On the optimal feedback control of linear quantum systems in the presence of thermal noise

TL;DR

This paper investigates how feedback control can generate non-classical states in linear quantum systems affected by thermal noise, revealing that higher thermal excitations can enhance squeezing and entanglement under optimal measurement conditions.

Contribution

It derives analytical bounds for steady-state squeezing and entanglement in bosonic systems with thermal baths, highlighting the role of measurement efficiency and thermal noise.

Findings

Larger thermal excitations can increase steady-state squeezing and entanglement with high measurement efficiency.

Optimal feedback based on weak measurements can outperform homodyne detection at higher temperatures.

Analytical bounds depend only on Hamiltonian parameters and bath thermal excitations.

Abstract

We study the possibility of taking bosonic systems subject to quadratic Hamiltonians and a noisy thermal environment to non-classical stationary states by feedback loops based on weak measurements and conditioned linear driving. We derive general analytical upper bounds for the single mode squeezing and multimode entanglement at steady state, depending only on the Hamiltonian parameters and on the number of thermal excitations of the bath. Our findings show that, rather surprisingly, larger number of thermal excitations in the bath allow for larger steady-state squeezing and entanglement if the efficiency of the optimal continuous measurements conditioning the feedback loop is high enough. We also consider the performance of feedback strategies based on homodyne detection and show that, at variance with the optimal measurements, it degrades with increasing temperature.