Exceptional point in self-consistent Markovian master equations

Abstract

Exceptional point (EP) denotes the non-Hermitian degeneracy, in which both eigenvalues and eigenstates become identical. By the conventional local Markovian master equation, EP can be constructed by parity-time (PT) or anti-PT symmetry in a system composed of coupled subsystems. However, the coupling between two systems makes the conventional local Markovian master equation become inconsistent. By using the self-consistent Markovian master equation, we show that there is no EP in the system composed of two bosonic subsystems. We further prove that the conventional local master equation can be valid only when the coupling strength is much smaller than the difference in resonance frequency between the two subsystems, rather than the resonance frequencies. In a system composed of three bosonic subsystems, EP can be obtained by adiabatically eliminating one of the three subsystems.

arXiv comment9 pages, 1 figure

References in corpus (32)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Loss-induced suppression and revival of lasing
• Topological energy transfer in an optomechanical system with exceptional points
• Quantum vacuum properties of the intersubband cavity polariton field
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Dissipation and Ultrastrong Coupling in Circuit QED
• Quantum Noise Theory of Exceptional Point Sensors
• On the Local and Global Approaches to Quantum Transport and Violation of the Second-law of Thermodynamics
• Reconciliation of quantum local master equations with thermodynamics
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Light stops at exceptional points
• Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation
• Chiral Coherent Perfect Absorption on Exceptional Surfaces
• Dynamically encircling an exceptional point in a real quantum system
• Observation of anti-PT symmetry phase transition in the magnon-cavity-magnon coupled system
• Non-additive dissipation in open quantum networks out of equilibrium
• Non-Hermitian engineering of terahertz light using exceptional points in electrically tuneable collective light-matter interactions
• Enhanced sensing of weak anharmonicities through coherences in dissipatively coupled anti-PT symmetric systems
• Exceptional magnetic sensitivity of PT-symmetric cavity magnon polaritons
• Dissipation and Thermal Noise in Hybrid Quantum Systems in the Ultrastrong Coupling Regime
• Langevin Approach to Quantum Optics with Molecules
• Topological quantum state control through exceptional-point proximity
• Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory
• Enhancement of quantum heat engine by encircling a Liouvillian exceptional point
• Thermodynamic consistency of the optomechanical master equation
• Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems
• Local master equations may fail to describe dissipative critical behavior
• Quantum Thermometry with a Dissipative Quantum Rabi System
• The effect of thermal photons on exceptional points in coupled resonators
• Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{P}\mathcal{T}$ symmetry
• Quantum phases transition revealed by the exceptional point in Hopfield-Bogoliubov matrix