Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{P}\mathcal{T}$ symmetry

Abstract

We study symmetries of open bosonic systems in the presence of laser pumping. Non-Hermitian Hamiltonians describing these systems can be parity-time ($\mathcal{P}\mathcal{T}$) symmetric in special cases only. Systems exhibiting this symmetry are characterised by real-valued energy spectra and can display exceptional points, where a symmetry-breaking transition occurs. We demonstrate that there is a more general type of symmetry, i.e., rotation-time ($\mathcal{R}\mathcal{T}$) symmetry. We observe that $\mathcal{R}\mathcal{T}$-symmetric non-Hermitian Hamiltonians exhibit real-valued energy spectra which can be made singular by symmetry breaking. To calculate the spectra of the studied bosonic non-diagonalisable Hamiltonians we apply diagonalisation methods based on bosonic algebra. Finally, we list a versatile set rules allowing to immediately identifying or constructing $\mathcal{R}\mathcal{T}$-symmetric Hamiltonians. We believe that our results on the $\mathcal{R}\mathcal{T}$-symmetric class of bosonic systems and their spectral singularities can lead to new applications inspired by those of the $\mathcal{P}\mathcal{T}$-symmetric systems.

arXiv comment9 pages, 3 figures. This is a preprint of an article published in Scientific Reports. The final authenticated version is available online at: https://doi.org/10.1038/s41598-020-76787-8

References in corpus (35)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• 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
• Spawning rings of exceptional points out of Dirac cones
• 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
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Quantum Noise Theory of Exceptional Point Sensors
• Sensing with exceptional surfaces: combining sensitivity with robustness
• Direct detection of quantum entanglement
• Inverse design of third-order Dirac exceptional points in photonic crystals
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Deterministic quantum nonlinear optics with single atoms and virtual photons
• Exceptional Points in Atomic Spectra
• Higher-order exceptional point in a cavity magnonics system
• Incident Direction Independent Wave Propagation and Unidirectional Lasing
• Non-Hermitian Acoustic Metamaterials: the role of Exceptional Points in sound absorption
• Controlled-phase Gate using Dynamically Coupled Cavities and Optical Nonlinearities
• All-real spectra in optical systems with arbitrary gain and loss distributions
• Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory
• Quantum scissors - finite-dimensional states engineering
• Time-dependent $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics in generic non-Hermitian systems
• Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry
• Wave emission and absorption at spectral singularities
• Generalized Berry phase for a bosonic Bogoliubov system with exceptional points
• Geometric phase and phase diagram for non-Hermitian quantum XY model
• Spectrum and normal modes of non-hermitian quadratic boson operators
• Effective non-Hermitian physics for degenerate ground states of a nonHermitian Ising model with $\mathcal{R}\mathcal{T}$ symmetry
• Creating a switchable optical cavity with controllable quantum-state mapping between two modes

Cited by in corpus (7)

• Generating high-order quantum exceptional points in synthetic dimensions
• Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities
• The effect of thermal photons on exceptional points in coupled resonators
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Exceptional point in self-consistent Markovian master equations
• Localization with non-Hermitian off-diagonal disorder