General Displaced SU (1,1) number states-revisited

TL;DR

This paper introduces a new class of displaced number states based on su(1,1) symmetry, utilizing the Barut-Girardello displacement operator, revealing unique statistical and squeezing properties with potential applications as photon-added coherent states.

Contribution

It presents a novel construction of displaced number states using the Barut-Girardello operator, expanding the family of nonlinear coherent states with distinctive statistical features.

Findings

States exhibit significant squeezing and anti-bunching effects.

States can be tuned to exhibit various statistical behaviors.

States act as new photon-added coherent states with unique properties.

Abstract

The most general displaced number states, based on the bosonic and an irreducible representation(IREP) of the Lie algebra symmetry of su(1, 1) and associated to the Calogero-Sutherland model are introduced. Here, we utilize the Barut-Girardello displacement operator instead of the Klauder- Perelomov counterpart, to construct new kind of the displaced number states which can be classified in nonlinear coherent states regime, too, with special nonlinearity functions. They depend on two parameters, and can be converted into the well known Barut-Girardello coherent and number states respectively, depending on which of the parameters equal to zero. A discussion of the statistical properties of these states is included. Significant are their squeezing properties and anti bunching effects which can be raised by increasing the energy quantum number. Depending on the particular choice of the parameters of the above scenario, we are able to determine the status of compliance with flexible statistics. Major parts of the issue is spent on something that these states, in fact, should be considered as new kind of photon-added coherent states, too. Which can be reproduced through an iterated action of a creation operator on new nonlinear Barut-Girardello coherent states. Where the latter carry, also, outstanding statistical features.