On the Number States and the Annihilation/Creation Operators Related to the Continuous Wavelet Transformation

Fuminori Sakaguchi

Fuminori Sakaguchi, Masahito Hayashi

A kind of annihilation/creation relation related to the coherent states associated with the irreducible unitary representation of the affine group is reinterpreted as an annihilation/creation r,elation associated with the irreducible unitary representation of the algebra su(l,l), by adding another generator to the two generators of the unitary representation of the affine group ..

Zhiguo Zhang, Mark Kon

Carlos R. Handy, Romain Murenzi

Xue-xiang Xu, Hong‐Chun Yuan, Yan Wang

We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal state (TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number, Mandel Q -parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.

Su‐Yong Lee, Hyunchul Nha

We study a coherent superposition $t\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}+r{\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}}^{\ifmmode\dagger\else\textdagger\fi{}}$ of field annihilation and creation operators acting on continuous variable systems and propose its application for quantum state engineering. Specifically, it is investigated how the superposed operation transforms a classical state to a nonclassical one, together with emerging nonclassical effects. We also propose an experimental scheme to implement this elementary coherent operation and discuss its usefulness to produce an arbitrary superposition of number states involving up to two photons.