Quantum and Semiclassical Optics Journal of the European Optical Society Part B

A Hermitian operator conjugate to the number operator

M. L. Arroyo Carrasco, H. M. Moya-Cessa

Published Jun 1, 1997• 6 citations

Abstract

It is shown that, departing from Dirac's intensity - phase commutator, a Hermitian operator can be found, conjugate to the number operator, N. We also show that this operator is equivalent to that given by Turski.

DOI: 10.1088/1355-5111/9/3/001

Related papers

On the Hermitian Optical Phase Operator

Stephen Mark Barnett, David Thomas Pegg

It has long been believed that no Hermitian optical phase operator exists. However, such an operator can be constructed from the phase states. We demonstrate that its properties are precisely in accord with the results of semiclassical and phenomenological approaches when such approximate methods are valid. We find that the number-phase commutator differs from that originally postulated by Dirac. This difference allows the consistent use of the commutator for inherently quantum states. It also leads to the correct periodic phase behaviour of the Poisson bracket in the classical regime.

Journal of Modern OpticsJan 1, 1989541 citations

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

Xu, Xue-Fen

理论物理通讯：英文版Jan 1, 20080 citations

A Hermitian Opetator Conjugate to Two-Mode Number-Difference Operator

Hong-Yi Fan, Yihua Wang

For the Shapiro-Wagner-Hradil phase detection description the canonical commutation relation between phase angle ψ and two-mode number-difference operator D = a † a - b † b is constructed. Departing from [ ψ , D ] = - i , the phase angle Hermitian operator is derived in the newly obtained representation ⟨ ξ |, where| ξ ⟩ is the common eigenket of a + b † and b + a † .

Chinese Physics LettersJun 1, 19985 citations

A consistent Lie algebraic representation of quantum phase and number operators

Mario Rasetti

A consistent realization of the quantum operators corresponding to the canonically conjugate phase and number variables is proposed, resorting to the irreducible unitary representations of the Lie algebra su(1,1), as proposed by Kastrup.

arXiv:cond-mat/0211081Nov 5, 20022 citations

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

Xuefen Xu

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco–Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operator and the three-mode number combination operator. It is shown that these operators are on the same footing in the entangled state representation as the one of Turski in the coherent state representation.

Communications in Theoretical PhysicsOct 1, 20080 citations

Phase Operator Associated with the Radiation Field

Minoru Hirayama, H.-M. Zhang

A method is explored to define a hermitian phase operator associated with a mode of the radiation field. Although the basic principle to define it uniquely is still lacking, the phase operator introduced through ad hoc assumptions exhibits some interesting properties.

Progress of Theoretical PhysicsDec 1, 19952 citations