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 $\hat{I}\cdot$, the Ohmicity parameter $s$, and the cutoff frequency $\ddot{I}{‰}_c$ 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 $\ddot{I}{‰}_{c}t$ is independent of $\ddot{I}{‰}_c$, 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 $\hat{I}\cdot$, $s$ and the temperature $T$. Our results demonstrate that, for any Ohmic environment, provided that $\ddot{I}{‰}_c{t}_{\text{opt}}\ll 1$, ${\mathcal{Q}}_{\text{opt}}$ 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 $T/\ddot{I}{‰}_c$ 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.

9 pages,6 figures