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Journal of Physics B Atomic and Molecular Physics

Time dependence of multiphoton scattering processes

P. Stehle

Published Feb 14, 1982• 3 citations
Publisher

Abstract

The time-dependent amplitudes describing the evolution of the state of a system consisting of an atom illuminated by a single-mode laser starting at time t=0 are given. They are used to derive the time dependence of the spectrum of resonance fluorescence of a three-level atom and to obtain a description of the time and frequency correlation of successively scattered photons.

DOI
10.1088/0022-3700/15/3/021

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The time-dependent amplitudes describing the evolution of the state of a system consisting of an atom illuminated by a single-mode laser starting at time t=0 are given. They are used to derive the time dependence of the spectrum of resonance fluorescence of a three-level atom and to obtain a description of the time and frequency correlation of successively scattered photons.
Extending the concept of the time-dependent physical spectrum introduced by Eberly and Wodkiewicz (1977) the authors present a formula for the n-fold time-resolved correlation spectrum depending on n time and n frequency arguments. The corresponding measuring device consists of n coupled photodetectors with frequency resolving equipment in front of each. As an application the authors consider the resonance fluorescence radiation of a two-level atom irradiated monochromatically. Under certain conditions the authors derive a simple expression for the n-fold detection probability of photons at time t i (i=1, . . ., n) with frequencies belonging to the central peak or to one of the sidebands of the fluorescence triplet.
Attention is focused on the dynamic evolution of the emission spectrum following abrupt excitation of a near-resonant two-level absorber by a strong laser field. The multiphoton character of the absorption-emission process is evident in the AC Stark splitting of the spectrum, which begins approximately half an atomic lifetime after excitation, if the laser field is strong enough. Analytic expressions for the spectra are given of arbitrary laser field strength, atomic lifetime, laser-atom detuning, and the bandwidth of the spectrometer used to analyse the spectrum. Selected graphs are included to illustrate various time-dependent features of the spectrum. The influence on the transient spectrum of three different states of atomic excitation prior to laser irradiation and the effect on the spectrum of irradiation by a phase-noisy laser are also considered. Comparison of the transient spectra from atoms initially prepared in ' pi /2' and '3 pi /2' states show clearly that phase relationships between the irradiating field and the emitting dipole are important even in fluorescence.
Using the concept of the time-dependent physical spectrum introduced by Eberly and Wodkiewicz (1977) the authors develop the theoretical basis of time-resolved correlation spectroscopy. The corresponding measuring device consists of two coupled photodetectors with frequency resolving equipment in front of each. A formula is presented for the time-resolved correlation spectrum depending on two time and two frequency arguments. It may be used to gain insight into the time correlation of photons with given frequencies. The authors apply the theory to the resonance fluorescence radiation of a two-level atom irradiated monochromatically. It is shown that in the case of a weak irradiation with large detuning the photons are emitted in a definite time order into the two sidebands of the fluorescence triplet. Under strong resonant irradiation the photons show up bunching (antibunching) behaviour if they belong to different (equal) sidebands. In addition to these results which are already known the authors present new results concerning intermediate situations.