Bound states, scattering states and resonant states in PT-symmetric open quantum systems

Abstract

We study a simple open quantum system with a PT-symmetric defect potential as a prototype to illustrate general features of PT-symmetric open quantum systems; however, the potential could be mimicked by a number of recent PT experiments. One key feature is the resonance in continuum (RIC), which appears in both the discrete spectrum and scattering spectrum. The RIC forms a standing wave extending throughout the spatial extent of the system, representing a resonance between the open environment and the central PT-symmetric potential. We illustrate that as one deforms the system parameters, the RIC may exit the continuum by splitting into a bound state and a virtual bound state at the band edge, a process that should be experimentally observable. We also study the exceptional points (EPs) at which two eigenvalues coalesce; we categorize these as either EP2As, at which two real-valued solutions coalesce before becoming complex-valued, or EP2Bs, for which the two solutions are complex on either side of the EP. The EP2As are associated with PT-symmetry breaking; we argue that these are more stable against parameter perturbation than the EP2Bs. We also study complex-valued solutions of the discrete spectrum for which the wave function is nevertheless spatially localized, something not allowed in traditional open quantum systems; we illustrate that these may form quasi-bound states in continuum (QBICs) under some circumstances. We also study the scattering properties of the system, including states that support invisible propagation and some general features of perfect transmission states. We finally construct scattering states that satisfy PT-symmetric boundary conditions; while these states do not conserve the traditional probability current, we introduce the PT-current that is preserved. The perfect transmission states appear as a special case of the PT-symmetric scattering states.

References in corpus (20)

• Making Sense of Non-Hermitian Hamiltonians
• Coherent Perfect Absorbers: Time-reversed Lasers
• Visualization of Branch Points in PT-Symmetric Waveguides
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Invisibility and PT-symmetry
• Bound states in the continuum in a single-level Fano-Anderson model
• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• Chirality of wave functions for three coalescing levels
• PT-symmetric quantum mechanics
• Quasi-bound states in continuum
• Nonanalytic enhancement of the charge transfer from adatom to one-dimensional semiconductor superlattice and optical absorption spectrum
• Systems of coupled PT-symmetric oscillators
• Amplification of non-Markovian decay due to bound state absorption into continuum
• Time-reversal symmetric resolution of unity without background integrals in open quantum systems
• Generalized Unitarity and Reciprocity Relations for PT-symmetric Scattering Potentials
• Equivalence of the effective Hamiltonian approach and the Siegert boundary condition for resonant states
• Statistics of Resonances in a Semi-infinite Disordered Chain
• Resonances in one-dimensional Disordered Chain

Cited by in corpus (41)

• Explicit definition of $\mathcal{P}\mathcal{T}$ symmetry for non-unitary quantum walks with gain and loss
• Quasi-bound states in the continuum induced by $\mathcal{P}\mathcal{T}$-symmetry breaking
• Non-Hermitian tight-binding network engineering
• Unitarity corridors to exceptional points
• Higher-order Time-Symmetry-Breaking Phase Transition due to meeting of an Exceptional Point and Fano Resonance
• Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry
• Bound states in the continuum in a two-dimensional PT-symmetric system
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• Designing lasing and perfectly absorbing potentials
• Spectral singularities of odd-$PT$-symmetric potential
• Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays
• Passage through exceptional point: Case study
• A new perspective on the Fano absorption spectrum in terms of complex spectral analysis
• $\mathcal{P}\mathcal{T}$ symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model
• Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system
• Non-Hermitian Hartman effect
• PT-symmetry breaking in resonant tunneling heterostructures
• Excepional Points from Hamiltonians of hybrid physical systems: Squeezing and anti-Squeezing
• Spectral and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric tight-binding chain with gain and loss
• Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations
• The Atomistic Green's Function method for acoustic and elastic wave-scattering problems
• Coherent single-spin electron resonance spectroscopy manifested at an exceptional-point singularity in a doped polyacetylene
• Resonant spectra of multipole-bound anions
• Phase Transitions and Virtual Exceptional Points in Quantum Emitters Coupled to Dissipative Baths
• Polar magneto-optic Kerr and Faraday effects in finite periodic \texorpdfstring{$\mathcal{P}\mathcal{T}$}{PT}-symmetric systems
• Spacing gain and absorption in a simple $\mathcal{P}\mathcal{T}$-symmetric model: spectral singularities and ladders of eigenvalues and resonances
• Broken Hermiticity phase transition in Bose-Hubbard model
• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Effects of disorder on non-unitary $\mathcal{P}\mathcal{T}$ symmetric quantum walks
• Contact interactions and Kronig-Penney Models in Hermitian and PT-symmetric Quantum Mechanics
• An investigation of $\mathcal{P}\mathcal{T}$-symmetry breaking in tight-binding chains
• Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields
• Characteristic determinant approach to the spectrum of one-dimensional $\mathcal{P}\mathcal{T}$-symmetric systems
• Weak-coupling bound states in semi-infinite topological waveguide QED
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states
• Characteristic influence of exceptional points in quantum dynamics
• Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians
• Swanson Hamiltonian: non-PT-symmetry phase