Signature of exceptional point phase transition in Hermitian systems

Abstract

Exceptional point (EP) is a spectral singularity in non-Hermitian systems. The passing over the EP leads to a phase transition, which endows the system with unconventional features that find a wide range of applications. However, the need of using the dissipation and amplification limits the possible applications of systems with the EP. In this work, we demonstrate an existence of signature of exceptional point phase transition in Hermitian systems that are free from dissipation and amplification. We consider a composite Hermitian system including both two coupled oscillators and their environment consisting only of several tens of degrees of freedom. We show that the dynamics of such a Hermitian system demonstrate a transition, which occurs at the coupling strength between oscillators corresponding to the EP in the non-Hermitian system. This transition manifests itself even in the non-Markovian regime of the system dynamics in which collapses and revivals of the energy occur. Thus, we demonstrate that the phase transition occurring at the passing over the EP in the non-Hermitian system manifests itself in the Hermitian system at all time. We discuss the experimental scheme to observe the signature of EP phase transition in the non-Markovian regime.

arXiv commentAccepted in Quantum, 2023-04-06

References in corpus (32)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Charge insensitive qubit design derived from the Cooper pair box
• Making Sense of Non-Hermitian Hamiltonians
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Manipulating the Quantum State of an Electrical Circuit
• The physics of exceptional points
• Non-Markovian dynamics in open quantum systems
• Topological energy transfer in an optomechanical system with exceptional points
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Photon-mediated interactions between distant artificial atoms
• Pump-induced Exceptional Points in Lasers
• Enhanced sensitivity operation of an optical gyroscope near an exceptional point
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Observation of the exceptional point in cavity magnon-polaritons
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Quantum Noise Theory of Exceptional Point Sensors
• Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms
• No exceptional precision of exceptional point sensors
• Nonexponential decay of a giant artificial atom
• Petermann-factor limited sensing near an exceptional point
• Higher-order exceptional point in a cavity magnonics system
• Non-Hermitian dynamics without dissipation in quantum systems
• Interacting Qubit-Photon Bound States with Superconducting Circuits
• Observation of a non-Hermitian phase transition in an optical quantum gas
• Parametric instability of non-Hermitian systems near the exceptional point
• On the time evolution at a fluctuating exceptional point
• Universal Critical Behaviors in Non-Hermitian Phase Transitions
• Exceptional points as lasing pre-thresholds in open-cavity lasers
• Strong-coupling-assisted formation of coherent radiation below the lasing threshold
• Environment-assisted strong coupling regime

Cited by in corpus (6)

• Non-Markovian Quantum Exceptional Points
• Quantum Metrology with Higher-order Exceptional Points in Atom-cavity Magnonics
• Emergent Liouvillian exceptional points from exact principles
• Non-standard quantum algebras and infinite-dimensional PT-symmetric systems
• Spontaneous symmetry emergence in a Hermitian system of coupled oscillators without symmetry
• Non-Markovian exceptional points in waveguide quantum electrodynamics