Dissipatively driven entanglement of two nuclear spin ensembles in a double quantum dot

Typically, quantum information schemes have been discussed in the context of isolated many-body systems subject to unitary dynamics. Here, dissipation has been identified as a mechanism that corrupts the useful quantum properties of the system under study. Recently, however, with the advent of novel ideas such as dissipative engineering, a paradigm shift could be observed in quantum physics. More and more approaches actively utilize dissipation as a driving force behind the emergence of coherent quantum phenomena. In this spirit, we propose a transport scheme for an electrically defined double quantum dot in which the two nuclear ensembles in the host environment are actively pumped into an entangled target state. Based on a self-consistent Holstein-Primakoff approximation, we derive an effective quantum master equation for the nuclear spins which features an unique entangled steady state; accordingly, long lasting entanglement is created deterministically. Prospects for the experimental realization of this proposal are briefly discussed.