Conditional displacement operator for traveling fields

TL;DR

This paper introduces an approximation method for the conditional displacement operator acting on traveling wave states using a Kerr medium setup, enabling new applications in nonclassical state generation and Wigner function measurement.

Contribution

Proposes a novel approximation of the conditional displacement operator with a Kerr medium between beam splitters, facilitating advanced quantum state manipulations.

Findings

Effective approximation of the conditional displacement operator.

Application to generate nonclassical states.

Method for measuring Wigner functions of arbitrary states.

Abstract

We show that the conditional displacement operator $\hat{U}_{CD}=\exp [\hat{b}^{\dagger}\hat{b}(\beta \hat{a}^{\dagger}-\beta ^{\ast}\hat{a})]$ acting upon an arbitrary state of traveling waves can be well approximated by the action of a Kerr medium placed between two beam splitters whose respective second ports are fed by highly excited coherent states. Applications to the generation of nonclassical states and measurement of Wigner function of arbitrary states are also considered.