Bi-frequency illumination: a quantum-enhanced protocol

We propose a quantum-enhanced sensing protocol to measure the response of a target object to the frequency of a probe in a noisy and lossy scenario. In our protocol, a bi-frequency state illuminates a target embedded in a thermal bath, whose reflectivity $\eta(\omega)$ is frequency-dependent. After a lossy interaction with the object, we estimate the parameter $\lambda = \eta(\omega_2)-\eta(\omega_1)$ in the reflected beam, which captures information about the response of the object to different electromagnetic frequencies. Computing the quantum Fisher information $H$ relative to the parameter $\lambda$ in an assumed neighborhood of $\lambda \sim 0$ for a two-mode squeezed state ($H_Q$), and a coherent state ($H_C$), we show that a quantum enhancement in the estimation of $\lambda$ is obtained when $H_Q / H_C >1$. This quantum advantage grows with the mean reflectivity of the probed object, and is noise-resilient. We derive explicit formulas for the optimal observables, and propose a general experimental scheme based on elementary quantum optical transformations. Furthermore, our work opens the way to applications in both radar and medical imaging, in particular in the microwave domain