Spin-charged point particle in a non-abelian external field with the generalized uncertainty relation

The dynamics of a particle carrying a non-abelian charge is studied in the presence of a minimal length. By choosing an appropriate non-abelian gauge field, the system identifies with the Hamiltonian of the Jaynes Cummings model whose solutions can be determined algebraically. The model has an underlying graded Lie algebra symmetry reminiscent of supersymmetric quantum mechanics. We calculate the energy levels and associated eigenstates using conservation of the number of excitations of the system. Then, we present the effect of the minimal length on the dynamics of the system and we are particularly interested in two particular cases, that of Rabi oscillations and that of the collapse-revival of the wave function. The results show that the higher the deformation parameter, the faster the oscillatory behavior of the atomic inversion.