Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator

TL;DR

This paper introduces nonlinear supercoherent states for the supersymmetric harmonic oscillator, explores their properties, and calculates geometric phases, extending the understanding of quantum states in supersymmetric systems.

Contribution

It develops a framework for nonlinear supercoherent states and analyzes their geometric phases, providing new insights into supersymmetric quantum systems.

Findings

Nonlinear supercoherent states are expressed in terms of deformed coherent states.

Heisenberg uncertainty relations are analyzed for special cases.

Geometric phases are computed for cyclic evolution of these states.

Abstract

Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.