Sufficient conditions for adiabaticity in open quantum systems

Abstract

The adiabatic approximation exhibits wide applicability in quantum mechanics, providing a simple approach for nontransitional dynamics in quantum systems governed by slowly varying time-dependent Hamiltonians. However, the standard adiabatic theorem is specifically derived for closed quantum systems. In a realistic open system scenario, the inevitable system-reservoir interaction must be taken into account, which strongly impacts the generalization of the adiabatic behavior. In this paper, we introduce sufficient conditions for the adiabatic approximation in open quantum systems. These conditions are simple yet general, providing a suitable instrument to investigate adiabaticity for arbitrary initial mixed states evolving under time local master equations. We first illustrate our results by showing that the adiabatic approximation for open systems is compatible with the description of quantum thermodynamics at thermal equilibrium, where irreversible entropy production is vanishing. We also apply our sufficient conditions as a tool in quantum control, evaluating the adiabatic behavior for the Hamiltonians of both the Deutsch algorithm and the Landau-Zener model under decoherence.

arXiv comment13 pages, 3 figures

References in corpus (26)

• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Adiabatic Quantum Computing
• Shortcuts to adiabaticity: concepts, methods, and applications
• The second law, Maxwell's daemon and work derivable from quantum heat engines
• Lewis-Riesenfeld invariants and transitionless tracking algorithm
• Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity
• Adiabatic Quantum Computation in Open Systems
• Adiabatic approximation in open quantum systems
• Experimental implementation of an adiabatic quantum optimization algorithm
• Beyond the Quantum Adiabatic Approximation: Adiabatic Perturbation Theory
• Sufficiency Criterion for the Validity of the Adiabatic Approximation
• Adiabaticity in open quantum systems
• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Superadiabatic dynamics in open quantum systems
• Adiabatic theorems for generators of contracting evolutions
• Adiabatic Approximation for weakly open systems
• Reverse engineering of a Hamiltonian by designing the evolution operators
• Adiabatic Markovian Dynamics
• Fast and robust control of two interacting spins
• Invariant-based inverse engineering for fluctuation transfer between membranes in an optomechanical cavity system
• Effective Hamiltonian approach to adiabatic approximation in open systems
• Adiabatic Perturbation Theory and Geometric Phases for Degenerate Systems
• Eigenstate Tracking in Open Quantum Systems
• Quantum thermodynamics in adiabatic open systems and its trapped-ion experimental realization
• Quantum gates by inverse engineering of a Hamiltonian
• Adiabatic quantum dynamics under decoherence in a controllable trapped-ion setup

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