Dissipative diffusion in quantum state preparation: from passive cooling to system-bath engineering

We investigate and compare two particle number conserving protocols for the preparation of a topologically nontrivial state. The first is derived from thermally coupling the system to a cold bath, while the second is based on engineered dissipation. We numerically study the time required to reach the target state as well as its robustness against physically important perturbations. Crucially, in both protocols the cooling capability is limited by dissipatively induced diffusion processes. The resulting quadratic scaling of the cooling time with system size is corroborated also analytically using mean-field approximations and a purely classical random walk model. Furthermore, we find that the engineered protocol admits a unique and stable dark state, which contributes to an ongoing discussion regarding the applicability of dissipative state preparation to many-body systems.