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

Abstract

Usually, when investigating exceptional points (EPs) of an open Markovian bosonic system, one deals with spectral degeneracies of a non-Hermitian Hamiltonian (NHH), which can correctly describe the system dynamics only in the semiclassical regime. A recently proposed quantum Liouvillian framework enables to completely determine the dynamical properties of such systems and their EPs (referred to as Liouvillian EPs, or LEPs) in the quantum regime by taking into account the effects of quantum jumps, which are ignored in the NHH formalism. Moreover, the symmetry and eigenfrequency spectrum of the NHH become a part of much larger Liouvillian eigenspace. As such, the EPs of an NHH form a subspace of the LEPs. Here we show that once an NHH of a dissipative linear bosonic system exhibits an EP of a certain finite order $n$, it immediately implies that the corresponding LEP can become of any higher order $m\ge n$, defined in the infinite Hilbert space. Most importantly, these higher-order LEPs can be identified by the coherence and spectral functions at the steady state. The coherence functions can offer a convenient tool to probe extreme system sensitivity to external perturbations in the vicinity of higher-order LEPs. As an example, we study a linear bosonic system of a bimodal cavity with incoherent mode coupling to reveal its higher-order LEPs; particularly, of second and third order via first- and second-order coherence functions, respectively. Accordingly, these LEPs can be additionally revealed by squared and cubic Lorentzian spectral lineshapes in the power and intensity-fluctuation spectra. Moreover, we demonstrate that these EPs can also be associated with spontaneous parity-time ($\mathcal{P}\mathcal{T}$) and anti-$\mathcal{P}\mathcal{T}$-symmetry breaking in the system studied.

arXiv comment15 pages, 4 figures

References in corpus (60)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Loss-induced suppression and revival of lasing
• Topological energy transfer in an optomechanical system with exceptional points
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• PT-Symmetric Phonon Laser
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Second-Order Topological Phases in Non-Hermitian Systems
• Anti-Parity-Time Symmetric Optics via Flying Atoms
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Spectral theory of Liouvillians for dissipative phase transitions
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Optomechanically-Induced Transparency in partiy-time-symmetric microresonators
• Quantum Noise Theory of Exceptional Point Sensors
• No exceptional precision of exceptional point sensors
• Petermann-factor limited sensing near an exceptional point
• Probing a dissipative phase transition via dynamical optical hysteresis
• Quantization of quasinormal modes for open cavities and plasmonic cavity-QED
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Perfectly absorbing exceptional points and chiral absorbers
• High-order exceptional points in optomechanics
• General Theory of Spontaneous Emission Near Exceptional Points
• Critical dynamical properties of a first-order dissipative phase transition
• Signatures of a dissipative phase transition in photon correlation measurements
• Synthetic parity-time symmetry breaking in a single microcavity
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope
• Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system
• Topological non-Hermitian origin of surface Maxwell waves
• Emergent equilibrium in many-body optical bistability
• Dynamical quantum phase transitions in non-Hermitian lattices
• Fluctuations and noise-limited sensing near the exceptional point of $\mathcal{P}\mathcal{T}$-symmetric resonator systems
• Effective spontaneous PT-symmetry breaking in hybridized metamaterials
• Exceptional Points in Random-Defect Phonon Lasers
• Critical slowing down in driven-dissipative Bose-Hubbard lattices
• Exceptional Points in a Non-Hermitian Topological Pump
• Chiral modes at exceptional points in exciton-polariton quantum fluids
• Symmetry-protected zero-mode laser with a tunable spatial profile
• PT-symmetric quantum Liouvillian dynamics
• Topological band theory for non-Hermitian systems from the Dirac equation
• Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
• Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
• Topological protection from exceptional points in Weyl and nodal line semimetals
• Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory
• Scully-Lamb quantum laser model for parity-time-symmetric whispering-gallery microcavities: Gain saturation effects and non-reciprocity
• High-order exceptional points in supersymmetric arrays
• 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
• Exceptional points of any order in a single, lossy, waveguide beamsplitter by photon-number-resolved detection
• Intensity fluctuations in bimodal micropillar lasers enhanced by quantum-dot gain competition
• Dynamical signatures of topological order in the driven-dissipative Kitaev chain
• $\mathcal{P}\mathcal{T}$-symmetry from Lindblad dynamics in an optomechanical system
• Quantum statistics of overlapping modes in open resonators
• Solving the quantum master equation of coupled harmonic oscillators with Lie algebra methods
• Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator
• Quantum theory of a two-mode open-cavity laser

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• $\mathcal{P}\mathcal{T}$ phase transition in open quantum systems with Lindblad dynamics
• Experimental demonstration of coherence flow in $\mathcal{P}\mathcal{T}$- and anti-$\mathcal{P}\mathcal{T}$-symmetric systems
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• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• Experimental observation of non-Markovian quantum exceptional points
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
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• Interaction-Induced Second-Order Skin Effect
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• Engineering nonequilibrium steady states through Floquet Liouvillians
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• Lindblad dynamics of open multi-mode bosonic systems: Algebra of bilinear superoperators, exceptional points and speed of evolution
• Asymptotic Exceptional Steady States in Dissipative Dynamics
• Third-order exceptional surface in a pseudo-Hermitian superconducting circuit
• Spectroscopic Signatures of a Liouvillian Exceptional Spectral Phase in a Collective Spin
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• Higher-order Liouvillian exceptional points in the dissipative dynamics of quadratic fermions