Excitation of Coherent States: Wave Function Development and Analysis

TL;DR

This paper develops a wave function approach to Excited Coherent States, analyzing their properties, quantum fluctuations, and squeezing behavior, providing new insights into their quantum-classical hybrid nature.

Contribution

It introduces a wave function derivation of ECS, linking them to quantum fluctuations and analyzing their squeezing properties in a generalized framework.

Findings

Derived ECS wave function as a blend of coherent and Fock states

Analyzed wave packet width and uncertainty relations for ECS

Presented conditions for quadrature squeezing in ECS

Abstract

Agarwal and Tara, in 1991 introduced a new class of states defined as m times application of creation operator to Coherent States known as Excited Coherent States (ECS) or Photon Added Coherent States (PACS). They are neither completely quantum nor completely classical. Here we present and develop these Excited Coherent Sates from a basic and more approachable Wave-function approach. We have derived the ECS wave function as a blend of Coherent States and Fock States and thus established them as a result of Quantum fluctuations (represented by Fock states) on Coherent States. We further derived and analyzed basic relations such as wave packet width and uncertainty relation in a more generalized form and presented their development with time. Another important property of ECS is Quadrature Squeezing. Here we also present a general analysis of squeezing in ECS and derived conditions on parameters for squeezing.