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Physical Review A

Multidimensional phase-sensitive single-molecule spectroscopy with time-and-frequency-gated fluorescence detection

Shaul Mukamel, Marten Richter

Published Jan 18, 2011• 26 citations
Publisher

Abstract

($n$ $+$ 1)-dimensional gated fluorescence signals induced by $n$ impulsive pulses are calculated using a superoperator formalism. The signals are given by a time-and-frequency convolution of a bare signal, expressed in terms of multipoint dipole correlation functions, with a gating spectrogram. Different groups of quantum pathways can be separated by their variation with the phases of the pulses (phase cycling), as is commonly done in nuclear magnetic resonance. Comparison is made with heterodyne-detected coherent signals.

DOI
10.1103/physreva.83.013815

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(nnn +++ 1)-dimensional gated fluorescence signals induced by nnn impulsive pulses are calculated using a superoperator formalism. The signals are given by a time-and-frequency convolution of a bare signal, expressed in terms of multipoint dipole correlation functions, with a gating spectrogram. Different groups of quantum pathways can be separated by their variation with the phases of the pulses (phase cycling), as is commonly done in nuclear magnetic resonance. Comparison is made with heterodyne-detected coherent signals.
Abstract Coherent multidimensional optical spectroscopy is broadly applied across the electromagnetic spectrum ranging from NMR to UV. These techniques reveal the properties of matter through the correlation plots of signal fields generated in response to sequences of short pulses with variable delays. Here we discuss a new class of multidimensional techniques obtained by the time-and-frequency-resolved photon coincidence counting measurements of N photons, which constitute a 2 N dimensional spectrum. A compact description of these signals is developed based on time-ordered superoperators rather than the normally ordered ordinary operators used in Glauber's photon counting formalism. The independent control of the time and frequency gate parameters reveals fine details of matter dynamics not available otherwise. These signal are illustrated for application to an anharmonic oscillator model with fluctuating energy and anharmonicity.
In response to quantum optical fields, pairs of molecules generate coherent nonlinear spectroscopy signals. Homodyne signals are given by sums over terms each being a product of Liouville space pathways of the pair of molecules times the corresponding optical field correlation function. For classical fields all field correlation functions may be factorized and become identical products of field amplitudes. The signal is then given by the absolute square of a susceptibility which in turn is a sum over pathways of a single molecule. The molecular pathways of different molecules in the pair are uncorrelated in this case (each path of a given molecule can be accompanied by any path of the other). However, entangled photons create an entanglement between the molecular pathways.We use the superoperator nonequlibrium Green's functions formalism to demonstrate the signatures of this pathway-entanglement in the difference frequency generation signal. Comparison is made with an analogous incoherent two-photon fluorescence signal.
We introduce molecular coherent three-quantum (3Q) two-dimensional (2D) fluorescence spectroscopy with phase cycling via shot-to-shot pulse shaping at a 1 kHz repetition rate. This allows us to acquire simultaneously, within a single scan, three fourth-order and six sixth-order signals correlating various one-quantum, two-quantum, and 3Q coherences. We demonstrate the approach on the dye molecule rhodamine 700 and reproduce all nine 2D data sets, including their absolute signal strengths, with simulations using a single, consistent set of model parameters. We observe a linear concentration dependence of all nonlinear signals, evidencing the absence of cascades and many-particle signals of noninteracting molecules. The single-beam, background-free implementation allows direct comparability between various nonlinear signal types and provides information about multiple excited states. Apart from molecules, the method is expected to be applicable to supramolecular systems, polymers, and solid-state materials with the prospect of revealing signatures of bi- and triexcitonic states.