Decoherence Sturdy Memories in the Presence of Quantum Dissipation

AbstractWe consider N identical oscillators coupled to a single environment and show that the conditions forthe existence of decoherence free subspaces are degeneracy of the oscillator frequencies and separabilityof the coupling with the environment. A formal exact equation for the evolution in the case of twooscillators is found and the decoherence free subspace is explicitly determined. A full analytical solu-tion for any initial condition and general parameters (frequencies and dissipation constants) is given inthe markovian approximation and zero temperature. We find that slight relaxation of degeneracy andseparability conditions leads to the appearence of two components in the dynamical evolution with verydifferent decoherence times. The ratio between the characteristic time of the weak and strong decoherentcomponents is given by τ WD /τ SD ≈k/δk, where δk is a measure of the nonseparability of the couplingto the environment and k is the mean decay constant of the oscillators. 1 Introduction