Physical Review A

Dual eigenkets of the Susskind-Glogower phase operator

Hong-Yi Fan, Min Xiao

Published Dec 1, 1996• 67 citations

Abstract

By contour integration we show that the phase operator ${\mathit{e}\mathit{\^{}}}^{\mathrm{\ensuremath{-}}\mathit{i}\mathrm{\ensuremath{\varphi}}}$ (one of the pair of Susskind-Glogower operators) also possesses eigenkets |\ensuremath{\gamma}${\mathrm{〉}}_{\mathrm{*}}$, which are the dual vector of ${\mathit{e}\mathit{\^{}}}^{\mathit{i}\mathrm{\ensuremath{\varphi}}}$'s eigenkets. The properties of |\ensuremath{\gamma}${\mathrm{〉}}_{\mathrm{*}}$ are studied and we see that |\ensuremath{\gamma}${\mathrm{〉}}_{\mathrm{*}}$ and ${\mathit{e}\mathit{\^{}}}^{\mathit{i}\mathrm{\ensuremath{\varphi}}}$'s eigenkets can also make up a phase-state representation. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physreva.54.5295

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Physical Review A

Dual eigenkets of the Susskind-Glogower phase operator

Hong-Yi Fan, Min Xiao

Published Dec 1, 1996• 67 citations

Publisher

Abstract

By contour integration we show that the phase operator

{\mathit{e}\mathit{\^{}}}^{\mathrm{\ensuremath{-}}\mathit{i}\mathrm{\ensuremath{\varphi}}}

(one of the pair of Susskind-Glogower operators) also possesses eigenkets |\ensuremath{\gamma}

{\mathrm{〉}}_{\mathrm{*}}

, which are the dual vector of

{\mathit{e}\mathit{\^{}}}^{\mathit{i}\mathrm{\ensuremath{\varphi}}}

's eigenkets. The properties of |\ensuremath{\gamma}

{\mathrm{〉}}_{\mathrm{*}}

are studied and we see that |\ensuremath{\gamma}

{\mathrm{〉}}_{\mathrm{*}}

and

{\mathit{e}\mathit{\^{}}}^{\mathit{i}\mathrm{\ensuremath{\varphi}}}

's eigenkets can also make up a phase-state representation. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physreva.54.5295

Related papers

Dual eigenvectors of the Susskind-Glogower phase operators for a two-mode field

Xuefen Xu

Chinese Journal of Quantum ElectronicsJan 1, 20060 citations

Generalization of Susskind-Glogower Phase Operators and Inverse Field Operators to q -Deformed Case

Hong-Yi Fan

We analyze some properties of Susskind-Glogower (SG) phase operators and by making use of inverse field operators. The generalization of the analysis to q -deformed case is given.

Communications in Theoretical PhysicsJun 1, 19932 citations

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C V Sukumar

arXiv:1809.03844Physical Review AFeb 1, 19933 citations

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By contour integration we show that the phase operator

{\mathit{e}\mathit{\^{}}}^{\mathrm{\ensuremath{-}}\mathit{i}\mathrm{\ensuremath{\varphi}}}

(one of the pair of Susskind-Glogower operators) also possesses eigenkets |\ensuremath{\gamma}

{\mathrm{〉}}_{\mathrm{*}}

, which are the dual vector of

{\mathit{e}\mathit{\^{}}}^{\mathit{i}\mathrm{\ensuremath{\varphi}}}

's eigenkets. The properties of |\ensuremath{\gamma}

{\mathrm{〉}}_{\mathrm{*}}

are studied and we see that |\ensuremath{\gamma}

{\mathrm{〉}}_{\mathrm{*}}

and

{\mathit{e}\mathit{\^{}}}^{\mathit{i}\mathrm{\ensuremath{\varphi}}}

's eigenkets can also make up a phase-state representation. \textcopyright{} 1996 The American Physical Society.

{\hat{E}} = e^{i \hatϕ}

, thus defined is unitary and acts as a true ladder operator over all the states. It satisfies the commutation relation

[{\hat{E}}, {\hat{n}}] = {\hat{E}}

; consequently, the phase

\hatϕ

satisfies the canonical commutation relation

[{\hat{n}}, {\hatϕ}] = i

. The eigenstates of the Susskind Glogower operator are found. Our model is able to directly account for phase measurements when polarization changes cannot be neglected and at the same time gives a well defined phase operator.