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Physical Review A

Comment on “Resonance fluorescence near a photonic band edge: Dressed-state Monte Carlo wave-function approach”

Klaus Mølmer, Søren Bay

Published Jan 1, 1999• 10 citations
Publisher

Abstract

Quang and John have, in a recent paper [Phys. Rev. A $56,$ 4273 (1997)], proposed a dressed-state Monte Carlo wave-function (MCWF) approach to a laser-driven two-level atom coupled to a structured radiation reservoir. In this Comment, we argue that this approach is at variance with the underlying physical idea of the MCWF technique, that it is at variance with basic formal requirements for the MCWF technique to apply, and that it produces spurious and unphysical quantitative results for wide ranges of parameters.

DOI
10.1103/physreva.59.904

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Quang and John have, in a recent paper [Phys. Rev. A 56,56,56, 4273 (1997)], proposed a dressed-state Monte Carlo wave-function (MCWF) approach to a laser-driven two-level atom coupled to a structured radiation reservoir. In this Comment, we argue that this approach is at variance with the underlying physical idea of the MCWF technique, that it is at variance with basic formal requirements for the MCWF technique to apply, and that it produces spurious and unphysical quantitative results for wide ranges of parameters.
We introduce a dressed-state Monte Carlo wave-function technique to describe resonance fluorescence in a broad class of non-Markovian reservoirs with strong atom-reservoir interaction. The method recaptures photon localization effects which are beyond the Born and Markovian approximations, and describes the influence of the driving field on the atom-reservoir interaction. Using this approach, we predict a number of fundamentally new features in resonance fluorescence near the edge of a photonic band gap. In particular, the atomic population exhibits inversion for moderate applied field intensity. For a low external field intensity, the atomic system retains a long-time memory of its initial state.
A numerical method of calculating the non-Markovian evolution of a driven atom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing a set of additional, virtual density matrices which follow, to the level of approximation of the algorithm, all the possible trajectories of the photons in the electromagnetic field. The technique is perturbative in the sense that more virtual density matrices are required as the product of the effective memory time and the effective coupling strength becomes larger. The number of density matrices required is given by 3M{3}^{M}3M where M is the number of time steps per memory time. The technique is applied to the problem of a driven two-level atom radiating close to a photonic band gap and the steady-state correlation function of the atom is calculated.
Resonance fluorescence consists of photon absorption and photon reemission by an atom interacting with a monochromatic, resonant and intense laser wave. The aim of this paper is to show that all fluorescence signals can be quantitatively calculated through the dressed atom method and that simple physical pictures can be associated to the results obtained in this manner. In such a method, the compound system «atom plus laser photons interacting together» (atom dressed by the laser photons) is first considered and the emission of fluorescence photons is then included as a radiative relaxation of this new quantum system. Emission frequencies thus appear as allowed Bohr frequencies of the dressed atom and Rabi nutation appears as a quantum beat signal between dressed states. Photon correlation and photon counting signals are well understood when fluorescence is considered as a radiative cascade of the dressed atom downwards its energy diagram. Mixed analysis time-frequency, for example study of temporal correlations between photons emitted in some sidebands of the fluorescence spectrum, is suggested by the dressed atom approach. Finally, when compared with the well known optical Bloch equations method, the dressed atom is shown to have a larger validity domain for the Markov approximation On montre que la methode de l'atome habille permet un calcul quantitatif de tous les signaux de fluorescence et associe les resultats a des interpretations physiques simples. Discussion des resultats et presentation des avantages de cette methode
We present a detailed theory of dressed-state lasers, i.e., the lasers that operate due to the gain on an inverted transition between dressed states of a coupled atom-field system. We derive effective Hamiltonians that describe such lasers for the case of one- and two-photon resonances. We argue that, due to the presence of nearly resonant intermediate states, the use of gain media consisting of strongly driven two-level atoms provides an unorthodox yet promising means for achieving cw optical two-photon laser oscillation. We disscuss the stability properties of radiation generated by such media.