Temperature-enhanced quantum sensing for the cutoff frequency of Ohmic environments

TL;DR

This paper demonstrates that increasing temperature can significantly improve the sensitivity of quantum probes in estimating the cutoff frequency of Ohmic environments, revealing temperature as a resource for quantum sensing enhancement.

Contribution

It introduces the concept that temperature can be used to enhance quantum sensing performance, providing analytical results on optimal sensitivity dependence on environment parameters.

Findings

Optimal sensitivity peaks at a specific time for all environments.

Temperature increase can boost sensitivity by nearly two orders of magnitude.

Sensitivity reaches an upper bound at zero temperature and scales with temperature at high T.

Abstract

We investigate the quantum sensing performance of a dephasing qubit as a probe in Ohmic environments, characterized by the coupling strength $\eta$, the Ohmicity parameter $s$, and the cutoff frequency $\omega_c$ to be estimated. The performance is quantified by the dimensionless quantum signal-to-noise ratio $\mathcal{Q}$. We show that the evolution of $\mathcal{Q}$ with the scaled time $\omega_c t$ is independent of $\omega_c$, and peaks at an optimal time $t_{\text{opt}}$, yielding optimal sensitivity $\mathcal{Q}_{\text{opt}}$. We analyze how $\mathcal{Q}_{\text{opt}}$ depends on $\eta$, $s$ and the temperature $T$. Our results demonstrate that, for any Ohmic environment, provided that $\omega_c t_{\text{opt}} \ll 1$, $\mathcal{Q}_{\text{opt}}$ always reaches the upper bound: $\mathcal{Q}_{\text{max}} = 0.648$ at zero temperature, and consistently attains $\mathcal{Q}_{\text{max}}/4$ at high temperatures. Remarkably, we find that increasing the scaled temperature $T/\omega_c$ can enhance $\mathcal{Q}_{\text{opt}}$ by nearly two orders of magnitude compared to its zero-temperature counterpart for certain Ohmic environments. Our work reveals that temperature can serve as a resource to enhance sensing precision, as it accelerates the encoding of the cutoff frequency information into the probe state, thereby enabling optimal measurement within a short time window.