Non-Hermitian Hamiltonian for a modulated Jaynes-Cummings model with PT symmetry

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Abstract

We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic $n${-}excitation subspace obey the same equations of motion that can be obtained from a emph{static} non-Hermitian Jaynes-Cummings Hamiltonian with ${mathcal PT}$ symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of ${mathcal PT}$ symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudo-bosons and pseudo-fermions, and discuss relevant mathematical and physical aspects.
Original languageEnglish
Pages (from-to)042134-1-042134-8
Number of pages8
JournalPHYSICAL REVIEW A
Volume91
Publication statusPublished - 2015

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symmetry
equations of motion
bosons
fermions
modulation
cavities
approximation
excitation
atoms

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

@article{38515ee202784fae9a813134ebae8461,
title = "Non-Hermitian Hamiltonian for a modulated Jaynes-Cummings model with PT symmetry",
abstract = "We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic $n${-}excitation subspace obey the same equations of motion that can be obtained from a emph{static} non-Hermitian Jaynes-Cummings Hamiltonian with ${mathcal PT}$ symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of ${mathcal PT}$ symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudo-bosons and pseudo-fermions, and discuss relevant mathematical and physical aspects.",
author = "Salvatore Spagnolo and Lucia Rizzuto and Margherita Lattuca and Fabio Bagarello and Roberto Passante and Fabio Bagarello",
year = "2015",
language = "English",
volume = "91",
pages = "042134--1--042134--8",
journal = "PHYSICAL REVIEW A",
issn = "1050-2947",

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TY - JOUR

T1 - Non-Hermitian Hamiltonian for a modulated Jaynes-Cummings model with PT symmetry

AU - Spagnolo, Salvatore

AU - Rizzuto, Lucia

AU - Lattuca, Margherita

AU - Bagarello, Fabio

AU - Passante, Roberto

AU - Bagarello, Fabio

PY - 2015

Y1 - 2015

N2 - We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic $n${-}excitation subspace obey the same equations of motion that can be obtained from a emph{static} non-Hermitian Jaynes-Cummings Hamiltonian with ${mathcal PT}$ symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of ${mathcal PT}$ symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudo-bosons and pseudo-fermions, and discuss relevant mathematical and physical aspects.

AB - We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic $n${-}excitation subspace obey the same equations of motion that can be obtained from a emph{static} non-Hermitian Jaynes-Cummings Hamiltonian with ${mathcal PT}$ symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of ${mathcal PT}$ symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudo-bosons and pseudo-fermions, and discuss relevant mathematical and physical aspects.

UR - http://hdl.handle.net/10447/133343

M3 - Article

VL - 91

SP - 042134-1-042134-8

JO - PHYSICAL REVIEW A

JF - PHYSICAL REVIEW A

SN - 1050-2947

ER -