New classes of nonlinear vector coherent states of generalized spin-orbit Hamiltonians

TL;DR

This paper introduces new classes of nonlinear vector coherent states for generalized spin-orbit Hamiltonians, expanding the mathematical framework and exploring their properties without relying solely on annihilation operators.

Contribution

It develops an alternative construction of nonlinear vector coherent states for generalized spin-orbit Hamiltonians, including a new family parameterized by unit vectors on the S^3 sphere.

Findings

Defined an annihilation operator considering finite-dimensional state spaces.

Derived a class of nonlinear vector coherent states expressed via generalized displacement operators.

Identified a new family of NVCSs parameterized by S^3 unit vectors.

Abstract

This paper deals with an extension of our previous work [J. Phys. A: Math. Theor. {\bf 40} F817] by considering an alternative construction of canonical and deformed vector coherent states (VCSs) of the Gazeau-Klauder type associated with generalized spin-orbit Hamiltonians. We define an annihilation operator which takes into account the finite dimensional space of states induced by the $k$-photon transition processes of the two-level atom interacting with the single-mode radiation field. The class of nonlinear VCSs (NVCSs) corresponding to the action of the annihilation operator is deduced and expressed in terms of generalized displacement operators. Various NVCSs including their "dual" counterparts are also discussed. Still by using the Hilbert space structure, a new family of NVCSs parameterized by unit vectors of the $S^3$ sphere has been identified without making use of the annihilation operator.