Degrees and signatures of broken PT-symmetry in (non-uniform) lattices

Abstract

We investigate the robustness of parity- and time-reversal ($\mP\mT$) symmetric phase in an $N$-site lattice with position-dependent, parity-symmetric hopping function and a pair of imaginary, $\mP\mT$-symmetric impurities. We find that the "fragile" $\mP\mT$-symmetric phase in these lattices is stronger than its counterpart in a lattice with constant hopping. With an open system in mind, we explore the degrees of broken $\mP\mT$-symmetry and their signatures in single-particle wavepacket evolution. We predict that when the $\mP\mT$-symmetric impurities are closest to each other, the time evolution of a wavepacket in an even-$N$ lattice is remarkably different from that in an odd-$N$ lattice. Our results suggest that $\mP\mT$-symmetry breaking in such lattices is accompanied by rich, hitherto unanticipated, phenomena.

5 figures

References in corpus (11)

• Repulsively bound atom pairs in an optical lattice
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
• Physics counterpart of the PT non-hermitian tight-binding chain
• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• Gegenbauer-solvable quantum chain model
• Conditional observability
• Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems

Cited by in corpus (37)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• PT Symmetric Aubry-Andre Model
• Optical waveguide arrays: quantum effects and PT symmetry breaking
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• PT spectroscopy of the Rabi problem
• Spontaneous PT symmetry breaking in non-Hermitian coupled cavities array
• Perfect State Transfer in PT-symmetric Non-Hermitian Networks
• Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry
• Convective and absolute PT symmetry breaking in tight-binding lattices
• Origin of maximal symmetry breaking in even PT-symmetric lattices
• Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point
• Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system
• Hermitian dynamics in a class of pseudo-Hermitian networks
• Hermitian scattering behavior for the non-Hermitian scattering center
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• Non-Hermitian interferometer: Unidirectional amplification without distortion
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Dynamics, disorder effects, and PT-symmetry breaking in waveguide lattices with localized eigenstates
• Long-range entangled zero-mode state in a non-Hermitian lattice
• PT-symmetric optical superlattices
• Quantum transport in non-Hermitian impurity array
• Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system
• Parity-time symmetry under magnetic flux
• Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry
• PT symmetric lattices with a local degree of freedom
• PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring
• An attractor dynamics in a non-Hermitian two-level system
• Semi-localization transition driven by a single asymmetrical tunneling
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Disorder effects in tunable waveguide arrays with parity-symmetric tunneling
• Exceptional spectrum and dynamic magnetization
• Dissipation-induced bound states as a two-level system
• Discrete solitons dynamics in $\mathcal{P}\mathcal{T}$-symmetric oligomers with complex-valued couplings
• Parity-Time Symmetry Breaking in Coupled Nanobeam Cavities