Time-Convolutionless Master Equation Applied to Adiabatic Elimination
arXiv:2409.08332 · doi:10.1103/PhysRevA.111.052206
Abstract
In open quantum systems theory, reduced models are invaluable for conceptual understanding and computational efficiency. Adiabatic elimination is a useful model reduction method for systems with separated timescales, where a reduced model is derived by discarding rapidly decaying degrees of freedom. So far, adiabatic elimination has been formulated using a geometric approach, which provides a versatile and general framework. This article introduces a reformulation of adiabatic elimination through the framework of the time-convolutionless (TCL) master equation, a widely recognized tool for computing projected time evolution in open quantum systems. We show that the TCL master equation formulation yields results equivalent to those obtained from the geometric formulation. By applying the TCL master equation formulation to typical examples, we demonstrate a practical methodology for performing adiabatic elimination calculation. This study not only bridges two previously independent approaches, thereby making the adiabatic elimination method accessible to a broader audience, but also enables the analysis of complex cases that are challenging within the geometric formulation. Additionally, it reveals a geometric interpretation of the TCL master equation formalism.
11+11 pages, 3+2 figures. Major updates include the addition of a source code link (Ref. [57]) and a new Appendix E discussing applicability to an infinite-dimensional system
References in corpus (32)
- Non-Hermitian Physics
- Dynamically protected cat-qubits: a new paradigm for universal quantum computation
- Effective operator formalism for open quantum systems
- Non-perturbative treatment of non-Markovian dynamics of open quantum systems
- Observation of the Mott Insulator to Superfluid Crossover of a Driven-Dissipative Bose-Hubbard System
- Towards a theory of metastability in open quantum dynamics
- Controlling spin relaxation with a cavity
- Dissipation induced Tonks-Girardeau gas in an optical lattice
- Kinetic constraints, hierarchical relaxation and onset of glassiness in strongly interacting and dissipative Rydberg gases
- Accuracy Assessment of Perturbative Master Equations -- Embracing Non-Positivity
- Staying positive: going beyond Lindblad with perturbative master equations
- Two-qubit spectroscopy of spatiotemporally correlated quantum noise in superconducting qubits
- Quantum control of a cat-qubit with bit-flip times exceeding ten seconds
- Atom-only descriptions of the driven-dissipative Dicke model
- Generalized Schrieffer-Wolff Formalism for Dissipative Systems
- Exceptional points of the Lindblad operator of a two-level system
- Numerically exact treatment of many body self-organization in a cavity
- Dissipative Universal Lindbladian Simulation
- Dynamic nuclear polarization as kinetically constrained diffusion
- Calculation of coherences in Foerster and modified Redfield theories of excitation energy transfer
- Misbelief and misunderstandings on the non--Markovian dynamics of a damped harmonic oscillator
- Theory of absorption lineshape in monolayers of transition metal dichalcogenides
- Smoking-gun signatures of non-Markovianity of a superconducting qubit
- Adiabatic Elimination and Sub-space Evolution of Open Quantum Systems
- Open quantum systems beyond Fermi's golden rule: Diagrammatic expansion of the steady-state time-convolutionless master equation
- Recursive approach for non-Markovian time-convolutionless master equations
- Feynman-Vernon influence functional approach to quantum transport in interacting nanojunctions: An analytical hierarchical study
- Eternal Adiabaticity
- Projection based adiabatic elimination of bipartite open quantum systems
- Quantum adiabatic elimination at arbitrary order for photon number measurement
- Complete positivity violation of the reduced dynamics in higher-order quantum adiabatic elimination
- Tutorial: projector approach to master equations for open quantum systems