Quantum theory of temporally mismatched homodyne measurements with applications to optical-frequency-comb metrology

The fields of precision timekeeping and spectroscopy increasingly rely on\noptical frequency comb interferometry. However, comb-based measurements are not\ndescribed by existing quantum theory because they exhibit both large mode\nmismatch and finite strength local oscillators. To establish this quantum\ntheory, we derive measurement operators for homodyne detection with arbitrary\nmode overlap. These operators are a combination of quadrature and\nintensity-like measurements, which inform a filter that maximizes the\nquadrature measurement signal-to-noise ratio. Furthermore, these operators\nestablish a foundation to extend frequency-comb interferometry to a wide range\nof scenarios, including metrology with nonclassical states of light.\n