Quantum engineering of a synthetic thermal bath for bosonic atoms in a one-dimensional optical lattice via Markovian feedback control

TL;DR

This paper presents a scheme using Markovian feedback control to engineer a synthetic thermal bath for bosonic atoms in a 1D optical lattice, achieving high fidelity thermal states across various regimes and system sizes.

Contribution

The authors develop a feedback-based method to create synthetic thermal baths for bosonic gases in optical lattices, accurately reproducing thermal states even in complex, larger systems.

Findings

Exact thermal states for double- and triple-well systems.

High fidelity (>0.9) at low and high temperatures.

Performance varies with system size and temperature, especially in intermediate regimes.

Abstract

We propose and investigate a scheme for engineering a synthetic thermal bath for a bosonic quantum gas in a one-dimensional optical lattice based on Markovian feedback control. The performance of our scheme is quantified by the fidelity between the steady state of the system and the effective thermal state. For double-well and triple-well systems with non-interacting particles, the steady state is found to be an exact thermal state, which is attributed to the fact that the transfer rates between all pairs of coupled eigenstates satisfy detailed balance condition. The scenario changes when there are more lattice sites, where the detailed balance condition does not hold any more, but remains an accurate approximation. Remarkably, our scheme performs very well at low and high temperature regimes, with the fidelity close to one. The performance at the intermediate temperature regime (where a crossover into a Bose condensed regime occurs) is slightly worse, and the fidelity shows a gentle decrease with increasing system size. We also discuss the interacting cases. In contrast to the non-interacting cases, the scheme is found to perform better at a higher temperature. Another difference is that the minimal temperature that can be engineered is nonzero and increases with the interaction strength.