Generalized coherent states with shifted (displaced) arguments

TL;DR

This paper introduces a method to construct generalized coherent states with shifted arguments using nonlinear ladder operators and displacement operators, with potential applications in quantum optics.

Contribution

It presents a novel procedure for creating shifted argument coherent states based on nonlinear operators and normal ordering techniques, extending existing frameworks.

Findings

Derived expressions consistent with existing literature

Verified properties of shifted coherent states

Potential applications in quantum optics, such as Wigner operator calculations

Abstract

In the paper we developed a procedure for constructing generalized coherent states with shifted argument, as a result of the action of the generalized displacement operator. This was based on the action of a pair of nonlinear ladder operators, which generate nonlinear coherent states. To examine the properties of coherent states with shifted argument, the rules of the normal operator ordering technique (DOOT) were used. The results obtained were verified for a series of particular cases, obtaining expressions consistent with those in the literature. The expressions obtained will be, among others, useful in quantum optics, e.g. for calculating the Wigner operator in the representation of coherent states.