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

Chinese Physics Letters

Even and Odd Phase Coherent States Associated with the Pegg-Barnett Hermitian Phase Theory

Jiu-Yun Zhu, Le‐Man Kuang

Published Apr 1, 1996• 0 citations
Publisher

Abstract

Even and odd phase coherent states associated with the Pegg-Barnett Hermitian phase theory are introduced. Even and odd coherent-state formalism of the Pegg-Barnett phase operator is given in terms of the projection operator in the even and odd coherent-state space. The number-phase uncertainty relation is investigated for these states.
DOI
10.1088/0256-307x/13/4/009

Related papers

Even and odd phase coherent states for Hermitian phase operator theory

Le‐Man Kuang, Jiu-Yun Zhu

Even and odd phase coherent states associated with the Hermetian phase operator theory are introduced in terms of the creation operation of the phase quanta defined in a finite-dimensional phase state space. Some mathematical and physical properties of these quantum states are studied in some detail. It is shown that the even phase coherent states together with the odd ones build an overcomplete Hilbert space. Even and odd coherent-state formalism of the Pegg - Barnett phase operator is given in terms of the projection operator in the even and odd phase coherent-state space. The number - phase uncertainty relation is investigated for these quantum states. It is shown that even and odd phase coherent states are not minimum uncertainty and intelligent states for the number and phase operators.

Journal of Physics A Mathematical and General•Feb 21, 1996•3 citations

Phase-coherent states and their squeezing properties

Le‐Man Kuang, Xin Chen

Phase-coherent states associated with the Pegg-Barnett (PB) phase operator formalism are introduced in terms of the algebraic properties of the PB phase theory. The phase-coherent-state representation of the PB phase states and the PB phase operators is obtained. Squeezing properties of these coherent states with respect to the phase quadrature operators are studied. The number-phase squeezing and number-phase uncertainty relations are also investigated in detail for a two-state system. Some new number-phase minimum uncertainty states are found.

Physical Review A•Nov 1, 1994•19 citations

Phase properties of odd and even circular states

Wang Yue-Yuan, Liu Zheng-jun, Liao Qing-Hong +1 more

Phase properties of the even and odd circular states are studied within the Hermitian phase formalism of Pegg and Barnett. Exact analytical formulas for the distribution function and the variance of the phase operator are obtained and used to examine whether or not the even and odd circular states exhibit photon-number squeezing and phase squeezing.

Chinese Physics B•May 1, 2010•4 citations

Phase properties of excited coherent states

Ravinder Nath, Satish Kumar Muthu

The phase properties of states generated by excitations on a coherent state have been studied by evaluating the expression for the phase probability distribution, using the recent formalism of Pegg and Barnett in which the existence of a Hermitian optical phase operator has been shown. This distribution has been further used to evaluate the variance of the phase operator and the number - phase uncertainty product.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Aug 1, 1996•8 citations

Unitary and Hermitian phase operators for the electromagnetic field

Yee Kin Tsui, Michael F. Reid

Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)] have proposed a formalism for a Hermitian optical phase operator, constructed from the so-called phase states. In this paper we give an alternative derivation. We begin by defining a unitary phase operator ${e}^{i\stackrel{^}{\ensuremath{\varphi}}}$ from the relationship $\stackrel{^}{a}={e}^{i\stackrel{^}{\ensuremath{\varphi}}}R(\stackrel{^}{N})$ ($\stackrel{^}{a}$ is an annihilation operator for a single-mode boson field), but borrow the idea of a finite- (but arbitrarily large) dimensional space from Pegg and Barnett. Finally, we comment on an experiment to determine quantum phase uncertainty. Our analysis uses the operator ${e}^{i\stackrel{^}{\ensuremath{\varphi}}}$, which we feel is a more natural choice than $\stackrel{^}{\ensuremath{\varphi}}$. The use of ${e}^{i\stackrel{^}{\ensuremath{\varphi}}}$ also avoids the multivalued problems associated with $\stackrel{^}{\ensuremath{\varphi}}$.

Physical Review A•Jul 1, 1992•11 citations

Pegg–Barnett coherent states

I. Ramos-Prieto, Luis A Andrade-Morales, Francisco Soto +1 more

In this paper, we show that the Pegg–Barnett formalism accepts coherent states constructed as eigenstates of the annihilation operator, considering both the number and the phase. These operators are defined within a ( s + 1 ) -dimensional Hilbert space H s and with periodic conditions. The coherent states that we find are determined by the eigenvalue of the annihilation operator, which leads to a discrete spectrum. This approach allows calculation of the discrete-finite counterpart of the Wigner function in a phase space defined by the variables of number and phase.

Journal of the Optical Society of America B•Dec 12, 2019•4 citations
Even and odd phase coherent states associated with the Hermetian phase operator theory are introduced in terms of the creation operation of the phase quanta defined in a finite-dimensional phase state space. Some mathematical and physical properties of these quantum states are studied in some detail. It is shown that the even phase coherent states together with the odd ones build an overcomplete Hilbert space. Even and odd coherent-state formalism of the Pegg - Barnett phase operator is given in terms of the projection operator in the even and odd phase coherent-state space. The number - phase uncertainty relation is investigated for these quantum states. It is shown that even and odd phase coherent states are not minimum uncertainty and intelligent states for the number and phase operators.
Phase-coherent states associated with the Pegg-Barnett (PB) phase operator formalism are introduced in terms of the algebraic properties of the PB phase theory. The phase-coherent-state representation of the PB phase states and the PB phase operators is obtained. Squeezing properties of these coherent states with respect to the phase quadrature operators are studied. The number-phase squeezing and number-phase uncertainty relations are also investigated in detail for a two-state system. Some new number-phase minimum uncertainty states are found.
Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)] have proposed a formalism for a Hermitian optical phase operator, constructed from the so-called phase states. In this paper we give an alternative derivation. We begin by defining a unitary phase operator ${e}^{i\stackrel{^}{\ensuremath{\varphi}}}$ from the relationship $\stackrel{^}{a}={e}^{i\stackrel{^}{\ensuremath{\varphi}}}R(\stackrel{^}{N})$ ($\stackrel{^}{a}$ is an annihilation operator for a single-mode boson field), but borrow the idea of a finite- (but arbitrarily large) dimensional space from Pegg and Barnett. Finally, we comment on an experiment to determine quantum phase uncertainty. Our analysis uses the operator ${e}^{i\stackrel{^}{\ensuremath{\varphi}}}$, which we feel is a more natural choice than $\stackrel{^}{\ensuremath{\varphi}}$. The use of ${e}^{i\stackrel{^}{\ensuremath{\varphi}}}$ also avoids the multivalued problems associated with $\stackrel{^}{\ensuremath{\varphi}}$.
In this paper, we show that the Pegg–Barnett formalism accepts coherent states constructed as eigenstates of the annihilation operator, considering both the number and the phase. These operators are defined within a ( s + 1 ) -dimensional Hilbert space H s and with periodic conditions. The coherent states that we find are determined by the eigenvalue of the annihilation operator, which leads to a discrete spectrum. This approach allows calculation of the discrete-finite counterpart of the Wigner function in a phase space defined by the variables of number and phase.