Wigner function of an arbitrary-photon-catalyzed optical coherent state

Xue-xiang Xu, Hong‐Chun Yuan

余之松 YU Zhi-song, 任桂华 REN Gui-hua, 范洪义 FAN Hong-yi

Hong‐Chun Yuan, Xue-xiang Xu, Heng-Mei Li +2 more

We theoretically generate a kind of photon-catalyzed optical coherent states (PCOCSs) by heralded interference between any photons and coherent state via a non-degenerate parametric amplifier, which is also just a Laguerre polynomial excited coherent state. Based on obtaining the probability of successfully detecting them (also the normalization factor), the nonclassical properties of the PCOCSs are analytically investigated according to autocorrelation function, quadrature squeezing, and the negativity of the Wigner function. It is found that the nonclassicality depends on the amplitude of the coherent state, the catalysis photon number, and amplifier parameter. The negative volume of their Wigner function can be enlarged by increasing the catalysis photon number. These parameters may be effectively used to improve and enhance the nonclassical characteristics.

Min Xie, Weidong Zhou, Wei Ye +2 more

Abstract In this work, we propose a scheme for generating non-classical quantum catalyzed states, named Laguerre polynomial-weighted squeezed states, via inputting a single-mode squeezed vacuum state and an m -photon Fock state by quantum catalysis and two-mode squeezing. The non-classical properties of the generated catalyzed state are investigated using the degree of squeezing and Wigner function. It is found that these non-classical properties, including squeezing degree and the negativity of the Wigner function, can be improved and modulated by both squeezing parameters and the catalyzed photon number.

V. P. Karasev, V. I. Puzyrevskii

Ji‐Suo Wang, Meng Xiang-Guo

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, this paper derives the Wigner functions for the photon-depleted even and odd coherent states (PDEOCSs). Moreover, in terms of the Wigner functions with respect to the complex parameter α the nonclassical properties of the PDEOCSs are discussed. The results show that the nonclassicality for the state |β, m ⟩ o (or |β, m ⟩ e ) is more pronounced when m is even (or odd). According to the marginal distributions of the Wigner functions, the physical meaning of the Wigner functions is given. Further, the tomograms of the PDEOCSs are calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.