Dynamical invariants and nonadiabatic geometric phases in open quantum systems

Abstract

We introduce an operational framework to analyze non-adiabatic Abelian and non-Abelian, cyclic and non-cyclic, geometric phases in open quantum systems. In order to remove the adiabaticity condition, we generalize the theory of dynamical invariants to the context of open systems evolving under arbitrary convolutionless master equations. Geometric phases are then defined through the Jordan canonical form of the dynamical invariant associated with the super-operator that governs the master equation. As a by-product, we provide a sufficient condition for the robustness of the phase against a given decohering process. We illustrate our results by considering a two-level system in a Markovian interaction with the environment, where we show that the non-adiabatic geometric phase acquired by the system can be constructed in such a way that it is robust against both dephasing and spontaneous emission.

9 pages, 3 figures. v2: minor corrections and subsection IV.D added. Published version

References in corpus (19)

• Holonomic Quantum Computation
• Geometric quantum computation with NMR
• Geometric Manipulation of Trapped Ions for Quantum Computation
• Geometric phase in open systems
• Adiabatic Quantum Computation in Open Systems
• Adiabatic approximation in open quantum systems
• Non-Abelian phases, charge pumping, and quantum computation with Josephson junctions
• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Geometric phase distributions for open quantum systems
• Holonomic quantum computation in the presence of decoherence
• Adiabatic Approximation for weakly open systems
• Phases of quantum states in completely positive non-unitary evolution
• Noncyclic geometric phase and its non-Abelian generalization
• Geometric phase for open quantum systems and stochastic unravellings
• Berry's Phase in the Presence of a Dissipative Medium
• Geometric phase for an adiabatically evolving open quantum system
• Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants
• Adiabatic Approximation in the Density Matrix Approach: Non-Degenerate Systems
• Nonadiabatic geometric phase induced by a counterpart of the Stark shift

Cited by in corpus (20)

• Shortcuts to adiabaticity: concepts, methods, and applications
• Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors
• Charge and spin dynamics driven by ultrashort extreme broadband pulses: a theory perspective
• Noise Resistant Quantum Control Using Dynamical Invariants
• Demonstration of dynamical control of three-level open systems with a superconducting qutrit
• Quantum computation in continuous time using dynamic invariants
• Shortcuts to adiabaticity for open quantum systems and a mixed-state inverse engineering scheme
• Non-adiabatic Fast Control of Mixed States based on Lewis-Riesenfeld Invariant
• Effective Hamiltonian Approach to Open Systems and Its Applications
• Dynamical invariants in non-Markovian quantum state diffusion equation
• Entanglement dynamics via geometric phases in quantum spin chains
• The Dynamical Invariant of Open Quantum System
• A general treatment of geometric phases and dynamical invariants
• A new kind of geometric phases in open quantum systems and higher gauge theory
• The driven-Markovian master equation based on the Lewis-Riesenfeld invariants theory
• Geometric Phase: a Diagnostic Tool for Entanglement
• Unified linear response theory of quantum electronic circuits
• High-fidelity Nuclear Coherent Population Transfer via the Mixed-State Inverse Engineering
• Quantum Transport Protected by Acceleration From Nonadiabaticity and Dissipation
• The effects of light-wave nonstaticity on accompanying geometric-phase evolutions