Generalized coherent and squeezed states based on the $h(1) \otimes su(2)$ algebra

TL;DR

This paper constructs generalized coherent and squeezed states based on the combined $h(1) imes su(2)$ algebra, linking them to supersymmetric oscillator states and related Hamiltonians.

Contribution

It introduces a new class of states minimizing the Schrödinger--Robertson uncertainty relation within the $h(1) imes su(2)$ algebra framework, connecting to supersymmetric and Jaynes--Cummings models.

Findings

States minimize the Schrödinger--Robertson uncertainty relation.

Established relations with supercoherent and supersqueezed states.

Derived Hamiltonians analogous to harmonic oscillator and Jaynes--Cummings models.

Abstract

States which minimize the Schr\"odinger--Robertson uncertainty relation are constructed as eigenstates of an operator which is a element of the $h(1) \oplus \su(2)$ algebra. The relations with supercoherent and supersqueezed states of the supersymmetric harmonic oscillator are given. Moreover, we are able to compute gneneral Hamiltonians which behave like the harmonic oscillator Hamiltonian or are related to the Jaynes--Cummings Hamiltonian.