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arXiv:quant-ph/9709054 · Journal of Modern Optics

An open-systems approach to calculating time-dependent spectra

Martti Havukainen, Stig Stenholm

Published Aug 1, 1998• 5 citations
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Abstract

A new method to calculate the spectrum using cascaded open systems and a master equation is presented. The method uses two-state analyser atoms which are coupled to the system of interest, whose spectrum of radiation is read from the excitation of these analyser atoms. The ordinary definitions of a spectrum uses two-time averages and Fourier transforms. The present method uses only one-time averages. The method can be used to calculate time-dependent as well as stationary spectra.

DOI
10.1080/09500349808230663

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A new method to calculate the spectrum using cascaded open systems and a master equation is presented. The method uses two-state analyser atoms which are coupled to the system of interest, whose spectrum of radiation is read from the excitation of these analyser atoms. The ordinary definitions of a spectrum uses two-time averages and Fourier transforms. The present method uses only one-time averages. The method can be used to calculate time-dependent as well as stationary spectra.
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In computing the spectra of quantum mechanical systems one encounters the Fourier transforms of time correlation functions, as given by the quantum regression theorem for systems described by master equations. Quantum state diffusion (QSD) gives a useful method of solving these problems by unravelling the master equation into stochastic trajectories; but there is no generally accepted definition of a time correlation function for a single QSD trajectory. In this paper we show how QSD can be used to calculate these spectra directly; by formally solving the equations which arise, we arrive at a natural definition for a two-time correlation function in QSD, which depends explicitly on the stochastic noise of the particular trajectory, and which agrees in the mean with the ensemble average definition of correlation functions.