Эволюция кутрита и контракция алгебры Ли su(3)

Abstract

The evolution of a three-level quantum system interacting with the environment with the symmetry of the Lie algebra su(3) (qutrit) is considered. The evolution of qutrit is obtained when interacting with the environment. The transverse relaxation of the qutrit (due to the diagonal Lindblad operators) has been studied, leading to zero (with the same speedfor the real and imaginary parts) off-diagonal elements of the density matrix. The dynamics of qutrit is obtained in the presence of both transverse and longitudinal relaxation, i.e. when the Lindblad operators are off-diagonal and there are transitions in the system between all energy levels. It is shown that the addition of the longitudinal relaxation ofthe qutrit in addition to the conversion of the offdiagonallements to zero, also affects the diagonal elements of its density matrix. As a result of dissipation, the quantum system becomes incoherent over time. In both cases, initially non-commuting quantum observables in the process of evolution acquire the properties of commuting classical observables,which algebraically manifests itself in the contraction of the algebra su(3).