Using Frequency Combs to Connect Homodyne and Heterodyne Detection

Homodyne and heterodyne measurements are incredibly important tools in both the optical and microwave regime. Traditionally these measurements utilize a continuous wave (CW) coherent source called the local oscillator (LO) that mixes with the signal and effectively amplifies the output. We will relax the assumption that the local oscillator is CW and instead investigate the possibilities of a frequency comb LO. To do this we must create a fully time-dependent treatment of homodyne detection. We have derived the Kraus operators and positive operator valued measures (POVMs) for these measurements giving us a complete picture of the process. Using these mechanisms we can analyze the traditional homodyne and heterodyne limits as well as create new types of measurements. One such measurement we are calling discrete heterodyne where elements of both homodyne and heterodyne are present in different frequency regimes