Quantum theory of cross-correlation heterodyne detection

Cross-correlation heterodyne detectors exhibit the potential for suppression of the detection quantum noise below shot noise without use of optical squeezing for capturing weak optical signals in low frequency bands. To understand the underlying mechanism, we develop a quantum theory to describe the noise performance of cross-correlation heterodyne detectors. By calculating the cross spectral density (CSD) of the photocurrent fluctuations from a cross-correlation heterodyne detector, we prove that its noise performance can break the shot noise limit and exceed that of a regular heterodyne detector for detection of coherent light. When the detected light signal is in a squeezed state, we show that the corresponding CSD value is negative and discuss how a negative CSD may be explored to improve the output signal-to-noise ratio of the detector contaminated by classical noises through tuning the parameter of the degree of squeezing. This work may find itself useful in space-based gravitational wave searching and a variety of other scientific research activities, such as observation of vacuum magnetic birefringence and telecommunications.