Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice
File(s)
Working paper
Author(s)
Longstaff, Bradley
Graefe, Eva-Maria
Type
Working Paper
Abstract
Exceptional points, at which two or more eigenfunctions of a Hamiltonian
coalesce, occur in non-Hermitian systems and lead to surprising physical
effects. In particular, the behaviour of a system under parameter variation can
differ significantly from the familiar Hermitian case in the presence of
exceptional points. Here we analytically derive the probability of a
non-adiabatic transition in a two-level system driven through two consecutive
exceptional points at finite speed. The system is Hermitian far away from the
exceptional points. In the adiabatic limit an equal redistribution between the
states coalescing in the exceptional point is observed, which can be
interpreted as a loss of information when passing through the exceptional
point. For finite parameter variation this gets modified. We demonstrate how
the transition through the exceptional points can be experimentally addressed
in a PT-symmetric lattice using Bloch oscillations.
coalesce, occur in non-Hermitian systems and lead to surprising physical
effects. In particular, the behaviour of a system under parameter variation can
differ significantly from the familiar Hermitian case in the presence of
exceptional points. Here we analytically derive the probability of a
non-adiabatic transition in a two-level system driven through two consecutive
exceptional points at finite speed. The system is Hermitian far away from the
exceptional points. In the adiabatic limit an equal redistribution between the
states coalescing in the exceptional point is observed, which can be
interpreted as a loss of information when passing through the exceptional
point. For finite parameter variation this gets modified. We demonstrate how
the transition through the exceptional points can be experimentally addressed
in a PT-symmetric lattice using Bloch oscillations.
Date Issued
2019-08-17
Date Acceptance
2019-10-18
Citation
Physical Review A: Atomic, Molecular and Optical Physics, 2019
Publisher
arXiv
Journal / Book Title
Physical Review A: Atomic, Molecular and Optical Physics
Copyright Statement
© 2019 The Authors
Sponsor
The Royal Society
Commission of the European Communities
Identifier
http://arxiv.org/abs/1906.03073v2
Grant Number
UF130339
758453
Subjects
quant-ph
quant-ph
physics.optics
Notes
slightly revised and extended version, 7 pages, 6 figures
Publication Status
Published