A Quantum Theory of Temporally Mismatched Homodyne Measurements with Applications to Optical Frequency Comb Metrology

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