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We study two anisotropically interacting spins coupled to optical phonons; werestrict our analysis to the regime of strong coupling to the environment, tothe antiadiabatic region, and to the subspace with zero value for $S^z_T$ (thez-component of the total spin). In the case where each spin is coupled to adifferent phonon bath, we assume that the system and the environment areinitially uncorrelated (and form a simply separable state) in the polaronicframe of reference. By analyzing the {polaron} dynamics through non-Markovianquantum master equation, we find that the system manifests a small amount ofdecoherence that decreases both with increasing non-adiabaticity and withenhancing strength of coupling; whereas, under the Markovian approximation, thepolaronic system exhibits a decoherence free behavior. For the situation whereboth spins are coupled to the same phonon bath, we also show that the system isdecoherence free in the subspace where $S^z_T$ is fixed. To suppressdecoherence through quantum control, we employ a train of pi pulses anddemonstrate that unitary evolution of the system can be retained. We proposerealization of a weakly decohering charge qubit from an electron in anoxide-based (tunnel-coupled) double quantum dot system.

Polaron dynamics and decoherence in an interacting two-spin system coupled to optical phonon environment