Projection based adiabatic elimination of bipartite open quantum systems

Abstract

Adiabatic elimination methods allow the reduction of the space dimension needed to describe systems dynamics which exhibits separation of time scale. For open quantum system, it consists in eliminating the fast part assuming it has almost instantaneously reached its steady-state and obtaining an approximation of the evolution of the slow part. These methods can be applied to eliminate a linear subspace within the system Hilbert space, or alternatively to eliminate a fast subsystems in a bipartite quantum system. In this work, we extend an adiabatic elimination method used for removing fast degrees of freedom within a open quantum system (Phys. Rev. A 2020, 101,042102) to eliminate a subsystem from an open bipartite quantum system. As an illustration, we apply our technique to a dispersively coupled two-qubit system and in the case of the open Rabi model.

arXiv comment11 pages, 2 figures

References in corpus (21)

• Confining the state of light to a quantum manifold by engineered two-photon loss
• Quantum many-body models with cold atoms coupled to photonic crystals
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Spectral theory of Liouvillians for dissipative phase transitions
• Dissipative production of a maximally entangled steady state
• The Dicke model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity
• Effective operator formalism for open quantum systems
• Critical Quantum metrology with a finite-component quantum phase transition
• Adiabatic Elimination in a Lambda System
• Procedures for Converting among Lindblad, Kraus and Matrix Representations of Quantum Dynamical Semigroups
• Quantum memories based on engineered dissipation
• Dissipative Phase Transition in the Open Quantum Rabi Model
• Kinetic constraints, hierarchical relaxation and onset of glassiness in strongly interacting and dissipative Rydberg gases
• Probing the Dynamics of Superradiant Quantum Phase Transition in a Single Trapped-Ion
• Perturbative approach to Markovian open quantum systems
• Generalized Schrieffer-Wolff Formalism for Dissipative Systems
• Quantum logic between atoms inside a high Q optical cavity
• Effective dynamics of strongly dissipative Rydberg gases
• Adiabatic Elimination and Sub-space Evolution of Open Quantum Systems
• Adiabatic Elimination of Gaussian Subsystems from Quantum Dynamics under Continuous Measurement
• Quantum Plasmonics with multi-emitters: Application to adiabatic control

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• 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
• Localization measures of parity adapted U($D$)-spin coherent states applied to the phase space analysis of the $D$-level Lipkin-Meshkov-Glick model
• Time-Convolutionless Master Equation Applied to Adiabatic Elimination
• Superoperator master equations for depolarizing dynamics
• Enhancing Nonreciprocity through Squeezing-Induced Symmetry Breaking