# Deformed Gazeau-Klauder Schr\"odinger-Cat States with Modified Commutation Relations

## TL;DR

This paper explores how quantum deformation, involving minimum length and maximum momentum, affects Schrödinger cat states, revealing non-classical properties and potential experimental implications in quantum optics.

## Contribution

It extends Gazeau-Klauder coherent states to deformed quantum mechanics, constructing and analyzing deformed Schrödinger cat states with new quantum gravitational features.

## Key findings

- Deformed cat states differ statistically from original states.
- Non-classical properties like squeezing are affected by deformation.
- Potential for experimental detection of quantum gravitational effects.

## Abstract

Generalized coherent states (GCs) under deformed quantum mechanics which exhibits intrinsic minimum length and maximum momentum have been well studied following Gazeau-Klauder approach. In this paper, as an extension to the study of quantum deformation, we investigate the famous Schrodinger cat states (SCs) under these two classes of quantum deformation. Following the concept of generalized Gazeau-Klauder Schrodinger cat states (GKSCs), we construct the deformed-GKSCs for both phenomenological models that exhibit intrinsic minimum length and (or) maximum momentum. All comparisons between minimum length and maximum momentum deformations are illustrated and plots are done in even and odd cat states since they are one of the most important classic statistical characteristics of SCs. Probability distribution and entropies are studied. In general, deformed cat states do not possess the original even and odd states statistical properties. Non-classical properties of the deformed-GKSCs are explored in terms of Mandel Q parameter, quadrature squeezing as well as Husimi quasi-probability distribution. Some of these distinguishing quantum-gravitational features may possibly be realized qualitatively and even be measured quantitatively in future experiments with the advanced development in quantum atomic and optics technology.