Generalized one-dimensional representation in quantum optics

József Janszky, Петер Адам, I. Földesi +1 more

József Janszky

As a generalization of the optical Schroedinger cats discrete and continuous sets of coherent states are considered on a circle and on a straight line in the a-plane. The interference fringes between the coherent states of the Schroedinger cats form the characteristic pattern of the nonclassical states in Wigner function picture. Continuos superpositions of coherent states on these one-dimensional manifolds can serve as an orthonormal basis for representation of any states.

Alfred Wünsche

The fundamentals of Fan's method of integration within ordered products are investigated and it is shown that it is a reliable calculation method in quantum optics. Differentiation within ordered products is included into the considerations. The integrations are, in applications to single boson modes, mostly one-dimensional or two-dimensional integrations over phase-space variables. We examine some examples of integration within ordered products and compare them with calculations of results by other methods such as Lie group methods. A new representation of the main class of quasiprobabilities including the Wigner and the Husimi-Kano quasiprobability is derived by the method. Different representations of squeezing operators are related by the method and discussed. As a further new result, the position and momentum representation of the general unitary squeezing operators are derived and specialized to cases with squeezing in the direction of the coordinate axes which were earlier dealt with by the method under consideration.

Ravinder Rupchand Puri

展德会 ZHAN De-hui, 范洪义 FAN Hong-yi

Foldesi, I., Janszky, J., Adam, P. +1 more

The possibility of representing the quantum states of a harmonic oscillator not on the whole alpha-plane but on its one dimensional manifolds is considered. It is shown that a simple Gaussian distribution along a straight line describes a quadrature squeezed state while a similar Gaussian distribution along a circle leads to the amplitude squeezed state. The connection between the one dimensional representations and the usual Glauber representation is discussed.