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Field-driven geometrical phases in a time-periodic quantum system

Brusheim, Patrik LU and Xu, Hongqi LU (2009) In Physical Review B (Condensed Matter and Materials Physics) 79(20).
Abstract
We apply Floquet theory to explore the geometry of the Hilbert space under the influence of a time-periodic field. The geometrical phase is found to be induced by field-driven hybridizations when the photon energy of the driving field is close to the transition energies of the states of a quantum system. The phases of two hybridized states are phase locked to each other. We show that the geometrical phase is in general related to the Rabi frequency of the hybrid states. We also show that when the photon energy is equal to the transition energy of two states the geometrical phase acquired by each state is given exactly by an integer multiple of pi, independent of the strength of the driving field. We illustrate the derived generic... (More)
We apply Floquet theory to explore the geometry of the Hilbert space under the influence of a time-periodic field. The geometrical phase is found to be induced by field-driven hybridizations when the photon energy of the driving field is close to the transition energies of the states of a quantum system. The phases of two hybridized states are phase locked to each other. We show that the geometrical phase is in general related to the Rabi frequency of the hybrid states. We also show that when the photon energy is equal to the transition energy of two states the geometrical phase acquired by each state is given exactly by an integer multiple of pi, independent of the strength of the driving field. We illustrate the derived generic properties of the geometric phase with an experimentally realizable quantum-wire system. It is shown that the interference between conductance channels in the wire presents a way to identify the geometrical phase. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
geometry, Hilbert spaces, quantum theory, quantum wires, equation, Schrodinger
in
Physical Review B (Condensed Matter and Materials Physics)
volume
79
issue
20
publisher
American Physical Society
external identifiers
  • wos:000266501500081
  • scopus:67649544712
ISSN
1098-0121
DOI
10.1103/PhysRevB.79.205323
language
English
LU publication?
yes
id
2d4fbac0-4d0f-4910-b292-09d9e85c8813 (old id 1443504)
date added to LUP
2009-07-24 12:48:08
date last changed
2017-01-01 05:52:50
@article{2d4fbac0-4d0f-4910-b292-09d9e85c8813,
  abstract     = {We apply Floquet theory to explore the geometry of the Hilbert space under the influence of a time-periodic field. The geometrical phase is found to be induced by field-driven hybridizations when the photon energy of the driving field is close to the transition energies of the states of a quantum system. The phases of two hybridized states are phase locked to each other. We show that the geometrical phase is in general related to the Rabi frequency of the hybrid states. We also show that when the photon energy is equal to the transition energy of two states the geometrical phase acquired by each state is given exactly by an integer multiple of pi, independent of the strength of the driving field. We illustrate the derived generic properties of the geometric phase with an experimentally realizable quantum-wire system. It is shown that the interference between conductance channels in the wire presents a way to identify the geometrical phase.},
  articleno    = {205323},
  author       = {Brusheim, Patrik and Xu, Hongqi},
  issn         = {1098-0121},
  keyword      = {geometry,Hilbert spaces,quantum theory,quantum wires,equation,Schrodinger},
  language     = {eng},
  number       = {20},
  publisher    = {American Physical Society},
  series       = {Physical Review B (Condensed Matter and Materials Physics)},
  title        = {Field-driven geometrical phases in a time-periodic quantum system},
  url          = {http://dx.doi.org/10.1103/PhysRevB.79.205323},
  volume       = {79},
  year         = {2009},
}