$\mathcal{P}\mathcal{T}$ phase transition in open quantum systems with Lindblad dynamics

Abstract

We investigate parity-time ($\mathcal{P}\mathcal{T}$) phase transitions in open quantum systems and discuss a criterion of Liouvillian $\mathcal{P}\mathcal{T}$ symmetry proposed recently by Huber \textit{et al}. [J. Huber \textit{et al}., SciPost Phys. $\text{9}$, 52 (2020)]. Using the third quantization, which is a general method to solve the Lindblad equation for open quadratic systems, we show, with a proposed criterion of $\mathcal{P}\mathcal{T}$ symmetry, that the eigenvalue structure of the Liouvillian clearly changes at the $\mathcal{P}\mathcal{T}$ symmetry breaking point for an open 2-spin model with exactly balanced gain and loss if the total spin is large. In particular, in a $\mathcal{P}\mathcal{T}$ unbroken phase, some eigenvalues are pure imaginary numbers while in a $\mathcal{P}\mathcal{T}$ broken phase, all the eigenvalues are real. From this result, it is analytically shown for an open quantum system including quantum jumps that the dynamics in the long time limit changes from an oscillatory to an overdamped behavior at the proposed $\mathcal{P}\mathcal{T}$ symmetry breaking point. Furthermore, we show a direct relation between the criterion of Huber \textit{et al}. of Liouvillian $\mathcal{P}\mathcal{T}$ symmetry and the dynamics of the physical quantities for quadratic bosonic systems. Our results support the validity of the proposed criterion of Liouvillian $\mathcal{P}\mathcal{T}$ symmetry.

arXiv comment21 pages, 6 figures

References in corpus (51)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Non-Hermitian Physics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• The physics of exceptional points
• Quantum trajectories and open many-body quantum systems
• Open Quantum Systems. An Introduction
• Experimental Study of Active LRC Circuits with PT-Symmetries
• On the Integrability of the Rabi Model
• The elusive memristor: properties of basic electrical circuits
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Observation of parity-time symmetry breaking in a single spin system
• Quantum state tomography across the exceptional point in a single dissipative qubit
• Spectral theory of Liouvillians for dissipative phase transitions
• Dissipative Phase Transition in Central Spin Systems
• Observation of PT phase transition in a simple mechanical system
• Tenfold Way for Quadratic Lindbladians
• Unconventional magnetism via optical pumping of interacting spin systems
• Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion
• Critical dynamical properties of a first-order dissipative phase transition
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Dissipative Phase Transition in the Open Quantum Rabi Model
• PT-Symmetric Plasmonic Metamaterials
• Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model
• PT-symmetric photonic quantum systems with gain and loss do not exist
• PT-symmetric quantum Liouvillian dynamics
• PT-symmetry breaking in the steady state of microscopic gain-loss systems
• Excited-state quantum phase transition in the Rabi model
• Critical behavior of dissipative two-dimensional spin lattices
• Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
• Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$ symmetries
• Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory
• On the uniqueness of the steady-state solution of the Lindblad-Gorini-Kossakowski-Sudarshan equation
• Quantum master equation with balanced gain and loss
• Emergence of PT-symmetry breaking in open quantum systems
• Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model
• Dynamical signatures of topological order in the driven-dissipative Kitaev chain
• On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
• Non-equilibrium magnetic phases in spin lattices with gain and loss
• Generating high-order quantum exceptional points in synthetic dimensions
• Symmetry-protected coherent relaxation of open quantum systems
• Emergent $\mathcal{P}\mathcal{T}$ symmetry in a double-quantum-dot circuit QED set-up
• Quantum correlations in $\mathcal{P}\mathcal{T}$-symmetric systems
• Quantum Rabi Model with Two-Photon Relaxation
• Generic examples of PT-symmetric qubit (spin 1/2) Liouvillians
• Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics

Cited by in corpus (26)

• Operator growth and Krylov construction in dissipative open quantum systems
• Dynamical Control of Quantum Heat Engines Using Exceptional Points
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Enhancement of quantum heat engine by encircling a Liouvillian exceptional point
• Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond
• The non-reciprocal Dicke model
• Nonreciprocal Synchronization of Active Quantum Spins
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations
• Many-Body Open Quantum Systems
• Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
• Dissipative time crystals originating from parity-time symmetry
• Chiral quantum heating and cooling with an optically controlled ion
• Quantum phase transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric transverse-field Ising spin chains
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries
• Dynamical Signatures of Liouvillian Flat Band
• Generation of entanglement and non-stationary states via competing coherent and incoherent bosonic hopping
• Recognizing critical lines via entanglement in non-Hermitian systems
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Mixedness timescale in non-Hermitian quantum systems
• Lindblad dynamics of open multi-mode bosonic systems: Algebra of bilinear superoperators, exceptional points and speed of evolution
• Continuous time crystals as a PT symmetric state and the emergence of critical exceptional points
• Enhanced charging in open Rabi and Dicke quantum batteries
• Topological enhancement of a PT-symmetric Su-Schrieffer-Heeger quantum battery
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• Higher-order Liouvillian exceptional points in the dissipative dynamics of quadratic fermions