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

TL;DR

This paper compares passive cooling and engineered dissipation protocols for preparing topologically nontrivial quantum states, highlighting the fundamental limits imposed by dissipative diffusion processes and analyzing their efficiency and stability.

Contribution

It introduces and analyzes two particle number conserving protocols, revealing the quadratic scaling of cooling time and the stability of the engineered dark state.

Findings

Cooling time scales quadratically with system size.

Engineered dissipation admits a unique, stable dark state.

Dissipative diffusion limits cooling efficiency.

Abstract

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.