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

arXiv:quant-ph/0210067 · Journal of Physics A Mathematical and General

Superpositions ofSU(3) coherent states via a nonlinear evolution

Kae Nemoto, Barry C. Sanders

Published Mar 2, 2001• 23 citations
arXivHTMLPDF

Abstract

We show that a nonlinear Hamiltonian evolution can transform an SU (3) coherent state into a superposition of distinct SU (3) coherent states, with a superposition of two SU (2) coherent states presented as a special case. A phase-space representation is depicted by projecting the multi-dimensional Q -symbol for the state to a spherical subdomain of the coset space. We discuss realizations of this nonlinear evolution in the contexts of nonlinear optics and Bose-Einstein condensates.

DOI
10.1088/0305-4470/34/10/309

Related papers

A Comparative Analysis of a Nonlinear Phase Space Evolution of SU(2) and SU(1,1) Coherent States

Rodrigo D. Aceves, Miguel Baltazar, Ivan F. Valtierra +1 more

We carried out a comparative study of the phase space evolution of SU(2) and SU(1,1) coherent states generated by the same nonlinear two-mode Hamiltonian. We analyze the dynamics of the Wigner functions in the respective phase spaces and discuss the principal associated physical effects: the squeezing of the appropriate observables and the Schrödinger’s cat state generation characteristic of both the considered symmetry groups.

Quantum Reports•Jul 5, 2025•1 citation

SU(m,n) coherent states in the bosonic representation and their generation in optical parametric processes

Ravinder Rupchand Puri

The coherent states of SU(m,n) transformations arising in the description of certain multimode nonlinear parametric processes bilinear in boson operators are constructed. The nonclassical properties of the coherent states of SU(m) and those of SU(m,1) are identified. The dynamics generated by SU(m,n) Hamiltonian is studied.

Physical Review A•Dec 1, 1994•27 citations

Entangled coherent states for systems withSU(2) andSU(1,1) symmetries

Xiao-Guang Wang, Barry C. Sanders, Shaohua Pan

Entangled SU (2) and SU (1,1) coherent states are developed as superpositions of multiparticle SU (2) and SU (1,1) coherent states. As a special example of entangled SU (2) coherent states, entangled binomial states are introduced and these entangled binomial states enable the contraction from entangled SU (2) coherent states to entangled harmonic oscillator coherent states. Entangled SU (2) coherent states are discussed in the context of pairs of qubits. We also introduce the entangled negative binomial states and entangled squeezed states as examples of entangled SU (1,1) coherent states. A method for generating the entangled SU (2) and SU (1,1) coherent states is discussed and degrees of entanglement calculated. Two types of SU (1,1) coherent states are discussed in each case: Perelomov coherent states and Barut-Girardello coherent states.

arXiv:quant-ph/0001073•Journal of Physics A Mathematical and General•Oct 5, 2000•112 citations

Generalized coherent states forSU(n) systems

Kae Nemoto

Generalized coherent states are developed for SU ( n ) systems for arbitrary n . This is done by first iteratively determining explicit representations for the SU ( n ) coherent states and then determining parametric representations useful for applications. For SU ( n ), the set of coherent states is isomorphic to a coset space SU ( n )/ SU ( n -1), and thus shows the geometrical structure of the coset space. These results provide a convenient (2 n -1)-dimensional space for the description of arbitrary SU ( n ) systems. We further obtain the metric and measure on the coset space and show some properties of the SU ( n ) coherent states.

arXiv:quant-ph/0004087•Journal of Physics A Mathematical and General•May 3, 2000•83 citations

Dynamics of SU(1,1) coherent states

Christopher C. Gerry

We derive the most general Hamiltonian which preserves the Perelomov SU(1,1) coherent states under time evolution. It is shown that the Hamiltonian of the degenerate parametric oscillator from nonlinear optics, which does not preserve ordinary coherent states, does preserve the SU(1,1) coherent states under time evolution.

Physical Review A•Apr 1, 1985•170 citations

Coherent states for four-mode systems in quantum optics

Bindu A. Bambah, G. S. Agarwal

We introduce and study the properties of a class of coherent states for the group SU(1,1)\ifmmode\times\else\texttimes\fi{}SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We also derive a phase space representation based on pair coherent states rather than the standard harmonic-oscillator coherent states. We discuss the utility of the resulting ``bi-pair coherent states'' in the context of four-mode interactions in quantum optics.

Physical Review A•Jun 1, 1995•10 citations
We show that a nonlinear Hamiltonian evolution can transform an SU (3) coherent state into a superposition of distinct SU (3) coherent states, with a superposition of two SU (2) coherent states presented as a special case. A phase-space representation is depicted by projecting the multi-dimensional Q -symbol for the state to a spherical subdomain of the coset space. We discuss realizations of this nonlinear evolution in the contexts of nonlinear optics and Bose-Einstein condensates.
Entangled SU (2) and SU (1,1) coherent states are developed as superpositions of multiparticle SU (2) and SU (1,1) coherent states. As a special example of entangled SU (2) coherent states, entangled binomial states are introduced and these entangled binomial states enable the contraction from entangled SU (2) coherent states to entangled harmonic oscillator coherent states. Entangled SU (2) coherent states are discussed in the context of pairs of qubits. We also introduce the entangled negative binomial states and entangled squeezed states as examples of entangled SU (1,1) coherent states. A method for generating the entangled SU (2) and SU (1,1) coherent states is discussed and degrees of entanglement calculated. Two types of SU (1,1) coherent states are discussed in each case: Perelomov coherent states and Barut-Girardello coherent states.
Generalized coherent states are developed for SU ( n ) systems for arbitrary n . This is done by first iteratively determining explicit representations for the SU ( n ) coherent states and then determining parametric representations useful for applications. For SU ( n ), the set of coherent states is isomorphic to a coset space SU ( n )/ SU ( n -1), and thus shows the geometrical structure of the coset space. These results provide a convenient (2 n -1)-dimensional space for the description of arbitrary SU ( n ) systems. We further obtain the metric and measure on the coset space and show some properties of the SU ( n ) coherent states.
We introduce and study the properties of a class of coherent states for the group SU(1,1)\ifmmode\times\else\texttimes\fi{}SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We also derive a phase space representation based on pair coherent states rather than the standard harmonic-oscillator coherent states. We discuss the utility of the resulting ``bi-pair coherent states'' in the context of four-mode interactions in quantum optics.