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Physical Review A

Two-level system interacting with a finite-bandwidth thermal cavity mode

J. I. Cirac, Helmut Ritsch, P. Zoller

Published Oct 1, 1991• 56 citations
Publisher

Abstract

The interaction of a two-level system with a single quantized mode of the radiation field of finite bandwidth in a thermal state and coupled to background vacuum modes is considered theoretically. A hierarchy of equations for atom-field moments is derived and solved in terms of continued fractions. The population inversion, the spectrum of resonance fluorescence, and the photon statistics of the cavity mode are calculated.

DOI
10.1103/physreva.44.4541

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The interaction of a two-level atom with a single mode of the radiation field is examined. The cavity mode is damped by coupling to a reservoir in a squeezed state, and the atom is also driven by an external laser field. A master equation for the atomic density operator in the bad-cavity limit is derived. The effect of the squeezing in the stationary population inversion and in the resonance spectrum of the light emitted by the atom into the background modes is studied. The results are compared with the numerical solution of the full master equation for the atom-plus-cavity mode-density operator.
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The interaction of a two-level atom with a single-mode radiation field through multiphoton transitions is studied in terms of the dressed-state formalism. It is shown that when only certain dressed states are initially excited, population trapping occurs. We particularize these results for some well-known models of one- and two-photon transitions. Photon statistics of the cavity mode is analyzed in terms of the quasiprobability distribution Q(\ensuremath{\alpha}). It is shown that when population trapping occurs some two-time correlation functions become stationary, which allows one to obtain the resonance spectrum as the Fourier transform of the two-time dipole autocorrelation function.
Analysis of the effects of a finite bandwidth squeezed input on the atomic dynamics and radiative properties of a coherently pumped two-level atom trapped in a resonant cavity is presented. It is found that the atom prefers to stay in the lower energy level more often at steady state regardless of the strength of the coherent radiation and squeezed input. Pronounced dipping in the population inversion occurs when the finiteness of the bandwidth of the reservoir modes is taken into consideration. Moreover, due to the narrowing of the bandwidth, the spectral width of the emitted radiation turns out to increase and the height of the central line to decrease with the strength of the squeezed input. The peaks of the sidebands become prominent and shifted side ways with the strength of the amplification constant of the parametric oscillation. It is also found that the emitted radiation exhibits photon anti-bunching, whereas the photon statistics oscillates between sub- and super-Poissonian. Unfortunately, the successively emitted cavity radiation does not exhibit squeezing despite the presence of the squeezed input.
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