Optimizing stochastic trajectories in exact quantum jump approaches of interacting systems

Abstract

The quantum jump approach, where pairs of state vectors follow Stochastic Schroedinger Equation (SSE) in order to treat the exact quantum dynamics of two interacting systems, is first described. In this work the non-uniqueness of such stochastic Schroedinger equations is investigated to propose strategies to optimize the stochastic paths and reduce statistical fluctuations. In the proposed method, called the 'adaptative noise method', a specific SSE is obtained for which the noise depends explicitly on both the initial state and on the properties of the interaction Hamiltonian. It is also shown that this method can be further improved by introduction of a mean-field dynamics. The different optimization procedures are illustrated quantitatively in the case of interacting spins. A significant reduction of the statistical fluctuations is obtained. Consequently a much smaller number of trajectories is needed to accurately reproduce the exact dynamics as compared to the SSE without optimization.

12 pages, 5 figures, revised version

References in corpus (4)

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• Nonequilibrium open quantum systems with multiple bosonic and fermionic environments: A hierarchical equations of motion approach
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• Exact stochastic simulation of dissipation and non-Markovian effects in open quantum systems
• Exact Stochastic Unraveling of an Optical Coherence Dynamics by Cumulant Expansion
• Stochastic analysis and simulation of spin star systems
• Stochastic Schroedinger equation from optimal observable evolution
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