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

We investigate the quantum sensing performance of a dephasing qubit as a probe in Ohmic environments, characterized by the coupling strength η, the Ohmicity parameter s, and the cutoff frequency ω_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 ω_c t is independent of ω_c, and peaks at an optimal time t_opt, yielding optimal sensitivity mathcal{Q}_opt. We analyze how mathcal{Q}_opt depends on η, s and the temperature T. Our results demonstrate that, for any Ohmic environment, provided that ω_c t_opt ll 1, mathcal{Q}_opt always reaches the upper bound: mathcal{Q}_max = 0.648 at zero temperature, and consistently attains mathcal{Q}_max/4 at high temperatures. Remarkably, we find that increasing the scaled temperature T/ω_c can enhance mathcal{Q}_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.