Quantum sensing of supersensitivity for the Ohmic quantum reservoir

We propose an approach to implement a supersensitive estimation of the key parameters of the Ohmic-family spectral density with coherent spin states as the quantum sensor. This method can dramatically improve the estimation precision of the reservoir coupling strength as well as the cutoff frequency of the spectral density, by using both the number of spins $N$ and encoding time $t$ as effective resources. The quantum Fisher information indicates that the estimation sensitivity of the spectral density can surpass the shot-noise limit for all the sub-Ohmic, Ohmic, and super-Ohmic reservoirs. In particular, for super-Ohmic reservoirs, the precision can achieve a scaling $\ensuremath{\propto}1/(Nt)$. We also present the measurement scheme which can saturate the quantum Cram\'er-Rao bound.