Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Theoretical Physics

Three-Mode Nonlinear Bogoliubov Transformations

Gang Ren, Song Tong-Qiang

Published Sep 27, 2007• 7 citations
Publisher
DOI
10.1007/s10773-007-9544-6

Related papers

A nonlinear Bogoliubov transformation

Jacob Katriel

Physics Letters A•Jan 1, 2003•11 citations

Algebraic approach to the Tavis-Cummings model with three modes of oscillation

E. Choreño, D. Ojeda-Guillén, V. D. Granados

We study the Tavis-Cummings model with three modes of oscillation by using four different algebraic methods: the Bogoliubov transformation, the normal-mode operators, and the tilting transformation of the SU(1, 1) and SU(2) groups. The algebraic method based on the Bogoliubov transformation and the normal-mode operators lets us obtain the energy spectrum and eigenfunctions of a particular case of the Tavis-Cummings model, while with the tilting transformation we are able to solve the most general case of this Hamiltonian. Finally, we compute some expectation values of this problem by means of the SU(1, 1) and SU(2) group theory. The authors of the article agree to the retraction of the article effective 21 September 2023

arXiv:1710.10945•Journal of Mathematical Physics•Jul 1, 2018•6 citations

Nonlinear Bogolyubov-Valatin transformations: Two modes

K. Scharnhorst, J.-W. van Holten

arXiv:1002.2737•Annals of Physics•May 22, 2011•6 citations

A Comment on "Algebraic approach to the Tavis-Cummings model with three modes of oscillation" [J. Math. Phys. 59, 073506 (2018)]

Viani S. Morales-Guzman, Jorge G. Hirsch

Choreño et al. [J. Math. Phys. 59, 073506 (2018)] reported analytic solutions to the resonant case of the Tavis-Cummings model, obtained by mapping it to a Hamiltonian with three bosons and applying a Bogoliubov transformation. This comment points out that the Bogoliubov transformation employed is not unitary, cannot be inverted, and cannot enforce the symmetries of the model.

arXiv:2303.04883•Mar 8, 2023•0 citations

Universal linear Bogoliubov transformations through one-way quantum computation

Ryuji Ukai, Jun–ichi Yoshikawa, Noriaki Iwata +2 more

We show explicitly how to realize an arbitrary linear unitary Bogoliubov (LUBO) transformation on a multimode quantum state through homodyne-based one-way quantum computation. Any LUBO transformation can be approximated by means of a fixed, finite-sized, sufficiently squeezed Gaussian cluster state that allows for the implementation of beam splitters (in form of three-mode connection gates) and general one-mode LUBO transformations. In particular, we demonstrate that a linear four-mode cluster state is a sufficient resource for an arbitrary one-mode LUBO transformation. Arbitrary-input quantum states including non-Gaussian states could be efficiently attached to the cluster through quantum teleportation.

arXiv:0910.0660•Physical Review A•Mar 16, 2010•63 citations

On Bogoliubov transformations. II. The general case

Simon N. M. Ruijsenaars

Annals of Physics•Nov 1, 1978•68 citations
We study the Tavis-Cummings model with three modes of oscillation by using four different algebraic methods: the Bogoliubov transformation, the normal-mode operators, and the tilting transformation of the SU(1, 1) and SU(2) groups. The algebraic method based on the Bogoliubov transformation and the normal-mode operators lets us obtain the energy spectrum and eigenfunctions of a particular case of the Tavis-Cummings model, while with the tilting transformation we are able to solve the most general case of this Hamiltonian. Finally, we compute some expectation values of this problem by means of the SU(1, 1) and SU(2) group theory. The authors of the article agree to the retraction of the article effective 21 September 2023
We show explicitly how to realize an arbitrary linear unitary Bogoliubov (LUBO) transformation on a multimode quantum state through homodyne-based one-way quantum computation. Any LUBO transformation can be approximated by means of a fixed, finite-sized, sufficiently squeezed Gaussian cluster state that allows for the implementation of beam splitters (in form of three-mode connection gates) and general one-mode LUBO transformations. In particular, we demonstrate that a linear four-mode cluster state is a sufficient resource for an arbitrary one-mode LUBO transformation. Arbitrary-input quantum states including non-Gaussian states could be efficiently attached to the cluster through quantum teleportation.