Quantum resolution limit via coherent polarization Raman spectroscopy

As one of the milestones in early‐era nonlinear Raman studies, Akhmanov et al. [Sov. Phys. JETP 47, 667 (1978)] and Koroteev et al. [Phys. Rev. Lett. 43, 398 (1979)] have demonstrated that polarization coherent anti‐Stokes Raman scattering (CARS) spectroscopy can resolve overlapping spectral lines that cannot be resolved by means of spontaneous Raman scattering spectroscopy and argued that the resolution of this method is unlimited. Here, we show that information theory offers useful insights into this remarkable result. We demonstrate that spectral super‐resolution attainable in polarization CARS can be understood in terms of the Fisher information and the pertinent Cramér–Rao lower bound. We show that, with a suitable polarization arrangement, coherent Raman scattering can be tailored to yield super‐resolving spectral modes that provide a nonvanishing Fisher information even for deeply sub‐Rayleigh spectral features, preventing the variance of spectral measurements from diverging no matter how fine these spectral features are. When the nonresonant coherent background scattering can be efficiently suppressed, the Fisher information of such super‐resolving modes reaches its upper bound as dictated by its quantum version—the quantum Fisher information. We show that spectral super‐resolution attainable with polarization CARS can be understood in terms of the Fisher information and the pertinent Cramér–Rao lower bound. With a suitable polarization arrangement, coherent Raman scattering can be tailored to yield super‐resolving spectral modes that provide a nonvanishing Fisher information even for deeply sub‐Rayleigh spectral features. When the nonresonant coherent background scattering can be efficiently suppressed, the Fisher information of such super‐resolving modes reaches its upper bound—the quantum Fisher information.