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Journal of Physics B Atomic Molecular and Optical Physics

Emission spectrum of two-mode nonlinear Jaynes-Cummings model

Jian Feng, Gao Yun-feng, Mingsheng Zhan

Published Nov 10, 2000• 6 citations
Publisher

Abstract

The emission spectrum of a single atom in a two-mode Jaynes-Cummings model including any form of nonlinearity of both the two-mode fields and the intensity-dependent atom-field coupling is studied. A general expression for the emission spectrum is given as an explicit function of any nonlinear terms presented in the model. The effects of the nonlinearities on the spectrum are demonstrated for several important examples. It is shown that features of the emission spectrum are influenced significantly by the kinds of intensity-dependent atom-field coupling and the nonlinearities of the two-mode fields. It is also found in an analytic way that the effects on the emission spectrum of both the specific intensity-dependent nonlinear medium and the initial two-mode field photon statistics can be counterbalanced in some special cases.

DOI
10.1088/0953-4075/33/22/324

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The emission spectrum of a single atom in a two-mode Jaynes-Cummings model including any form of nonlinearity of both the two-mode fields and the intensity-dependent atom-field coupling is studied. A general expression for the emission spectrum is given as an explicit function of any nonlinear terms presented in the model. The effects of the nonlinearities on the spectrum are demonstrated for several important examples. It is shown that features of the emission spectrum are influenced significantly by the kinds of intensity-dependent atom-field coupling and the nonlinearities of the two-mode fields. It is also found in an analytic way that the effects on the emission spectrum of both the specific intensity-dependent nonlinear medium and the initial two-mode field photon statistics can be counterbalanced in some special cases.
The emission spectrum of a single atom in the nonlinear coupling J-C (Jaynes-Cummings) model including any forms of nonlinearities of both the field and the intensity-dependent atom-field coupling is studied.The effects of nonlinearities on the spectrum are demonstrated.It is shown that features of the emission spectrum are influenced significantly by the kinds of the field nonlinearity term R(a+a) and the intensity-dependent atom-field nonlinear coupling factor f(a+a).The structure of the spectrum is quite different from that of the standard J-C model.It is found that when f(a+a)=1/(a+a)1/2,the emission spectra always show the definite three-peak structure for any initial state of the field,which implies that the effects on the emission spectrum of both the specific intensity-dependent nonlinear medium with f(a+a)=1/(a+a)1/2 and the initial field photon statistics can be counterbalanced.This feature is analyzed with an analytic method.
The authors have investigated the spectrum of the emitted light by a single atom interacting with a single mode of the radiation in an ideal cavity via the intensity-dependent coupling (the Jaynes-Cummings model with intensity-dependent coupling see B. Buck, Phys. Lett., vol.A81, p.132 (1981)). From the authors' results it follows that in the resonant case the two-peaked structure of the spectrum associated with the vacuum-field Rabi splitting is preserved for any initial state of the radiation field (e.g. number state, thermal state, coherent state and the squeezed vacuum) with an arbitrary average number of photons.
The atom emission spectra of a nonlinear Jaynes-Cummings model with an additional Kerr medium are investigated.The emission spectrum expression is derived.The numerical results for the initial field in pure number state,coherent state and squeezed vacuum state are calculated,respectively.The influences of Kerr effect and initial field intensity on the spectrum structure are discussed.It is found that Kerr medium affects the symmetry of the spectrum structure for all initial field states except vacuum.When the initial field is pure number state,all peaks of the spectra shift toward right and the left peak(s) rise and right peaks decline along with accretion of Kerr effect.When the initial field is coherent state,two complicated multi-peak structure each like an arched comb appears for strong field.The Kerr effect makes left peaks higher and right peaks lower.When the initial field is squeezed vacuum state,only left sideband appears.The peak-number of the sideband increases due to the accretion of the Kerr effect or the initial field intensity.
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.
The time-dependent two-photon emission spectra of a two-level atom interacting with a single-mode radiation field in an ideal cavity have been studied. The expressions of the system operators as a function of time have been derived based on the two-photon Jaynes-Cummings model and Heisenberg equation. As a result, the theoretical curves of the time-dependent two-photon emission spectra have been given. The features of two-photon emission spectra depend not only on the photon statistical distribution of the initial field, such as the thermal field, the squeezed vacuum field, and the coherent field, but also on the passband width of the filter detector \ensuremath{\Gamma}. The two-photon emission spectra exhibit multi- peaked structures when \ensuremath{\Gamma}(two-photon coupling constant).