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Molecular crystals and liquid crystals science technology. Section A, Molecular crystals and liquid crystals/Molecular crystals and liquid crystals science and technology. Section A, Molecular crystals and liquid crystals

Stochastic Model Description of Single Molecule Spectroscopy

Elisabeth Paule, Petr Chvosta, P. Reineker

Published Jun 1, 1996• 4 citations
Publisher

Abstract

We calculate the optical line shape of a single molecule in a solid matrix taking into account its relaxation and the interaction with the host. Under the influence of the environment, described by an ensemble of TLSs, the optical transition frequency of the guest molecule is time dependent. Its dynamics is simulated by dichotomic stochastic processes.

DOI
10.1080/10587259608037888

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We calculate the optical line shape of a single molecule in a solid matrix taking into account its relaxation and the interaction with the host. Under the influence of the environment, described by an ensemble of TLSs, the optical transition frequency of the guest molecule is time dependent. Its dynamics is simulated by dichotomic stochastic processes.
Various theories that use the sudden jump model to explain the time dependence of the optical band of a single molecule in a fluctuating environment are analyzed. It is shown that the dynamic theory of the optical band, based on the Hamiltonian of the system, should necessarily include the initial conditions for the quantum system. We show how these initial conditions should be chosen for the dynamic theory to properly describe the quantum jumps of the optical band of a single molecule. Unlike stochastic theories based on the sudden jump model, the dynamic theory predicts several absorptances of a single molecule and directly connects the absorptance fluctuations with this fact. The theory is used to account for the time dependence of the broadening of experimentally measured lines of individual molecules.
Experiments with single quantum systems are at the frontier of modern physics. Probing single molecules allows for very precise control of light-matter interaction and for quantum optical studies. Moreover, a single guest molecule in a solid host matrix is a very sensitive probe of local dynamics in its nano-environment. Fluorescence excitation spectroscopy on single molecules is a powerful tool for spectroscopic characterizations at highest resolution, as information can be revealed that is not accessible in experiments on ensembles of molecules. The detection of the fluorescence signal of a single absorber is achieved by exploiting the high spectral selectivity given by the ratio (10 10) of homogeneous to inhomogeneous linewidths of optical transitions at cryogenic temperatures (zero-phonon transitions). Two-photon fluorescence excitation, a fundamental nonlinear optical process, was observed on a single quantum system [1]. Single diphenyl-octatetraene molecules trapped in an n-tetradecane matrix were excited from the 1Ag ground to the lowest excited singlet state by simultaneous absorption of two photons using a single-mode cw laser. Excited molecules were observed through weak one-photon emission resulting from a symmetry breaking induced by the crystal field. The fundamental principles and the experimental technique of single molecule spectroscopy will be introduced briefly and some particular single molecule experiments presented. This work was done in collaboration with T. Plakhotnik, A. Renn and U.P. Wild
A theory is formulated for time dependent fluctuations of the spectrum of a single molecule in a dynamic environment. In particular, we investigate the photon counting statistics of a single molecule undergoing a spectral diffusion process. Based on the stochastic optical Bloch equation, fluctuations are characterized by Mandel's QQQ parameter yielding the variance of number of emitted photons and the second order intensity correlation function, g(2)(t)g^{(2)}(t)g(2)(t). Using a semi-classical approach and linear response theory, we show that the QQQ parameter can be described by a three-time dipole correlation function. This approach gene ralizes the Wiener-Khintchine formula that gives the average number of fluorescent photons in terms of a one-time dipole correlation function. We classify the time ordering properties of the three-time dipole correlation function, and show that it can be represented by three different pulse shape functions similar to those used in the context of nonlinear spectroscopy. An exact solution is found for a single molecule whose absorption frequency undergoes a two state random telegraph process (i.e., the Kubo-Anderson sudden jump process.) Simple expressions are obtained from the exact solution in the slow and fast modulation regimes based on appropriate approximations for each case. In the slow modulation regime QQQ can be large even in the long time limit, while in the fast modulation regime it becomes small.
Optical spectroscopy provides a useful tool for probing the structure and dynamics of solids. Over the years, optical methods have evolved from absorption spectroscopy to more complex methods such as spectral hole burning, photon echoes, and luminescence line narrowing. The absorption spectrum provides information about inhomogeneous broadening, while the latter approaches provide information about the systematics of the homogeneous line shape information that is often obscured by inhomogeneous broadening. When external perturbations such as strain or electric fields are applied, details of the local site can be obtained. Recently, the ultimate limit of optical spectroscopy has been attained, in which the spectral properties of individual single impurity molecules in a solid can be measured, with all ensemble averaging removed. This novel regime has provided additional, previously unobtainable, information on a highly local scale, such as the direct observation of the spectral shifting of a single molecule produced by configurational transitions of the host. It is to be expected that further surprises await us in this new frontier of single-molecule spectroscopy in solids.
By severely reducing the number of solute molecules in the illuminated sample, the optical resonances of individual molecules can be resolved in a fluorescence excitation spectrum. Single molecule lines can be studied as a function of time and temperature: sudden jumps of their resonance frequencies are due to spectral diffusion processes. The signal from a single molecule displays specific correlations which makes time-resolved studies possible. Here, emphasis is put on photon-bunching arising from intersystem crossing (ISC). ISC rates are deduced from the observed decay rates of the correlation and are found to differ from molecule to molecule. A single molecule is a truly local probe of its environment by means of which fundamental studies of the matrix dynamics as well as nanophysics experiments may be undertaken.