Multiple steady states and dark states induced by nonlocal dissipation in a double quantum dot

Both multiple steady states and dark states have potential applications in the quantum information processing in the presence of dissipation. Here, we propose to implement multiple steady states and dark states in a double quantum dot (DQD) system using quantum reservoir engineering. By coupling the DQD to shared reservoirs, multiple steady states of both four-and two-fold degeneracy can be achieved for specific parameters. It is proved that the occurrence of such multiple steady states is attributed to the strong symmetry of the Lindblad master equation. The multiple steady states can be well revealed by the occupation number of the DQD, which exhibits a discontinuity at the strong-symmetric points and changes drastically in the vicinities of these points. In the regime of unique steady state, the system can be stabilized to a pure state, dubbed dark state, with intact coherence in spite of the dissipation. Our work shows that a variety of novel steady states can be implemented in the DQD system, which paves the way for engineering multiple steady states and dark states in the DQD system.