Broadband pulsed quadrature measurements with calorimeters

A fundamental problem in quantum optics is to measure a quadrature operator of a mode described by a shape in the time or frequency domain. This can be done by pulsed homodyne detection, in which the signal and a high-amplitude pulsed local oscillator (LO) interfere on a beam splitter whose output ports are monitored by photodetectors. The quadrature value is proportional to the difference between the photodetectors' signals. When the shape of the mode is too broad in frequency, the lack of uniform spectral response of detectors prevents direct application of this technique. We show that pulsed homodyne detection can be generalized to broadband pulsed (BBP) homodyne detection with detectors such as calorimeters that detect total energy instead of total photon number. This generalization has applications in measurements of femtosecond pulses and, speculatively, of Rindler modes. We analyze how the implemented measurement approaches an ideal quadrature measurement with growing LO amplitude, and we prove that the moments of the measurement converge to the moments of the quadrature and that the measurement distributions converge weakly.