Generalized Grassmann variables for quantum kit (k-level) systems and Barut–Girardello coherent states for su(r + 1) algebras

Abstract

This paper concerns the construction of su(r + 1) Barut-Girardello coherent states in term of generalized Grassmann variables. We first introduce a generalized Weyl-Heisenberg algebra A(r) (r ≥ 1) generated by r pairs of creation and annihilation operators. This algebra provides a useful framework to describe qubit and qukit (k-level) systems. It includes the usual Weyl-Heisenberg and su(2) algebras. We investigate the corresponding Fock representation space. The generalized Grassmann variables are introduced as variables spanning the Fock-Bargmann space associated with the algebra A(r). The Barut-Girardello coherent states for su(r + 1) algebras are explicitly derived and their over-completion properties are discussed.

Lewis-Riesenfeld quantization and SU(1, 1) coherent states for 2D damped harmonic oscillator

“…Lie algebraic group through different approaches. The Barut-Girardello and the Perelomov coherent states gained lot of applications, for instance in the fields of quantum optics [35,36], quantum computation [37,38] and quantum mechanics [39][40][41].…”

Photon-added BarutGirardello like coherent states of time-dependent Landau problem

“…Nine years later, these coherent states introduced by Glauber have inspired respectively Barut-Girardello [11] and Perelomov [12] in constructing the coherent states for su(1, 1) Lie algebraic group basing on the procedures (i) and (ii) respectively. These states also satisfy the Klauder's minimum conditions (iv,v,vi) and have interesting applications in quantum optics, quantum computation and quantum mechanics [13,14,15,16,17].…”