Optical waveguide arrays: quantum effects and PT symmetry breaking

Abstract

Over the last two decades, advances in fabrication have led to significant progress in creating patterned heterostructures that support either carriers, such as electrons or holes, with specific band structure or electromagnetic waves with a given mode structure and dispersion. In this article, we review the properties of light in coupled optical waveguides that support specific energy spectra, with or without the effects of disorder, that are well-described by a Hermitian tight-binding model. We show that with a judicious choice of the initial wave packet, this system displays the characteristics of a quantum particle, including transverse photonic transport and localization, and that of a classical particle. We extend the analysis to non-Hermitian, parity and time-reversal ($\mathcal{P}\mathcal{T}$) symmetric Hamiltonians which physically represent waveguide arrays with spatially separated, balanced absorption or amplification. We show that coupled waveguides are an ideal candidate to simulate $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians and the transition from a purely real energy spectrum to a spectrum with complex conjugate eigenvalues that occurs in them.

16 pages, 12 figures, Invited Review for European Physics Journal - Applied Physics

References in corpus (11)

• Making Sense of Non-Hermitian Hamiltonians
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Coherent Perfect Absorbers: Time-reversed Lasers
• Quantum walks of correlated particles
• Realization of quantum walks with negligible decoherence in waveguide lattices
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a necklace of coupled optical waveguides
• Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices
• Spectral and transport properties of time-periodic PT-symmetric tight-binding lattices
• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• Tunable waveguide lattices with non-uniform parity-symmetric tunneling
• Level density and level-spacing distributions of random, self-adjoint, non-Hermitian matrices

Cited by in corpus (45)

• A review of progress in the physics of open quantum systems: theory and experiment
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• PT spectroscopy of the Rabi problem
• Nearby states in non-Hermitian quantum systems
• Regularization of the spectral singularity in $\mathcal{P}\mathcal{T}$-symmetric systems by all order nonlinearities: Nonreciprocity and optical isolation
• A review on quantum information processing in cavities
• PT-restoration via increased loss-gain in PT-symmetric Aubry-Andre model
• Passive $\mathcal{P}\mathcal{T}$-symmetry breaking transitions without exceptional points in dissipative photonic systems
• Observation of slowly decaying eigenmodes without exceptional points in Floquet, dissipative, synthetic circuits
• Conserved quantities in parity-time symmetric systems
• $\mathcal{P}\mathcal{T}$-symmetry from Lindblad dynamics in an optomechanical system
• Emergent $\mathcal{P}\mathcal{T}$ symmetry in a double-quantum-dot circuit QED set-up
• Quantum information dynamics in a high-dimensional parity-time-symmetric system
• Revisiting the optical $PT$-symmetric dimer
• Maximal quantum entanglement at exceptional points via unitary and thermal dynamics
• Interplay between Fano resonance and $\mathcal{P}\mathcal{T}$ symmetry in non-Hermitian discrete systems
• Multiply Degenerate Exceptional Points and Quantum Phase Transitions
• Photonic realization of topologically protected bound states in domain-wall waveguide arrays
• Conserved quantities, exceptional points, and antilinear symmetries in non-Hermitian systems
• Observation of two PT transitions in an electric circuit with balanced gain and loss
• PT-symmetric optical superlattices
• Floquet exceptional contours in Lindblad dynamics with time-periodic drive and dissipation
• Dynamics of finite dimensional non-hermitian systems with indefinite metric
• Scheme for realizing quantum dense coding via entanglement swapping
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a Kitaev chain with one pair of gain-loss potentials
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• PT-symmetry breaking with divergent potentials: lattice and continuum cases
• Connecting active and passive $\mathcal{P}\mathcal{T}$-symmetric Floquet modulation models
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• Excepional Points from Hamiltonians of hybrid physical systems: Squeezing and anti-Squeezing
• Parity-time symmetric systems with memory
• Non-Markovian anti-parity-time symmetric systems: theory and experiment
• Photon propagation through linearly active dimers
• Non-Hermitian Model for Asymmetrical Tunneling
• Generating high-order exceptional points in coupled electronic oscillators using complex synthetic gauge fields
• Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• $\mathcal{P}\mathcal{T}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities
• Stability of time-periodic $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonians with different periodicities
• Conserved quantities in non-Hermitian systems via vectorization method
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Sublattice signatures of transitions in a $\mathcal{P}\mathcal{T}$-symmetric dimer lattice
• Demonstration of imaginary-mass particles by optical simulation in non-Hermitian systems
• Remarks on the preservation of no-signaling principle in parity-time-symmetric quantum mechanics
• PT-symmetry enabled stable modes in multi-core fiber