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

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.