We study two anisotropically interacting spins coupled to optical phonons; we restrict our analysis to the regime of strong coupling to the environment, to the antiadiabatic region, and to the subspace with zero value for $S_T^z$ (the $z$ component of the total spin). In the case where each spin is coupled to a different phonon bath, we assume that the system and the environment are initially uncorrelated (and form a simply separable state) in the polaronic frame of reference. By analyzing the polaron dynamics through a non-Markovian quantum master equation, we find that the system manifests a small amount of decoherence that decreases both with increasing nonadiabaticity and with enhancing strength of coupling; whereas, under the Markovian approximation, the polaronic system exhibits a decoherence-free behavior. For the situation where both spins are coupled to the same phonon bath, we also show that the system is decoherence-free in the subspace where $S_T^z$ is fixed. To suppress decoherence through quantum control, we employ a train of $\pi$ pulses and demonstrate that unitary evolution of the system can be retained. We propose realization of a weakly decohering charge qubit from an electron in an oxide-based (tunnel-coupled) double-quantum-dot system.

• Received 19 August 2013
• Revised 11 January 2014

DOI:https://doi.org/10.1103/PhysRevB.89.064311