Quantum trajectories: memory and continuous observation

Abstract

Starting from a generalization of the quantum trajectory theory (based on the stochastic Schrödinger equation - SSE), non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in this article is based on the introduction of random coefficients in the usual linear SSE. A major interest is that this allows to develop a consistent theory of quantum measurement in continuous time for these non-Markovian quantum trajectory models. In this context, the notions of instrument, a priori and a posteriori states are rigorously described. The key point is that by starting from a stochastic equation on the Hilbert space of the system, we are able to respect the complete positivity of the mean dynamics for the statistical operator and the requirements of the axioms of quantum measurement theory. The flexibility of the theory is next illustrated by a concrete physical model of a noisy oscillator where non Markovian effects come from random environment, coloured noises, randomness in the stimulating light, delay effects. The statistics of the emitted photons and the heterodyne and homodyne spectra are studied and we show how these quantities are sensible to the non-Markovian features of the system dynamics, so that, in principle, the observation and analysis of the fluorescence light could reveal the presence of non-Markovian effects and allow for a measure of the spectra of the noises affecting the system dynamics.

21 pages, RevTeX4-1; minor corrections

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Cited by in corpus (12)

• Capturing Non-Markovian Dynamics on Near-Term Quantum Computers
• Interaction-induced correlations and non-Markovianity of quantum dynamics
• Markovian embedding of non-Markovian quantum collisional models
• Interference of Quantum Trajectories
• Post-Markovian quantum master equations from classical environment fluctuations
• Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics
• Stochastic Schrödinger Equations for Markovian and non-Markovian cases
• Stochastic unravellings of non-Markovian completely positive and trace preserving maps
• On the relationship between a quantum Markov semigroup and its representation via linear stochastic Schroedinger equations
• On the unraveling of open quantum dynamics
• Numerical solution of stochastic master equations using stochastic interacting wave functions
• Stochastic wave-function unravelling of the generalized Lindblad equation