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Journal of Experimental and Theoretical Physics

Dynamic theory of two-photon correlators in the spectroscopy of single impurity centers

Игорь Сергеевич Осадько

Published May 1, 1998• 24 citations
Publisher

Abstract

A dynamic theory of two-photon correlators measured in experiments with single molecular impurity centers has been developed. The theory takes into account the interaction between optically active electrons of an impurity center and phonons, excitations in tunneling systems of polymers and glasses, and transverse electromagnetic field. Both the correlator measured in the start-stop regime and the “full” correlator have been analyzed, and equations for these correlators have been derived. An equation relating these two correlators has been also obtained. The effect of the triplet level of an impurity molecule on the correlators leading to bunching of spontaneously emitted photons has been studied. The two-photon correlators have been calculated numerically, and their dependence on the incident light frequency and time between the pairs of detected photons in various realistic situations has been derived.

DOI
10.1134/1.558558

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A dynamic theory of two-photon correlators measured in experiments with single molecular impurity centers has been developed. The theory takes into account the interaction between optically active electrons of an impurity center and phonons, excitations in tunneling systems of polymers and glasses, and transverse electromagnetic field. Both the correlator measured in the start-stop regime and the “full” correlator have been analyzed, and equations for these correlators have been derived. An equation relating these two correlators has been also obtained. The effect of the triplet level of an impurity molecule on the correlators leading to bunching of spontaneously emitted photons has been studied. The two-photon correlators have been calculated numerically, and their dependence on the incident light frequency and time between the pairs of detected photons in various realistic situations has been derived.
A dynamic theory of two-photon correlators for a single impurity center developed recently by the author [I. S. Osad’ko, Zh. Éksp. Teor. Fiz. 113 , 1606 (1998) [JETP 86 , 875 (1998)] has been generalized to the case in which the center interacts with nonequilibrium two-level systems (TLSs) in polymers and glasses. Quantum tunneling transitions in TLS manifest themselves as random jumps of a spectral line of an impurity center. These jumps can be either spontaneous or light-induced. Interaction between the impurity center and many nonequilibrium TLSs, which exist in polymers, results in a time dependence of the optical dephasing rate 1/ T 2 of an impurity molecule, i.e., in spectral diffusion. This paper describes how the jumps of the spectral line manifest themselves in the two-photon correlator, which can be measured in experiments.
Fluorescence photons emitted by a single molecule trapped in a solid at low temperature are correlated in time. A simple theory of the correlation pattern is presented, including in the same formalism photon antibunching from coherent Rabi oscillations and photon bunching due to incoherent quantum transitions between electronic levels. The correlation method is applied to single pentacene molecules in a para-terphenyl crystal. A clear photon bunching allows us to determine the ISC rates for each molecule. We attribute the scatter of our results for the transition rate between excited singlet and triplet states, and the difference with the average value taken from the literature, to molecular distortions induced by crystal defects in our small sample. We conclude that the correlation method associated to single molecule spectroscopy has a great potential to study dynamical processes on intermediate time scales in condensed matter.
We show that the second-order, two-time correlation functions for phonons and photons emitted from a vibronic molecule in a thermal bath result in bunching and antibunching (a purely quantum effect), respectively. Signatures relating to phonon exchange with the environment are revealed in photon-photon correlations. We demonstrate that cross-correlation functions have a strong dependence on the order of detection giving insight into how phonon dynamics influences the emission of light. This work offers new opportunities to investigate quantum effects in condensed-phase molecular systems.
Even though the quantized interaction between light and matter in the photoelectric effect is considered one of the cornerstones in the development of quantum mechanics, it was long thought impossible to directly observe the quantized nature of light itself. The advent of light-intensity autocorrelation techniques in the 1950s, first developed to study the size of stars, changed little in this perception, until true single-photon correlation spectroscopy from trapped ions was proven to be possible in the late 1970s: Photons from a single quantum emitter tend to arrive in bunches, but each light quantum is spaced apart in time—it is antibunched. Initially considered only as the workhorse of atomic quantum optics, over the past two decades, photon correlation techniques have become a standard in fields as diverse as quantum-information processing, biological imaging, polymer physics, and materials science, in general. The technique is particularly useful for probing materials that are specifically designed to emit or absorb light in optoelectronic devices, such as light-emitting diodes, solar cells, or lasers. The central question in such studies is how large a mesoscopic piece of material can become and still behave as an atom-like source of single photons. What interactions may arise between multiple excitations within a material, and what sort of dark states may give rise to intermittency in the stream of photons? We review the many different classes of optoelectronic materials for which photon-correlation spectroscopy has proven to offer useful insight into excited-state dynamics, ranging from molecular, over semiconductor to metallic nanostructures. The technique is particularly suited to probing mesoscopic aggregates of organic semiconductors since each single molecule acts as a quantum emitter itself.
While two-photon absorption (TPA) and other forms of nonlinear interactions of molecules with isolated time-frequency-entangled photon pairs (EPP) have been predicted to display a variety of fascinating effects, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This paper presents a detailed theoretical study of quantum-enhanced TPA by both photon-number correlations and spectral correlations, including an account of the deleterious effects of dispersion. While such correlations in EPP created by spontaneous parametric down conversion can increase the TPA rate significantly in the regime of extremely low optical flux, we find that for typical molecules in solution this regime corresponds to such low TPA event rates as to be unobservable in practice. Our results support the usefulness of EPP spectroscopy in atomic or other narrow-linewidth systems, while questioning the efficacy of such approaches for broadband systems including molecules in solution.
Recently single photon emission has been observed for systems in which multiple excitons are generated by pulsed excitation. When fast pair annihilation of excitons takes place, finally a single exciton remains and single photon can be emitted. Its efficiency depends on the competition among pair annihilation, unimolecular nonradiative, and radiative processes. The efficiency of single photon emission is usually studied by measuring the correlation of emitted photons after pulsed excitation by the Hanbury-Brown and Twiss method. The photon correlation measured in this method is different from that calculated by taking into account all pairs of emitted photons, which was presented in a previous paper. We calculate the former rigorously for the first time in the case of multiple excitations and compare it with the latter. We also calculate correlation of arrival times of two photons by the Hanbury-Brown and Twiss method. These results should be useful for the analysis of the antibunching measurement by the Hanbury-Brown and Twiss method.