Canonical and nonlinear vector coherent states of generalized models with spin-orbit interaction

Abstract

Through canonical and f deformation quantizations, classes of nonlinear spin-orbit interaction models are considered. These generalized models are relevant in condensed matter physics and quantum optics in domains of nonlinear spin-Hall effect or of the multiphoton Jaynes-Cummings [Proc. IEEE 51, 89 (1963)] model, for instance. A spectral decomposition follows the exact diagonalization of the Hamiltonian and leads to the definition of ladder operators acting on the associated Hilbert space. Nonlinear vector coherent states are then constructed from a general lowering operator action. Explicit solutions of their related moment problems in ordinary and f-deformed theories are displayed, thus providing new classes of coherent states for such generalized spin-orbit models.

Oscillators in the Framework of Unified (q, α, β, γ, ν)-Deformation and Their Oscillator Algebras

“…In this last case, we also discuss the uniqueness of the solution of the Stieltjes moment problem. The following investigations of the properties of the (q; α, β, γ; ν)-deformed oscillator algebra and its applications can be found in works [8,[40][41][42][43][44][45].…”

Vector coherent states for nanoparticle systems

“…Ever since, they have been widely used in a variety of symmetry problems in quantum mechanics in general, and in particular for quantum optical models ( [9], [10], [8]), as well as for the study of spectra of two-level atomic systems in electromagnetic fields, for instance in the famous Jaynes-Cummings model ( [11]). In previous works, in the context of quantum optics, a new formulation of VCSs for nonlinear spin-orbit Hamiltonian model [1] in terms of the matrix eigenvalue problem for generalized annihilation operators has been provided. Let us cite also the VCSs of Gazeau-Klauder type [12], constructed for a Hamiltonian describing the interaction between a single mode, (a, a † ) of the radiation field with the frequency ω and 2 fermion levels with energies ǫ 1 , ǫ 2 , and creation and annihilation operators c † j , c j , j = 1, 2.…”

Quaternionic vector coherent states for spin-orbit interactions

“…with the same change of variables as in (4). The annihilation and creation operators given, respectively, by…”

“…which lead to the generalized dimensionless spin-orbit interaction established in [4] as: (22) and (23), the generalized Hamiltonians describing a 2D electron gas mixing with full Rashba and Dresselhaus SO interactions, and effective Zeeman coupling in a perpendicular magnetic field background are given in both relevant gauge symmetries by…”

“…All these aspects motivate the investigations of the properties of the SO Hamiltonian systems. Recently, standard and nonlinear vector coherent states (VCS) have been constructed for relevant generalized models in quantum optics for nonlinear spin-Hall effect [4] and for the Jaynes-Cummings model in the rotating wave approximation [3]. See also references quoted in these works.…”