Adiabatic approximation in open quantum systems

Abstract

We generalize the standard quantum adiabatic approximation to the case of open quantum systems. We define the adiabatic limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of independently evolving Jordan blocks. We then establish validity and invalidity conditions for this approximation and discuss their applicability to superoperators changing slowly in time. As an example, the adiabatic evolution of a two-level open system is analysed.

v4: 13 pages, 1 figure. Published version. v3: Time condition for adiabaticity improved and references updated

References in corpus (17)

• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Holonomic Quantum Computation
• Geometric quantum computation with NMR
• Geometric Manipulation of Trapped Ions for Quantum Computation
• The Bloch Vector for N-Level Systems
• Non-Abelian Berry connections for quantum computation
• Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
• Adiabatic Theorem without a Gap Condition
• Genuine quantum trajectories for non-Markovian processes
• Non-Abelian phases, charge pumping, and quantum computation with Josephson junctions
• From Completely Positive Maps to the Quantum Markovian Semigroup Master Equation
• Spin-1/2 geometric phase driven by decohering quantum fields
• Optical Holonomic Quantum Computer
• An Adiabatic Theorem without a Gap Condition: Two level system coupled to quantized radiation field
• Geometric phases of mesoscopic spin in Bose-Einstein condensates
• Geometric phase for an adiabatically evolving open quantum system
• Imaginary Phases in Two-Level Model with Spontaneous Decay

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