Generation of coherent states of photon-added type via pathway of eigenfunctions

TL;DR

This paper constructs a new class of coherent quantum states using eigenfunctions of specific differential operators, resulting in states that are squeezed, sub-Poissonian, and resemble photon-added states, expanding the understanding of quantum state generation.

Contribution

It introduces a novel method to generate coherent states via eigenfunctions of differential operators, providing explicit forms and properties of these states.

Findings

States are normalized and form a resolution of unity.

Generated states are squeezed and sub-Poissonian.

States resemble photon-added quantum states.

Abstract

We obtain and investigate the regular eigenfunctions of simple differential operators x^r d^{r+1}/dx^{r+1}, r=1, 2, ... with the eigenvalues equal to one. With the help of these eigenfunctions we construct a non-unitary analogue of boson displacement operator which will be acting on the vacuum. In this way we generate collective quantum states of the Fock space which are normalized and equipped with the resolution of unity with the positive weight functions that we obtain explicitly. These states are thus coherent states in the sense of Klauder. They span the truncated Fock space without first r lowest-lying basis states: |0>, |1>, ..., |r-1>. These states are squeezed, are sub-Poissonian in nature and are reminiscent of photon-added states at Agarwal et al.