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Physical Review A

Nonlinear spectroscopy with time- and frequency-gated photon counting: A superoperator diagrammatic approach

Konstantin E. Dorfman, Shaul Mukamel

Published Jul 9, 2012• 26 citations
Publisher

Abstract

We present a diagrammatic technique for calculating quantum-detected nonlinear optical signals using loop diagrams that act in the joint matter plus field space. This formalism, which is based on time-ordered superoperators keeps track of the entangled matter plus field state, making it most suitable for spectroscopy applications. Photon counting is recast as a time and frequency convolution of a bare signal, which is given by a correlation function of matter, and a gating spectrogram.

DOI
10.1103/physreva.86.013810

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Time- and frequency-gated two-photon counting is given by a four-time correlation function of the electric field. This reduces to two times with purely time gating. We calculate this function for entangled photon pulses generated by parametric down-conversion. At low intensity, the pulses consist of well-separated photon pairs, and crossover to squeezed light as the intensity is increased. This is illustrated by the two-photon absorption signal of a three-level model, which scales linearly for a weak pump intensity where both photons come from the same pair, and gradually becomes nonlinear as the intensity is increased. We find that the strong frequency correlations of entangled photon pairs persist even for higher photon numbers. This could help facilitate the application of these pulses to nonlinear spectroscopy, where these correlations can be used to manipulate congested signals.
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By variation of the photon statistics and the entanglement between time and frequency components, quantum states of light feature spectroscopy signals which are not subject to classical Fourier limitations on temporal and spectral resolution. This review surveys the properties of entangled photon pairs relevant to spectroscopic applications and it presents an intuitive diagrammatic approach which allows calculation of a variety of ultrafast, nonlinear spectroscopy signals from multilevel model systems exposed to quantum light.
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