Heat transport in an optical lattice via Markovian feedback control

TL;DR

This paper demonstrates how Markovian feedback control can create effective thermal baths in ultracold atomic systems, enabling the study of heat transport and steady states in a quantum simulation context.

Contribution

It introduces a method to simulate heat transport in quantum gases using feedback-controlled baths, bridging a gap in studying thermal properties of isolated quantum systems.

Findings

Heat current scales with system size similarly to classical systems.

Weak interactions and disorder do not alter the fundamental heat transport scaling.

Proposed measurement scheme for energy flow in quantum gases.

Abstract

Ultracold atoms offer a unique opportunity to study many-body physics in a clean and well-controlled environment. However, the isolated nature of quantum gases makes it difficult to study transport properties of the system, which are among the key observables in condensed matter physics. In this work, we employ Markovian feedback control to synthesize two effective thermal baths that couple to the boundaries of a one-dimensional Bose-Hubbard chain. This allows for the realization of a heat-current-carrying state. We investigate the steady-state heat current, including its scaling with system size and its response to disorder. In order to study large systems, we use semi-classical Monte-Carlo simulation and kinetic theory. The numerical results from both approaches show, as expected, that for non- and weakly interacting systems with and without disorder one finds the same scaling of the heat current with respect to the system size as it is found for systems coupled to thermal baths. Finally, we propose and test a scheme for measuring the energy flow. Thus, we provide a route for the quantum simulation of heat-current-carrying steady states of matter in atomic quantum gases.