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Physical Review A

Stochastic dynamics of a single impurity molecule from the viewpoint of continuous measurement theory

S. Ya. Kilin, Tatiana M. Maevskaya, Alexander P. Nizovtsev, Vyacheslav Shatokhin, P. R. Berman, Christian von Borczyskowski, Jörg Wrachtrup, L. Fleury

Published Feb 1, 1998• 15 citations
Publisher

Abstract

Stochastic dynamics of a laser-driven four-level system serving as a model for a single guest chromophore molecule in an amorphous polymer host is studied. The dynamics of ``slow'' transitions (spectral jumps), accompanied by instantaneous changes in the fluorescence frequency, is simulated on the basis of continuous measurement theory. It is shown that there is an opportunity to control the statistics of ``bright'' and ``dark'' periods by using laser fields to drive molecules having different tunneling rates for the ground and excited electronic states. The effect of population cycling in a four-level system and related effects of local heating or cooling of the environment are discussed.

DOI
10.1103/physreva.57.1400

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Stochastic dynamics of a laser-driven four-level system serving as a model for a single guest chromophore molecule in an amorphous polymer host is studied. The dynamics of slow'' transitions (spectral jumps), accompanied by instantaneous changes in the fluorescence frequency, is simulated on the basis of continuous measurement theory. It is shown that there is an opportunity to control the statistics of bright'' and ``dark'' periods by using laser fields to drive molecules having different tunneling rates for the ground and excited electronic states. The effect of population cycling in a four-level system and related effects of local heating or cooling of the environment are discussed.
With high-efficiency fluorescence excitation techniques optical spectra of single impurity molecules of perylene in a polyethylene matrix can be obtained at 1.5 K. Analysis of such spectra shows a variety of spectral diffusion effects, including fast (<2 s) resonance frequency changes on the 1–100-MHz scale, which lead to a range of apparent linewidths, as well as discontinuous jumps in the resonance frequency of 10–1000 MHz on a longer time scale. In addition, light-induced changes in the resonance frequency of a single molecule (persistent spectral hole burning) have been conclusively observed by showing that the burning time decreases with increased laser power. Surprisingly, hole-burned single molecules often spontaneously return to the original frequency in 1–100 s. Measurements of the burning time for a large number of hole-burning events for the same single molecule yield an exponential burn-time distribution, which is the first direct measurement to our knowledge of the stochastic kinetics of a single molecule. Analysis of the signal-to-noise function appropriate to these experiments gives the conditions under which other systems may permit single-molecule detection: strong absorption, high fluorescence yield, weak bottlenecks in the optical pumping process, and low hole-burning quantum efficiency.
We propose a density-matrix theory for the four-level system consisting of a single optical two-level system (OTLS) coupled to a single two-level system tunneling along a vibrational coordinate (VTLS). Phonons induce jumping rates of the VTLS, but coherent tunneling has to be considered explicitly as well, because the Born-Oppenheimer potential of the tunnel variable may change upon optical excitation. The OTLS is subject to spontaneous emission and driven by a laser wave with arbitrary strength. Numerical simulations for various coupling cases reproduce limiting behaviors previously discussed separately in the literature, such as motional narrowing, cross transitions, optical saturation and pumping, and nonlinear effects. Our model also perfectly fits recent measurements of the spectra of a single molecule coupled to a single tunneling system in a disordered crystal.
We revisit the line-shape theory of a single molecule with anomalous stochastic spectral diffusion. Waiting time profiles for bath induced spectral jumps in the ground and excited states become different when a molecule, probed by continuous-wave laser field, reaches the steady state. This effect is studied for the stationary dichotomic continuous-time-random-walk spectral diffusion of a single two-level chromophore with power-law distributions of waiting times. Correlated waiting time distributions, line shapes, two-point fluorescence correlation function, and Mandel Q parameter are calculated for arbitrary magnitude of laser field. We extended previous weak field results and examined the breakdown of the central limit theorem in photon statistics, indicated by asymptotic power-law growth of Mandel Q parameter. Frequency profile of the Mandel Q parameter identifies the peaks of spectrum, which are related to anomalous spectral diffusion dynamics.
The feasibility of manipulating the single molecule absorption-emission cycle using picosecond stimulated emission depletion (STED) is investigated using a stochastic computer simulation. In the simulation the molecule is subjected to repeated excitation and depletion events using time delayed pairs of excitation (PUMP) and depletion (DUMP) pulses derived from a high repetition rate pulsed laser system. The model is used to demonstrate that a significant and even substantial reduction in the occurrence of 'dark states' in the fluorescence emission can be achieved using stimulated emission depletion. Variation in the PUMP-DUMP window allows precise control of the fluorescence yield with substantial increases in the fluorescence intensity observed at early PUMP-DUMP delays.
In this paper, single-molecule spectroscopy experiments based on continuous laser excitation are characterized through an open quantum system approach. The evolution of the fluorophore system follows from an effective Hamiltonian microscopic dynamic where its characteristic parameters, i.e., its electric dipole, transition frequency, and Rabi frequency, as well as the quantization of the background electromagnetic field and their mutual interaction, are defined in an extended Hilbert space associated to the different configurational states of the local nanoenvironment. After tracing out the electromagnetic field and the configurational states, the fluorophore density matrix is written in terms of a Lindblad rate equation. Observables associated to the scattered laser field, such as optical spectrum, intensity-intensity correlation, and photon-counting statistics, are obtained from a quantum-electrodynamic calculation also based on the effective microscopic dynamic. In contrast with stochastic models, this approach allows one to describe in a unified way both the full quantum nature of the scattered laser field as well as the classical nature of the environment fluctuations. By analyzing different processes such as spectral diffusion, lifetime fluctuations, and light assisted processes, we exemplify the power of the present approach.