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Register a new userSolving non-Markovian open quantum systems with multi-channel reservoir coupling
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Added by
Curtis J. Broadbent
Publication date
2011
fields
Physics
and research's language is
English
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We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein-Uhlenbeck reservoir correlations numerically.
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Quantum sensing explores protocols using the quantum resource of sensors to achieve highly sensitive measurement of physical quantities. The conventional schemes generally use unitary dynamics to encode quantities into sensor states. In order to measure the spectral density of a quantum reservoir, which plays a vital role in controlling the reservoir-caused decoherence to microscopic systems, we propose a nonunitary-encoding optical sensing scheme. Although the nonunitary dynamics for encoding in turn degrades the quantum resource, we surprisingly find a mechanism to make the encoding time a resource to improve the precision and to make the squeezing of the sensor a resource to surpass the shot-noise limit. Our result shows that it is due to the formation of a sensor-reservoir bound state. Enriching the family of quantum sensing, our scheme gives an efficient way to measure the quantum reservoir and might supply an insightful support to decoherence control.
Non-Markovian reduced dynamics of an open system is investigated. In the case the initial state of the reservoir is the vacuum state, an approximation is introduced which makes possible to construct a reduced dynamics which is completely positive.
We introduce jumptime unraveling as a distinct method to analyze quantum jump trajectories and the associated open/continuously monitored quantum systems. In contrast to the standard unraveling of quantum master equations, where the stochastically evolving quantum trajectories are ensemble-averaged at specific times, we average quantum trajectories at specific jump counts. The resulting quantum state then follows a discrete, deterministic evolution equation, with time replaced by the jump count. We show that, for systems with finite-dimensional state space, this evolution equation represents a trace-preserving quantum dynamical map if and only if the underlying quantum master equation does not exhibit dark states. In the presence of dark states, on the other hand, the state may decay and/or the jumptime evolution eventually terminate entirely. We elaborate the operational protocol to observe jumptime-averaged quantum states, and we illustrate the jumptime evolution with the examples of a two-level system undergoing amplitude damping or dephasing, a damped harmonic oscillator, and a free particle exposed to collisional decoherence.
Perturbation theory (PT) is a powerful and commonly used tool in the investigation of closed quantum systems. In the context of open quantum systems, PT based on the Markovian quantum master equation is much less developed. The investigation of open systems mostly relies on exact diagonalization of the Liouville superoperator or quantum trajectories. In this approach, the system size is rather limited by current computational capabilities. Analogous to closed-system PT, we develop a PT suitable for open quantum systems. This proposed method is useful in the analytical understanding of open systems as well as in the numerical calculation of system properties, which would otherwise be impractical.
We treat several key stochastic equations for non-Markovian open quantum system dynamics and present a formalism for finding solutions to them via canonical perturbation theory, without making the Born-Markov or rotating wave approximations (RWA). This includes master equations of the (asymptotically) stationary, periodic, and time-nonlocal type. We provide proofs on the validity and meaningfulness of the late-time perturbative master equation and on the preservation of complete positivity despite a general lack of Lindblad form. More specifically, we show how the algebraic generators satisfy the theorem of Lindblad and Gorini, Kossakowski and Sudarshan, even though the dynamical generators do not. These proofs ensure the mathematical viability and physical soundness of solutions to non-Markovian processes. Within the same formalism we also expand upon known results for non-Markovian corrections to the quantum regression theorem. Several directions where these results can be usefully applied to are also described, including the analysis of near-resonant systems where the RWA is inapplicable and the calculation of the reduced equilibrium state of open systems.
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