We study propagation of low-intensity light in a medium within a one-dimensional ͑1D͒ model electrodynamics. It is shown that the coupled theory for light and matter fields may be solved, in principle exactly, by means of stochastic simulations that account for both collective linewidths and line shifts, and for quantum statistical position correlations of the atoms. Such simulations require that one synthesize atomic positions that have correlation functions appropriate for the given type of atomic sample. We demonstrate how one may simulate both a Bose-Einstein condensate ͑BEC͒ and a zero-temperature noninteracting Fermi-Dirac gas. Results of simulations of light propagation in such quantum degenerate gases are compared with analytical density expansions obtained by adapting the approach of Morice, Castin, and Dalibard ͓Phys. Rev. A 51, 3896 ͑1995͔͒ to the 1D electrodynamics. A BEC exhibits an optical resonance that narrows and stays somewhat below the atomic resonance frequency as collective effects set in with increasing atom density. The first two terms in the analytical density expansion are in excellent agreement with numerical results for a condensate. While fermions display a similar narrowing and shift of the resonance with increasing density, already in the limit of very dilute gas the linewidth is only half of the resonance linewidth of an isolated atom. We attribute this to the regular spacing between the atoms, which is enforced by the Pauli exclusion principle. The analytical density expansion successfully predicts the narrowing, and also gives the next term in the density expansion of the optical response in semiquantitative agreement with numerical simulations.

Recent numerical work has demonstrated how one of the bistable states of a driven, damped, anharmonic classical oscillator is metastable in the corresponding quantum oscillator ͓D. Enzer and G. Gabrielse, Phys. Rev. Lett. 78, 1211 ͑1997͔͒. Based on an analysis of the classical oscillator, we present a simple analytical treatment of the quantum oscillator. Calculated fluctuations in the quantum observables and the estimated decay rate of the metastable state are in an excellent agreement with the numerical results of Enzer and Gabrielse.

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