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Communications in Theoretical Physics

Population Dynamics and Emission Spectrum of a Cascade Three-Level Jaynes–Cummings Model with Intensity-Dependent Coupling in a Kerr-like Medium

Qingchun Zhou

Published Apr 1, 2006• 1 citation
Publisher

Abstract

By using the method of eigenvectors, the atomic populations and emission spectrum are investigated in a system that consists of a cascade three-level atom resonantly interacting with a single-mode field in a Kerr-like medium. The atom and the field are assumed to be initially in the upper atomic state and the Fock state, respectively. Results for models with intensity-dependent coupling and with intensity-independent coupling are compared. It is found that both population dynamics and emission spectrum show no indications of atom-field decoupling in the strong field limit if the intensity-dependent coupling is taken into account.

DOI
10.1088/0253-6102/45/4/030

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By using the method of eigenvectors, the atomic populations and emission spectrum are investigated in a system that consists of a cascade three-level atom resonantly interacting with a single-mode field in a Kerr-like medium. The atom and the field are assumed to be initially in the upper atomic state and the Fock state, respectively. Results for models with intensity-dependent coupling and with intensity-independent coupling are compared. It is found that both population dynamics and emission spectrum show no indications of atom-field decoupling in the strong field limit if the intensity-dependent coupling is taken into account.
The eigenfunction method is adopted to investigate atomic emission and cavity field spectra in the system containing a Λ-type three-level atom resonantly' interacting with a single-mode field.The atom is assumed initially in the upper atomic state and intensity-dependent coupling is taken into account.It is found that the splitting between the lower levels has a great influence on the spectral structure for both the emission spectrum and the cavity field spectrum.Combination of spectral lines does not take place with increasing intensity of the initial field and the cavity spectrum is not sensitive to the statistics of the initial field.
By using the method of eigenvalues and eigenstates, the emission and cavity-field spectra of a cascade three-level atom interacting with a single-mode electromagnetic field are studied in both intensity-dependent coupling (IDC) and intensity-independent coupling (IIC) cases. The photon statistics of the field on the spectra are investigated for the initial field in the pure number state, the coherent state and the thermal state. In the resonant case and the strong field limit, the pure-number-state emission spectrum exhibits six peaks and three peaks, respectively, for the IDC case and the IIC case. For a strong initial coherent state field or a strong thermal state field, the central structure of the emission spectrum at the field frequency is a doublet in the IDC case and a singlet in the IIC case. The cavity-field spectrum has three peaks in the IDC case and a single peak in the IIC case in the strong field limit for all of the three kinds of initial fields considered. Results indicate that in the emission spectrum merging of spectral peaks occurs for the IIC case as the initial field becomes stronger while it does not happen for the IDC case.
The cavity field spectrum of a cascade three-level atom interacting with single-mode field with Kerr-like medium in the cavity is investigated. The numerical results for the initial field in pure number state, coherent state and squeezed vacuum state are calculated, respectively. It is found that the Kerr-like medium affects the spectral structure even though the initial field is in vacuum when the atom is in upper level. In the case of strong input field, the number state spectrum shows two peaks with different heights; and the superposition state spectrum shows a multi-peak structure with an equal distance of two neighboring peaks. The spectral ``central frequency" shifts away from the resonant frequency with the increasing of average photon number.
A full quantum theory is applied to the investigation of the cavity field spectrum of a system containing the cascade three-level atom,initially in the most excited state,interacting with the single mode of a Kerr-medium filled cavity.The vacuum Rabi splitting of the system is found affected by Kerr nonlinearity,contrary to the two-level atom case.For an initial Fock-state field,the Kerr effects are mainly reflected by the asymmetry of the spectrum and a change in the number of spectral peaks if the coupling between the field and the Kerr medium is weak.The effects are also reflected by receding away from the resonant frequency of the central resonant peak in the absence of the Kerr medium if the field-medium coupling is strong.For an initial thermal field,the cavity spectrum can be a continuous band or discrete lines depending on the strength of the Kerr effect.
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.