Non-Markovian effects are important in a variety of physical quantum systems including exciton transport in photosynthetic light harvesting complexes, qubits and quantum control, and quantum optics. Yet despite their prevalence there remain many unanswered questions in the theoretical treatment of such systems. The exact equation which governs these dynamics where the system and bath are on similar time scales is challenging to solve in the general case. Many methods approximate the exact solution through perturbative techniques, and while they are effective for small perturbations about the Markovian limit, they can in general limit or destroy the positivity of the density matrix. Although Lindblad developed a general Markovian theory for open-system dynamics while maintaining the positivity of the density matrix, a general, practical non-Markovian analogue remains a significant problem. Here, we present an extension of Lindblad's theory through an ensemble of Lindbladian trajectories originating from different times in the system's history. This approach provides a complete account of the system's memory in a framework that preserves the positivity of the density matrix. We apply the theory to the Jaynes-Cummings model to capture non-Markovian dynamics in the weak and strong coupling regimes. We also apply our method to the strong coupling regime with detuning. Our method shows agreement within computational accuracy to the exact solution for all cases, including those that perturbative techniques cannot capture. As with Lindblad's theory, the present generalization requires physical insight from theory and/or experiments to select the appropriate system-bath parameters. Future work will further explore parameter choice and the application of these results to the more accurate description of non-Markovian quantum systems.

Non-Markovian dynamics: An extension of the Lindblad theory

2019 Spring National Meeting

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