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Physical Review A

Emission spectra of an atom in a cavity in the presence of a squeezed vacuum

Julio R. Gea-Banacloche, Rainer R. Schlicher, Muhammad Suhail Zubairy

Published Oct 1, 1988• 80 citations
Publisher

Abstract

We have investigated the interaction of a single atom with a single mode of the radiation field in an ideal cavity when the field is initially in a squeezed-vacuum state. In particular, we present results for the spectrum of the emitted light and for the time evolution of the squeezing inside the cavity. Our results contrast sharply with previous studies of single two-level atom interaction with a continuum of squeezed-vacuum modes. In particular, the results are shown to be insensitive to the initial phase of the atomic dipole relative to the squeezed field, and the squeezing is destroyed by the coherent interaction, in a time essentially independent of the initial degree of squeezing. Most features of the spectrum are very similar to those predicted for an initial thermal state, although the two-peaked structure associated with vacuum-field Rabi splitting is more apparent for a squeezed state with a small average number of photons than for a thermal state with the same number of photons.

DOI
10.1103/physreva.38.3514

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We have investigated the interaction of a single atom with a single mode of the radiation field in an ideal cavity when the field is initially in a squeezed-vacuum state. In particular, we present results for the spectrum of the emitted light and for the time evolution of the squeezing inside the cavity. Our results contrast sharply with previous studies of single two-level atom interaction with a continuum of squeezed-vacuum modes. In particular, the results are shown to be insensitive to the initial phase of the atomic dipole relative to the squeezed field, and the squeezing is destroyed by the coherent interaction, in a time essentially independent of the initial degree of squeezing. Most features of the spectrum are very similar to those predicted for an initial thermal state, although the two-peaked structure associated with vacuum-field Rabi splitting is more apparent for a squeezed state with a small average number of photons than for a thermal state with the same number of photons.
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 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 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).
We investigate effects that the presence of a second atom has on the dynamic characteristics of a field and an atom in a single-mode cavity, with particular reference to the nonclassical features of the atom–field interaction. The field statistics are marginally altered, but the field and the atomic dipole squeezing are significantly altered. The vacuum-field Rabi splitting, which produces only two peaks in the emission spectrum of an isolated atom, gives a far more complex spectrum when another atom is present in the cavity.
In this paper, we investigate the dynamics of fluorescent light emitted by a two-level atom interacts with squeezed vacuum reservoir is studied wisely using two-time correlation function and the master equation fundamentals approaches. We use the pertinent master equation to calculate the time-evolution of cavity filed operators as well as two-time correlation function. The mathematical analysis shows the fluorescent spectrum of light emitted by the atom is turned out to be a single peak at a Lorentz's frequency for both squeezed vacuum reservoir and thermal reservoir. On the other hand, we have identified that the squeezed vacuum reservoir input is responsible to the stimulated emission of photons from the atom. Moreover, it is identified that thermal reservoir is more efficient than squeezed vacuum reservoir to have valuable power spectrum. The power spectrum which characterizes the fluorescent light generated by a two-level atom has been summered as it is observed for both case; (i) when a two-level atom coupled to squeezed vacuum reservoir and (ii) when the two-level atom coupled to thermal reservoir. Finally, we generalized from the paper is that the power spectrum of generated light from a two-level atom coupled to thermal reservoir is greater than the power spectrum generated from a two-level atom coupled to squeezed vacuum reservoir. In contrast, more stimulated and squeezed photons are emitted in the case when the atom is coupled with squeezed vacuum reservoir.