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Results in Physics

Effect of cavity leakage on time-dependent spectrum of two atoms Tavis-Cummings model

Qiang Gao, Yunjie Xia

Published Jan 20, 2023• 0 citations
Publisher

Abstract

We study the atomic emission spectrum and cavity field spectrum of dipole–dipole coupled two atoms interacting with a single-mode radiation field in a non-ideal cavity. We solved the quantum master equation by a method that combined analytical analysis and numerical solution. The explicit expression of spectral peak position and numerical results of spectral structure are given for the atoms in entangled state and the field in vacuum initially. The results shown that the decay rate of cavity field has obvious influence on the intensity of spectra but a little effect on the spectral structure. The cavity dissipation makes also the measurement time an important factor in measuring spectral structure.

DOI
10.1016/j.rinp.2023.106231

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We study the atomic emission spectrum and cavity field spectrum of dipole–dipole coupled two atoms interacting with a single-mode radiation field in a non-ideal cavity. We solved the quantum master equation by a method that combined analytical analysis and numerical solution. The explicit expression of spectral peak position and numerical results of spectral structure are given for the atoms in entangled state and the field in vacuum initially. The results shown that the decay rate of cavity field has obvious influence on the intensity of spectra but a little effect on the spectral structure. The cavity dissipation makes also the measurement time an important factor in measuring spectral structure.
The emission spectrum of a two-level atom interacting dispersively with a single mode radiation field in the dissipative cavity is investigated. A general expression for the emission spectrum is derived. The numerical results for the initial field in coherent state are calculated. It is found that the spectrum structure is influenced significantly by the cavity damping constant κ, and the spectrum structure is dependent on the interaction time T when the cavity dissipation is present. Only one peak located at ω a appears in the atomic spectra for larger T.
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).
The emission spectrum of a pair of two-level atoms interacting with a single mode of radiation field in an ideal cavity is investigated, where the interaction of each atom with the field may be different. A general expression for the emission spectrum is presented and the spectrum is studied numerically when the radiation field is initially in the vacuum state, pure number state and squeezed-vacuum state, respectively. The effects of the ratio of two coupling constants (R=g 2 /g 1 ) on the emission spectrum are discussed. In contrast with the spectrum of a one-atom system, the spectrum of a two-atom system is much more complicated. Generally, the emission spectrum shows a 12-peak structure for the vacuum state and 16-peak structure for the pure number state. For the squeezed-vacuum state, it is found that the Rabi splitting is most apparent when R=1.
The cavity field spectrum of a pair of coupled two-level atoms interacting with single mode field is studied. The results for the initial fields in pure number state, coherent state or squeezed vacuum state are presented and discussed. The effect of dipole-dipole coupling constant gαp on the cavity field spectrum is analyzed. It is found that four Rabi peaks appear for small gαp and three Rabi peaks for large gα when the field is vacuum initially. When the field is pure number state initially, the structure of the cavity field spectrum is five peaks for weak field and three peaks for strong field. When the fields are in a coherent state or squeezed vacuum state, a multi-peak structure appears generally. The peak-position and peak-height of the spectrum are both influenced by gα, but this influence is evident for weak field only.
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 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.