Theory of quantum-enhanced spectroscopy with general Markovian light sources

Photonic states, such as NOON states and super-radiant states, are potentially useful for quantum-enhanced spectroscopy. However, generating these specific states, which are known to provide a quantum advantage, can be experimentally challenging. While several light sources, often comprising of multiple quantum emitters interacting with engineered optical modes, can be used to generate non-classical states of light, whether or not these states have quantum metrological potential remains less well understood. In this work, we develop a general frame-work to analyze quantum enhanced spectroscopy with generalized Markovian light sources. First, by exploiting a matrix-product state representation of the emitted photon state, we relate its quantum Fisher Information (QFI) in a spectroscopy setup to the Lindbladian governing the internal dynamics of the light source. We also use this relationship to elucidate the connection between the Lindbladian spectrum and the possibility of a quantum metrological advantage. Finally, we construct the optimal measurement (i.e. measurement saturating the quantum Cramer Rao bound) that requires only time-local photodetection, classical feedback and linear-optical elements for spectroscopy with the emitted photons.