Feedback cooling of fermionic atoms in optical lattices

TL;DR

This paper presents a measurement-based feedback control method to prepare topological insulator states with fermionic ultracold atoms in optical lattices, stabilizing desired states through engineered dissipative channels.

Contribution

It introduces a novel feedback control scheme for stabilizing topological insulator states in optical lattices, including exact and approximate methods for experimental constraints.

Findings

Successful preparation of 1D and Haldane's Chern insulator states demonstrated.

Fidelity between target and steady states calculated using exact diagonalization.

Comparison of mean occupation in larger systems using mean-field kinetic equations.

Abstract

We discuss the preparation of topological insulator states with fermionic ultracold atoms in optical lattices by means of measurement-based Markovian feedback control. The designed measurement and feedback operators induce an effective dissipative channel that stabilizes the desired insulator state, either in an exact way or approximately in the case where additional experimental constraints are assumed. Successful state preparation is demonstrated in one-dimensional insulators as well as for Haldane's Chern insulator, by calculating the fidelity between the target ground state and the steady state of the feedback-modified master equation. The fidelity is obtained numerically through exact diagonalization or via time evolution of the system with moderate sizes. For larger 2D systems, we compare the mean occupation of the single-particle eigenstates for the ground and steady state computed through mean-field kinetic equations.