Collision-model-based approach to non-Markovian quantum dynamics

Abstract

We present a theoretical framework to tackle quantum non-Markovian dynamics based on a microscopic collision model (CM), where the bath consists of a large collection of initially uncorrelated ancillas. Unlike standard memoryless CMs, we endow the bath with memory by introducing inter-ancillary collisions between next system-ancilla interactions. Our model interpolates between a fully Markovian dynamics and the continuous interaction of the system with a single ancilla, i.e., a strongly non-Markovian process. We show that in the continuos limit one can derive a general master equation, which while keeping such features is guaranteed to describe an unconditionally completely positive and trace-preserving dynamics. We apply our theory to an atom in a dissipative cavity for a Lorentzian spectral density of bath modes, a dynamics which can be exactly solved. The predicted evolution shows a significant improvement in approaching the exact solution with respect to two well-known memory-kernel master equations.

5+1 pages, 2 figures

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• All-optical non-Markovian stroboscopic quantum simulator
• Coarse graining a non-Markovian collisional model
• General structure of quantum collisional models
• Quantum non-Markovian piecewise dynamics from collision models
• Dynamical Casimir effect and minimal temperature in quantum thermodynamics
• Memory kernel approach to generalized Pauli channels: Markovian, semi-Markov, and beyond
• Quantum Critical Probing and Simulation of Colored Quantum Noise
• Lattice mapping for many-body open quantum systems and its application to atoms in photonic cystals