Low-noise Balanced Homodyne Detection with Superconducting Nanowire Single-Photon Detectors

Superconducting nanowire single-photon detectors (SNSPDs) have been widely used to study the discrete nature of quantum states of light in the form of photon-counting experiments. We show that SNSPDs can also be used to study continuous variables of optical quantum states by performing homodyne detection at a bandwidth of $400~\mathrm{kHz}$. By measuring the interference of a continuous-wave field of a local oscillator with the field of the vacuum state using two SNSPDs, we show that the variance of the difference in count rates is linearly proportional to the photon flux of the local oscillator over almost five orders of magnitude. The resulting shot-noise clearance of $(46.0\pm1.1)~\mathrm{dB}$ is the highest reported clearance for a balanced optical homodyne detector, demonstrating their potential for measuring highly squeezed states in the continuous-wave regime. In addition, we measured a $\mathrm{CMRR}=22.4~\mathrm{dB}$. From the joint click counting statistics, we also measure the phase-dependent quadrature of a weak coherent state to demonstrate our device's functionality as a homodyne detector.