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

Communications in Theoretical Physics

Generalized Bargmann Representation of Spin Coherent State

Fan Hong‐Yi, Junhua Chen

Published Apr 15, 2004• 0 citations
Publisher

Abstract

Based on the conclusion that the generalized Bargmann representation of a two-mode Fock state is a two-variable Hermite polynomial function [Hong-Yi Fan and Jun-hua Chen, Phys. Lett. A303 (2002) 311] we derive the generalized Bargmann representation of the spin coherent state and some new relations in the generalized function space.
DOI
10.1088/0253-6102/41/4/537

Related papers

Generalized Bargmann Representation of Spin Coherent State

FANHong-Yi, CHENJun-Hu

Based on the conclusion that the generalized Bargmann representation of a two-mode Fock state is a two-variable Hermite polynomial function /Hong-Yi Fan and Jun-hua Chen,Phys.Lett.A303(2002)311] we derive the generalized Bargmann representation of the spin coherent state and some new relations in the generalized function space.

理论物理通讯:英文版•Jan 1, 2004•0 citations

Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator's Wave Functions

Lu Hai-Liang, Fan Hong-Yi

We reveal that the two-variable Hermite function h m , n , which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator's wave functions. The Schmidt decomposition of h m , n is derived. It also turns out that h m , n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S ( r ) H m , n (μ a 1 † ,μ a 2 † )|00⟩, which is the minimum uncertainty state for sum squeezing, in ⟨η| representation is calculated.

Communications in Theoretical Physics•Jun 1, 2007•8 citations

A Possible Generalization of the Bargmann Space

Hong-Yi Fan

By virtue of the technique of integration within an ordered product of operators we show that the ordinary Bargmann space basis function can be extended to two-variable Hermite polynomials, the latter can span a generalized Bargmann space. The corresponding two-mode Hermite polynomial states are thus introduced and their properties are investigated.

Communications in Theoretical Physics•Jun 15, 1994•3 citations

New complex function space related to both entangled state representation and spin coherent state

Cui-hong Lv, Hong-Yi Fan

A new complex function space whose basis is the single-variable Hermite polynomial H2jξ*+τξ2τ is constructed, which is related to both entangled state representation and spin coherent state in Schwinger bosonic realization. New binomial theorem involving two-variable Hermite polynomial is derived, which helps to constitute the new complex function space. We also present a new integration transformation of the basis H2jξ*+τξ2τ with its reciprocal transformation which is useful to deriving some operator identities.

Journal of Mathematical Physics•Aug 1, 2015•4 citations

A New Approach for Deriving the Bipartite Entangled State Representation

YU Zhi-song

For the bipartite entangled state representation in quantum optics,the author present a new approach to analyze its expression in Fock space.The analysis naturally leads to the introduction of two-variable Hermite polynomials,which is sharply different with the usual single-variable Hermite polynomials.

Acta Sinica Quantum Optica•Jan 1, 2008•0 citations

Squeezed states and Hermite polynomials in a complex variable

S. Twareque Ali, K. Górska, A. Horzela +1 more

Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pure Appl. Math. 14, 187 (1961)].

arXiv:1308.4730•Journal of Mathematical Physics•Jan 1, 2014•17 citations
We reveal that the two-variable Hermite function h m , n , which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator's wave functions. The Schmidt decomposition of h m , n is derived. It also turns out that h m , n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S ( r ) H m , n (μ a 1 † ,μ a 2 † )|00⟩, which is the minimum uncertainty state for sum squeezing, in ⟨η| representation is calculated.
A new complex function space whose basis is the single-variable Hermite polynomial H2jξ*+τξ2τ is constructed, which is related to both entangled state representation and spin coherent state in Schwinger bosonic realization. New binomial theorem involving two-variable Hermite polynomial is derived, which helps to constitute the new complex function space. We also present a new integration transformation of the basis H2jξ*+τξ2τ with its reciprocal transformation which is useful to deriving some operator identities.
Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pure Appl. Math. 14, 187 (1961)].