Abstract
Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. We present an intuitive diagrammatic approach for calculating ultrafast spectroscopy signals induced by quantum light, focusing on applications involving entangled photons with nonclassical bandwidth properties - known as "time-energy entanglement". Nonlinear optical signals induced by quantized light fields are expressed using time ordered multipoint correlation functions of superoperators. These are different from Glauber's g- functions for photon counting which use normally ordered products of ordinary operators. Entangled photon pairs are not subjected to the classical Fourier limitations on the joint temporal and spectral resolution. After a brief survey of properties of entangled photon pairs relevant to their spectroscopic applications, different optical signals, and photon counting setups are discussed and illustrated for simple multi-level model systems.
Highlights
Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays
Two-photon-emitted fluorescence (TPEF) vs. type-I parametric down conversion (PDC)
Generation and entanglement control of photons produced by two independent molecules by time-and-frequency gated photon coincidence counting (PCC)
Summary
Nonlinear optics is most commonly and successfully formulated using a semiclassical approach whereby the matter degrees of freedom are treated quantum mechanically, but the radiation field is classical (Boyd, 2003; Scully and Zubairy, 1997). A clear signature of the quantumness of light is the scaling of optical signals with light intensities: Classical heterodyne χ(3) signals such as two photon absorption scale quadratically with the intensity, and require a high intensity to be visible against lower-order linear-scaling processes With entangled photons, such signals scale linearly (Dayan et al, 2004, 2005; Friberg et al, 1985; Georgiades et al, 1995; Javanainen and Gould, 1990). As the frequency of the pump pulse which creates the photons is varied in the right panel, the resonance is narrow in the frequency domain, as if it was created by a ns pulse This simultaneous time and frequency resolution along non Fourier conjugate axes is a hallmark of the time-energy entanglement, and its exploitation as a spectroscopic tool offers novel control knobs to manipulate the excited state distribution, and thereby enhance or suppress selected features in nonlinear spectroscopic signals.
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