  We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a non-ideal two level subspace, identified as the qubit and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model interaction we use can generate nonnegligible couplings between the qubit states and the higher levels upto $N\sim 10$. In contrast to the pure two-level system, in a multilevel system the quantum information may leak out of the qubit subspace through nonresonant as well as resonant excitations induced by the environment. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We numerically examine the relaxation and dephasing times as the environmental frequency spectrum, the environmental temperature, and the multilevel system parameters are varied. We observe the influence of all energy scales in the noise spectrum on the short time dynamics implying the dominance of nonresonant transitions at short times. The relaxation and dephasing times calculated, strongly depend on $N$ for $4< N<10$ and saturate for $10 <N$. We also examine double degenerate systems with $4 \le N$ and observe a strong suppression (almost by two orders of magnitude) of the low temperature relaxation and dephasing rates.   An important observation for $4 \le N$ in doubly degenerate energy configuration is that, we find a strong suppression of the RD rates for such systems relative to the singly degenerate ones. These results are also compared qualitatively with the relaxation rates found from the Fermi Golden Rule. 
Decoherence and dephasing in multilevel systems interacting with thermal   environment