Unitary Representations of Quantum Superpositions of two Coherent States and beyond

TL;DR

This paper introduces a new method for constructing unitary operators that generate superpositions of generalized coherent states, expanding the basis of the quantum harmonic oscillator and offering potential for further development.

Contribution

It presents a novel approach using hermitian operators to create superpositions of coherent states and extends the displaced Fock states basis in quantum harmonic oscillators.

Findings

Defined new basis in oscillator Hilbert space

Constructed unitary operators for superpositions of coherent states

Extended the displaced Fock states basis

Abstract

The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad hoc introduced set of hermitian operators, leads to the definition of new basis in the oscillator Hilbert space, extending in a natural way the displaced Fock states basis. The potential development of our method and our results is briefly outlined.