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Journal of Experimental and Theoretical Physics

Emergence of spectral line jumps and spectral diffusion in the two-photon correlator of a single impurity center

Игорь Сергеевич Осадько

Published Sep 1, 1999• 12 citations
Publisher

Abstract

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.

DOI
10.1134/1.559010

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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.
The spectral diffusion theory developed for explaining the logarithmic temporal broadening of the optical line of an individual impurity center and based on spontaneous tunnel transitions in a polymer or glass is supplemented by taking into account the tunnel transitions occurring in the center itself upon the absorption of a photon. This light-induced additional tunneling leads to a sharp temporal broadening of the optical line from an individual impurity molecule occurring against the background of a slower logarithmic line broadening. It is shown that the inclusion of light-induced tunneling can explain the difference in the temporal line broadening of three individual Terylene molecules introduced in polyethylene, which was measured in experiments by the group headed by M. Orrit [A. M. Boiron et al. , Chem. Phys. 247 , 119 (1999)].
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.
Recent advances in the optical detection and spectroscopy of single impurity centers in crystals has provided the possibility of obtaining information about defect-solid interactions on a truly local level. For the system composed of pentacene impurity molecules in the crystal p-terphenyl, single molecules have been studied using both absorption1 and fluorescence excitation2 techniques at liquid helium temperatures. The superior signal-to-noise of the latter technique has led to direct observations of the lifetime-limited Lorentzian homogeneous profile of a single pentacene impurity3 as well as the surprising observation of spontaneous spectral diffusion4. Spectral diffusion, or changes in the resonance frequency of an impurity molecule with time as a result of low-energy excitations (two-level system transitions (TLS)),5 is generally expected in amorphous hosts. Indeed, the presence of TLSs in amorphous solids is intimately connected with nonphotochemical mechanisms for persistent spectral hole-burning (PSHB) in amorphous materials6-8. Using perylene impurity molecules in poly(ethylene), we have observed the optical spectra of single molecules in a polymeric host for the first time. At 1.5K, individual perylene molecules show the expected spectral diffusion; moreover, we observe light-induced changes in resonance frequency, i.e., persistent spectral hole-burning, which allows one to envision optical storage on the single-molecule level.
The concept of the homogeneous spectral linewidth of an impurity center is more complicated in disordered media such as organic glasses and polymers than it is in crystals. In amorphous media the local environments for impurity centers are continuously changing with time. As a result transition frequencies of individual centers diffuse within the inhomogeneous broadened spectral contour, which is called spectral diffusion. When the timescale for spectral diffusion processes is much longer than the dephasing time, it is possible to distinguish homogeneous dephasing from spectral diffusion. On the other hand, when the timescales of spectral diffusion and dephasing processes are comparable these phenomena become indistinguishable.
We develop a systematic description of spectral diffusion of ideal chromophores interacting with incoherently relaxing two-state, localized environmental degrees of freedom ("spins") for general initial environment configurations. We remedy the existing, incomplete treatments by formulating the problem in terms of the proper correlation function and by obtaining an accurate solution for generic aperiodic arrangements of environmental spins, nearly free of the customary simplifying assumptions on the multiparticle spin coordinate distribution. We report and estimate, for the first time, the effects of the drift and distortion of a narrow spectral line that arise when the line is not in the center of the inhomogeneous band. While the drift turns out to be modest in most ensemble measurements, accounting for its effects is imperative in analyzing single chromophore spectral jumps, to which end the authors propose a novel experiment. Further, we argue that by employing a sufficiently large chromophore one can decouple the concentration of the fluctuating centers from the strength of their interaction with the chromophore. Finally, the additional line broadening, owing to a distribution of the central chromophore frequencies, is evaluated. Upper estimates for an analogous broadening stemming from a nonequilibrium environment are made.
We consider the spectral diffusion of a chromophore coupled through dipolar interactions to a regular lattice of flipping two-level systems. In particular, we calculate the spectral diffusion kernel, P(ω,t‖ω0), which is the conditional probability density that the chromophore will have transition frequency ω at time t, given that it had frequency ω0 at time 0. At very short times we find that the spectral diffusion kernel is Lorentzian, for any value of the two-level system excitation probability, p. For longer times the form of the spectral diffusion kernel depends on the value of p. We derive several approximate expressions for the spectral diffusion kernel, all of which go to the correct equilibrium distribution of frequencies for long times. For p≂1/2, when the frequency distribution is nearly Gaussian, we find that the spectral diffusion kernel is not at all Gaussian for short times. We compare all of our approximate expressions with numerically exact results. Motivated by certain optical spectral diffusion experiments on individual molecules in solids, we also calculate P(Δ;t), the distribution of spectral jumps, which is the probability density that the chromophore’s frequency will change by an amount Δ in time t. In a subsequent paper we will analyze these spectral diffusion experiments with our results.