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Journal of Suzhou University

Rate equations of single quantum

Peng Shuang-yan

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

The dynamic process of single quantum system's emitted photon is described by rate equations with absorbing boundary condition.The solution of these equations is given by using the Laplace technique and the delay function and the statistical law of single quantum system is obtained.

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The three-level dye molecule single quantum system interacting with a cw laser field is investigated.The dynamic process of a single-molecule emitted photon is described by rate equations with absorbing boundary condition.It is demonstrated that the dynamics of the single-molecule processes and the statistics of time-resolved photon detection can be conveniently described in terms of renewal stochastic processes.The approach of calculating the correlation function by calculating the delay function that is an important physics quantity reflecting single quantum system dynamic process is given,and explicit expressions of correlation functions for two-levels and two-states systems are derived.This approach can be used for calculate dynamics parameter of molecular transition based on the fluorescence intensity correlation function.
The aim of this work is to provide a new conceptually and practically useful method of obtaining the time development and particularly the decay of quantum states initially localized on a domain with dynamically open boundaries. A projection operator derivation and a Markoffian approximation is used to obtain an effective Hamiltonian capable of describing the dynamics on the open domain. The basic algebra is implemented for one dimensional systems and a series of test calculations presented which serve to verify the validity of the approximations and illustrate the accuracy of the new procedure. The absorbing boundary method developed here bears some resemblance to the optical potential methods and the Feshbach projection scheme used in scattering theory and can be applied to dissociation and ionization processes as well as to scattering processes.
The stream of photons emitted by a single quantum system such as a molecule or a nanocrystal is often statistically characterized by the distribution of delays between consecutive photons, or by the autocorrelation function of the intensity, or by the distributions of on- and off-times. We derive and discuss general relations between their Laplace transforms, addressing the influence of detection yield and background. Our analytical treatment applies to any distribution of delays and to random telegraph signals, including nonexponential distributions. We examine the special case of systems switching between two states characterized by different distributions of delays, where the switching can obey various statistics. We show that the second-order autocorrelation function keeps track of long-time fluctuations which are obviously lost in averaging the distributions of delays. We apply our formalism to random telegraphs, in particular to those with power-law distributions of on- and/or of off-times, which are encountered in the blinking of single semiconductor nanocrystals.
An open quantum system is usually characterized by a reduced ensemble density matrix, the dynamics of which is governed by a generalized Master equation. Transforming this equation of motion into the instantaneous diagonal basis of the corresponding reduced density matrix, we can separate the coherent and incoherent part of the dynamics: The coherent dynamics is incorporated in the time development of the diagonal basis states, while the coupling to the reservoirs leads to simple rate equations. Interpreting these rate equations as a stochastic point process allows one to simulate the stochastic time evolution (random telegraph signals, ``quantum jumps'') of single-quantum systems. The diagonal representation can be considered as a generalization of the dressed-state picture of open quantum systems. Numerical simulations (``quantum Monte Carlo'') allow one to derive various dynamical properties (including correlation functions) of single-quantum systems. This concept is applied to different two- and three-level scenarios (\ensuremath{\lambda} and \ensuremath{\nu} configuration), and its limitations are discussed.
It is in accordance with such experiments as single photon self-interference that a photon, conveying one radiation energy quantum " h × frequency", is spatially extensive and stretches an electromagnetic wave train. A wave train, hence an energy quantum, can only be emitted (or absorbed) by its source (or absorber) gradually. In both two processes the wave and "particle" attributes of the radiation field are simultaneously prominent, where an overall satisfactory theory has been lacking; for the latter process no known theoretical description currently exists. This paper presents a first principles treatment, in a unified framework of the classical and quantum mechanics, of the latter process, the emission (similarly absorption) of a single radiation quantum based on the dynamics of the radiation-emitting source, a charged oscillator, which is itself extensive across the potential well in which it oscillates. During the emission of one single radiation quantum, the extensive charged oscillator undergoes a continuous radiation damping and is non-stationary. This process is in this work treated using a quasi stationary approach, whereby the classical equation of motion, which directly facilitates the correspondence principle for a particle oscillator, and the quantum wave equation are established for each sufficiently brief time interval. As an inevitable consequence of the division of the total time for emitting one single quantum, a fractional Planck constant h is introduced. The solutions to the two simultaneous equations yield for the charged oscillator a continuously exponentially decaying Hamiltonian that is at the same time quantised with respect to the fractional- h at any instant of time; and the radiation wave field emitted over time stretches a wave train of finite length. The total system of the source and radiation field maintains at any time (integer n times) one whole energy quantum, ( n × ) h × frequency, in complete accordance with the standard notion of quantum mechanics and experiment.