Adiabatic Elimination and Sub-space Evolution of Open Quantum Systems

Abstract

Efficient descriptions of open quantum systems can be obtained by performing an adiabatic elimination of the fast degrees of freedom and formulating effective operators for the slow degrees of freedom in reduced dimensions. Here, we perform the construction of effective operators in frequency space, and using the final value theorem or alternatively the Keldysh theorem, we provide a correction for the trace of the density matrix which takes into account the non trace-preserving character of the evolution. We illustrate our results with two different systems, ones where the eliminated fast subspace is constituted by a continuous set of states and ones with discrete states. Furthermore, we show that the two models converge for very large dissipation and at coherent population trapping points. Our results also provide an intuitive picture of the correction to the trace of the density matrix as a detailed balance equation.

12 pages, 9 figures, improved literature review

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• A quantum optics approach to photoinduced electron transfer in cavities
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• Non-Hermitian Hamiltonians for Linear and Nonlinear Optical Response: a Model for Plexcitons
• Eternal Adiabaticity
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• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Time-convolutionless master equations for composite open quantum systems
• Parametric approximation as open quantum systems problem
• Complete positivity violation of the reduced dynamics in higher-order quantum adiabatic elimination
• Density operator approach to turbulent flows in plasma and atmospheric fluids
• Time-Convolutionless Master Equation Applied to Adiabatic Elimination
• Superoperator master equations for depolarizing dynamics
• Explicit formulas for adiabatic elimination with fast unitary dynamics
• Unconventional mechanism of virtual-state population through dissipation