Squeezing Properties Of Measurement Phase Operator In Superposed Squeezed Coherent States

The squeezing properties in the superposition of coherent States and squeezed state are investigated by means of the measurement phase operator introduced by Barnett and S M and Pagg D T. KeywordsA new kind of odd and even coherent states; measurement operator; squeezing.


Introduction
Recently, the discussion on phase of quantum optical field has given rise to a great many interest.It is known that in the quantum optical, the amplitude of field is directly proportional to square root of optic-quantum number operator and its phase is described by Susskind-Glogower phase operator exp( ) iϕ ± , however Susskind-Glogower phase operator are possessed of unitary trait, hence hermit operator isn't constructed by it.Though two hermit operator below are set , they have classical property because 2 2 cos sin 1 ϕ ϕ + ≠ .On purpose to overcome the difficulty, unitary exponential phase operator and measurement phase operator in optical field have defined by Pegg and Branett, and then the phase essence of optical field is studied in progress(PEGG D T, BARNETT S M. 1989)(BARNETT S M, PEGG D T. 1986).In some laboratories, the measurement phase operator usually corresponds to the measurement of phase, therefore the measurement phase operator has raised extensive concerns.Some classical properties are researched in detail for squeezing states, quasi-optical coherent states, squeezing optical number states, odd and even coherent states, Schrödinger cat states and so on.
In the quantum optics, coherent state and squeezed state are two very important states in the quantum optics (LYNCH R. 1987)(WALL D F. 1983)

The superposition of squeezed coherent states
Superposed coherent states is defined where β > and β − > are the coherent states, where By the same method, squeezing operator ( ) S ξ act on (3), and then obtain squeezed coherent , g β δ > , [ ] When 0 δ = and π , (6) become squeezed even odd coherent states , 0 [ ] The operator b is defined below ˆˆb ua va + = + , ˆˆb u a v a where â and â+ are Bose annihilation and creating operator, operator b and b+ have the same as commutation relation â and â+ ,i.e.

Orthogonal measurement phase operator
Pegg and Barnnet have defined orthogonal measurement phase operator below where , where n is average photon number in considered states in the paper, By means of the relation of measurement phase operator and optical number operator, the important equations are got 2 [cos ,sin ] , 2

Squeezing of measurement phase operator
In quantum-optical field, when two operators 1 Y and 2 Y don't satisfy reciprocal relation, its accuracy of measurement is restricted by measurement indeterminacy principle below If the inequality is right then there is squeezing effect in optical field component i Y .With the view of description degree of squeezing, When 0 i S < , it indicates that there is squeezing in the i Y .
From the expression (15), ( 16), the squeezing degrees of measurement phase operator are

The discussion of Squeezing effect of measurement phase operator
Through calculating, the expressions below are obtained

,
β and φ denotes the intensity and phase of coherent β > , r is squeezing factor, θ is squeezing angle, 26)In order to calculate above four values, â and â+ are denoted by b and b+ ˆâ u They are even coherent and odd coherent states respectively.