•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 11, 2006•0 citations
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 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 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).
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.
An exact solution is found for the collective model of two identical two-level atoms that resonantly interact with a two-mode quantum electromagnetic field in an ideal cavity via two-photon nondegenerate transitions. In the case under study, at the initial moment, both field modes are in the coherent state and atoms are in the excited state. The time dependences of the atomic probabilities, the mean number of photons in the modes, and the statistics and squeezing of the photon modes are studied based on the exact solution.