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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Monte Carlo simulations of non-Markovian open systems

Jyrki Piilo, Sabrina Maniscalco, Kalle‐Antti Suominen

Published Jun 7, 2007• 0 citations
Publisher

Abstract

Various Monte Carlo methods allow the simulation of the dynamics of open quantum systems. We highlight the central features a commonly used method for Markovian systems, i.e., Monte Carlo Wave Function method and another one used for non-Markovian systems, i.e., the doubled Hilbert space method. One of the open problems in the field has been the lack of the existence of Monte Carlo method with quantum jumps for non-Markovian systems. We characterize the key problems that should be solved in this context and give indications for the way towards the development of quantum jump method without auxiliary states for non-Markovian systems.

DOI
10.1117/12.728363

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Open quantum systems that interact with structured reservoirs exhibit non-Markovian dynamics. We present a quantum jump method for treating the dynamics of such systems. This approach is a generalization of the standard Monte Carlo wave function (MCWF) method for Markovian dynamics. The MCWF method identifies decay rates with jump probabilities and fails for non-Markovian systems where the time-dependent rates become temporarily negative. Our non-Markovian quantum jump approach circumvents this problem and provides an efficient unraveling of the ensemble dynamics.
The development and use of Monte Carlo algorithms plays a visible role in the study of non-Markovian quantum dynamics due to the provided insight and powerful numerical methods for solving the system dynamics. In the Markovian case, the connections between the various types of methods are fairly well understood while, for the non-Markovian case, there has so far been only a few studies. We focus here on two jumplike unravelings of non-Markovian dynamics: the non-Markovian quantum jump (NMQJ) method and the property state method by Gambetta, Askerud, and Wiseman (GAW). The results for simple quantum optical systems illustrate the connections between the realizations of the two methods and also highlight how the probability currents between the system and environment, or between the property states of the total system, are associated with the decay rates of time-local master equations and, consequently, with the jump rates of the NMQJ method.
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We demonstrate a scaling method for Monte Carlo wave-function simulations used to study the dynamics of non-Markovian open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values of arbitrary operators of interest can be calculated, all the quantities in the equation being easily obtainable from the scaled Monte Carlo simulations. In the optimal case, the scaling method can be used, within the weak coupling approximation, to reduce the size of the generated Monte Carlo ensemble by several orders of magnitude. Thus, the developed method allows faster simulations and makes it possible to solve the dynamics of the certain class of non-Markovian systems whose simulation would be otherwise too tedious because of the requirement for large computational resources.
We demonstrate a scaling method for non-Markovian Monte Carlo wave-function simulations used to study open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values of arbitrary operators of interest can be calculated, all the quantities in the equation being easily obtainable from the scaled Monte Carlo wave-function simulations. In the optimal case, the scaling method can be used, within the weak coupling approximation, to reduce the size of the generated Monte Carlo ensemble by several orders of magnitude. Thus, the developed method allows faster simulations and makes it possible to solve the dynamics of the certain class of non-Markovian systems whose simulation would be otherwise too tedious because of the requirement for large computational resources.