Non-Hermitian Hartman effect

Abstract

The Hartman effect refers to the rather paradoxical result that the time spent by a quantum mechanical particle or a photon to tunnel through an opaque potential barrier becomes independent of barrier width for long barriers. Such an effect, which has been observed in different physical settings, raised a lively debate and some controversies, owing to the correct definition and interpretation of tunneling times and the apparent superluminal transmission. A rather open question is whether (and under which conditions) the Hartman effect persists for inelastic scattering, i.e. when the potential becomes non-Hermitian and the scattering matrix is not unitary. Here we consider tunneling through a heterojunction barrier in the tight-binding picture, where the barrier consists of a generally non-Hermitian finite-sized lattice attached to two semi-infinite nearest-neighbor Hermitian lattice leads. We derive a simple and general condition for the persistence of the Hartman effect in non-Hermitian barriers, showing that it can be found rather generally when non-Hermiticity arises from non-reciprocal couplings, i.e. when the barrier displays the non-Hermitian skin effect, without any special symmetry in the system.

arXiv comment14 pages, 7 figures, accepted for publication in Annalen der Physik. In memory of Prof. Erasmo Recami, a great scientistic who passed away on July 2021 and who introduced me to the world of superluminal phenomena

References in corpus (54)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Localization transitions in non-Hermitian quantum mechanics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Non-Bloch Band Theory of Non-Hermitian Systems
• Non-Hermitian Chern bands
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Topologically protected midgap states in complex photonic lattices
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• New topological invariants in non-Hermitian systems
• Observation of arbitrary topological windings of a non-Hermitian band
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• How much time does a tunneling particle spend in the barrier region?
• Robust light transport in non-Hermitian photonic lattices
• Tunneling Time in Ultrafast Science is Real and Probabilistic
• Experimental evidence for Wigner's tunneling time
• Unified time analysis of photon and (nonrelativistic) particle Tunnelling, and the Superluminal group-velocity problem
• Perspective on topological states of non-Hermitian lattices
• Non-Bloch band collapse and chiral Zener tunneling
• Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field
• Non-Hermitian gauged topological laser arrays
• Topological classification of non-Hermitian systems with reflection symmetry
• Measurement of Superluminal optical tunneling times in double-barrier photonic bandgaps
• Observation of topological transport quantization by dissipation in fast Thouless pumps
• S-matrix theory for transmission through billiards in tight-binding approach
• Topological pumping of edge states via adiabatic passage
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Non-Hermitian skin effect beyond the tight-binding models
• Non-Hermitian tight-binding network engineering
• Non-Hermitian scattering on a tight-binding lattice
• Dynamical topological invariant for non-Hermitian Rice-Mele model
• Localization in non-Hermitian quantum mechanics and flux-line pinning in superconductors
• Observation of the Decrease of Larmor Tunneling Times with Lower Incident Energy
• Ultra-fast propagation of Schrödinger waves in absorbing media
• Hartman effect and spin precession in graphene
• Energy structure, density of states and transmission properties of the periodic 1D Tight-Binding lattice with a generic unit cell of $u$ sites
• Spin tunneling through an indirect barrier
• Klein tunnelling and Hartman effect in graphene junctions with proximity exchange field
• Tunneling times through barrier with inelasticity
• General(ized) Hartman effect
• Wigner's friends, tunnelling times and Feynman's "only mystery of quantum mechanics"

Cited by in corpus (6)

• Topological Non-Hermitian skin effect
• Tunneling time in coupled-channel systems
• Influence of spin on tunneling times in the super-relativistic regime
• Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids
• Attosecond dynamics of electron scattering by an absorbing layer
• Hartman Effect from a Geometrodynamic Extension of Bohmian Mechanics