Non-Hermitian Hartman Effect

Longhi; Stefano
Annalen der Physik 534, 2200250 (1-12) (2022)

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, that is, when
the potential becomes non-Hermitian and the scattering matrix is not unitary.
Here, tunneling through a heterojunction barrier in the tight-binding picture is
considered, where the barrier consists of a generally non-Hermitian
finite-sized lattice attached to two semi-infinite nearest-neighbor Hermitian
lattice leads. A simple and general condition is derived for the persistence of
the Hartman effect in non-Hermitian barriers, showing that it can be found
rather generally when non-Hermiticity arises from nonreciprocal couplings,
that is, when the barrier displays the non-Hermitian skin effect, without any
special symmetry in the system.

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