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Physical Review A

Theory of fluorescence and probe absorption in the presence of a driving field using semiclassical dressed states

P. R. Berman

Published Apr 1, 1996• 25 citations
Publisher

Abstract

A theory of resonance fluorescence in a monochromatic field and pump-probe spectroscopy is developed using semiclassical dressed states. The semiclassical dressed states are obtained via a rotation from the time-dependent state vectors in a field-interaction representation. Although the semiclassical dressed states are not stationary states as are the dressed states in a quantized-field formulation, they still offer all the conceptual advantages of a dressed-atom approach. Moreover, the line-shape formulas can be obtained directly from physically intuitive equations, without having to invoke the quantum regression theorem and without having to worry about cascades and coherences in the ladder of quantized dressed states. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.2627

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A theory of resonance fluorescence in a monochromatic field and pump-probe spectroscopy is developed using semiclassical dressed states. The semiclassical dressed states are obtained via a rotation from the time-dependent state vectors in a field-interaction representation. Although the semiclassical dressed states are not stationary states as are the dressed states in a quantized-field formulation, they still offer all the conceptual advantages of a dressed-atom approach. Moreover, the line-shape formulas can be obtained directly from physically intuitive equations, without having to invoke the quantum regression theorem and without having to worry about cascades and coherences in the ladder of quantized dressed states. \textcopyright{} 1996 The American Physical Society.
A semiclassical approach to the dressed-atom theory is presented in which dressed energies and states are determined from the solutions of the semiclassical coupled equations for the atomic probability amplitudes. The semiclassical approach has an advantage over the standard quantum-mechanical approach, especially when an atom interacting with a nonmonochromatic field is considered, because the standard approach requires diagonalization of an infinite-dimensional Hamiltonian matrix for an evaluation of dressed energies and states. Explicit expressions for dressed states of a two-level atom interacting with a resonant monochromatic, bichromatic, and trichromatic field are given.
The perturbation of atomic spectra by strong resonant optical driving fields can be analyzed to provide fundamental information regarding the physics of light–matter interaction. It is now well known that cw driving fields split the resonance fluorescence spectrum into three components and probe spectra (representing, for example, absorption from one terminal level of a strongly driven transition) into two components. These splittings are conveniently explained in terms of transitions between various eigenstates (dressed states1) of the coupled atom-field system.
The theory of resonance Raman effect, resonantly enhanced two-photon absorption, and resonance fluorescence---valid also for strong fields---is treated in a unified and simplified way. Dressed states, Bloch equations, and perturbation theory are used to calculate line positions, and integrated intensities both for steady state and transient excitation. The case of adiabatic following is solved explicitly; it occurs when an off-resonance incident pulse is turned on and off slowly. It leads to the identification of Raman scattering, two-photon absorption, and Rayleigh scattering with an adiabatic process while fluorescence and consecutive two-photon absorption with nonadiabaticity. Time-dependent spectra are defined in a rigorous way. Our formulas agree in the various limits with those that appear in the literature.
A theory of pump-probe spectroscopy is developed in which optical fields drive two-quantum, Raman-like transitions between ground-state sublevels. Three fields are incident on an ensemble of atoms. Two of the fields act as the pump field for the two-quantum transitions. The absorption or gain of an additional probe field is monitored as a function of its detuning from one of the fields which constitutes the pump field. Although the probe absorption spectrum displays features common to those found in pump-probe spectroscopy of single-quantum transitions, new interference effects are found to modify the spectrum. Many of these features can be explained within the context of a dressed-atom picture.
A canonical transformation, which diagonalizes the single-mode radiation Hamiltonian in the rotating wave approximation, is exploited to dress a two-level atom by the strong monochromatic driving field in the resonance fluorescence phenomenon. Langevin equations of motion are obtained for dressed atomic operators, and their solutions yield the amplitude of waves scattered into the fluorescence field. The power spectrum of the scattered field is obtained from the first-order correlation functions between dressed atomic operators. The results of the present treatment are compared with others, and advantages and disadvantages of the present method are discussed.
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