Role of the environmental spectrum in the decoherence and dephasing of multilevel quantum systems

Abstract

We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a nonideal 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 that we use is an rf-SQUID under macroscopic quantum coherence and coupled inductively to a flux noise characterized by an environmental spectrum. The model interaction can generate dipole couplings which can be appreciable between the qubit and the high levels. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We calculate the relaxation and dephasing times as the spectral parameters of the environment are varied. We observe that, these calculated time scales receive contribution from all available frequencies in the noise spectrum (even well above the system's resonant frequency scales) stressing the dominant role played by the nonresonant transitions. The relaxation and dephasing and the leakage times thus calculated, strongly depend on the appreciably interacting levels determined by the strength of the dipole coupling. Under the influence of these nonresonant and multilevel effects, the validity of the two level approximation is dictated not by the low temperature as conveniently believed, but by these multilevel dipole couplings as well as the availability of the environmental modes.