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Journal of Physics B Atomic and Molecular Physics

Theory of n-fold time-resolved correlation spectroscopy and its application to resonance fluorescence radiation

L. Knöll, G Weber

Published Sep 28, 1986• 22 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/19/18/012

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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.
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.
The authors give a theoretical description of the spectrally resolved intensity correlations of an electromagnetic field, in analogy with the definition of the physical time-dependent spectrum. The results are applied to evaluate the time correlations between the three lines in the spectrum of resonance fluorescence of a two-level atom. The authors include the possibility of a finite bandwidth of the incident radiation, and they allow for collisions with perturber atoms. Photons in the central Rayleigh line are emitted in a fully random fashion, without any correlation with previous or subsequent emissions. Two photons from the same sideband display antibunching in time, whereas two photons from opposite sidebands tend to bunch with a strong asymmetry in time. The effect of collisions and of a finite bandwidth is to diminish this asymmetry.
Recently, the concept of an ''NNN-photon spectrum'' -- a spectrally resolved NNN-photon correlation function -- has been introduced as an innovative quantum optics characterization tool that uniquely reveals information about pathways underlying the generation of light in a given source. Here, the authors investigate experimentally the three-photon spectrum of resonance fluorescence from a single semiconductor quantum dot. The observations agree with previous theoretical work, revealing significantly more pronounced photon antibunching at the Mollow triplet sidebands and more strongly correlated emission through virtual states compared to the two-photon counterpart.
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
Time-dependent features of the fluorescence radiation from a strongly driven three-level atom in a Raman configuration are studied applying the Eberly-W\'odkiewicz counting-rate definition of the spectrum. Using our earlier formalism, where we assume that one or both of the driving fields are intense, we obtain analytical expressions for the time-dependent fluorescence spectra. We have also studied the influence on the transient spectrum of the initial preparation of the atom in three different dressed states.