Quantifying Effective Heterodyne Detection Efficiency with SI-Traceable Standards

Abstract

Accurate calibration of coherent optical receivers is essential for reliable performance assessment in coherent communications, precision and quantum sensing, and continuous-variable quantum key distribution (CV-QKD), where the effective detection efficiency directly impacts channel parameter estimation. We present a methodology traceable to the International System of Units (SI) to determine the effective heterodyne detection efficiency of balanced receivers using shot-noise-referenced measurements. The protocol relies on two observables acquired with an electrical spectrum analyzer: the heterodyne beat-note power and the local oscillator shot-noise variance, with explicit treatment of the analyzer's equivalent noise bandwidth (ENBW). The photon flux in the signal path is referenced to SI units via calibrated radiometric standards. We first validate the protocol on a free-space receiver, demonstrating consistency with an independently constructed optical loss chain across a wide range of signal powers and under controlled, calibrated attenuation. Extending the same estimator to a fiber-coupled, polarization-maintaining balanced receiver confirms that the protocol is robust for practical coherent-receiver architectures and intermediate frequencies in the MHz range. These results establish a traceable, uncertainty-bounded framework for real-time receiver calibration, providing a practical route for CV-QKD and other coherent optical systems.

Figures (6)

• Figure 1: Principle of coherent balanced detection and key physical parameters. The local oscillator (LO), with coherent amplitude $\beta$, and the signal field, with coherent amplitude $\alpha$, are combined at the beam splitter (BS), which may exhibit a small splitting imbalance $(1/2 \pm \delta_{\tau})$ and finite insertion losses described by the coefficients $\tau_{\alpha}$ and $\tau_{\beta}$ for the signal and LO fields, respectively. The heterodyne signal is extracted from the differential photocurrent of two photodetectors with quantum efficiencies $\eta_{1}$ and $\eta_{2}$. Optical losses in the quantum channel are modeled by the effective transmission parameter $\eta_{\mathrm{opt}}$. Losses can be simulated using a half-wave plate (HWP) in combination with a polarizing beam splitter (PBS).
• Figure 2: Experimental setup. The experiment is organized in three blocks. Source preparation: two narrow-linewidth fiber lasers (primary: DFM’s Stabi$\lambda$aser $1542^{\varepsilon}$ and secondary: NKT Koheras Basik) are frequency-offset locked with a heterodyne optical phase-locked loop (OPLL), using the beat note detected on photodetector PD1. Protocol validation: the signal arm is power-stabilized with an electronic variable optical attenuator (EVOA) in an intensity-stabilization loop (ISL), monitored with a calibrated photodetector (Cal. PD), and attenuated to nW powers using a calibrated neutral density (ND) filter before being combined with the LO and detected on a balanced detector (BD). Use-case implementation: a fully polarization-maintaining fiber implementation where the signal is routed through a calibrated attenuation chain of asymmetric couplers before interfering with the LO in a symmetric coupler; the heterodyne spectrum is measured with a fiber-coupled balanced detector and an ESA.
• Figure 3: Free-space validation of the protocol. Blue dots: protocol-based estimate ($\eta_{\mathrm{prot}}$) with error bars. Green dashed line and band: independent loss-chain estimate ($\eta_{\mathrm{sep}}$). (a) $\eta_{\mathrm{prot}}$ versus signal power with the independent loss-chain estimate $\eta_{\mathrm{sep}} = 0.345 \pm 0.025$, $k=2$ shown as a band. (b) $\eta_{\mathrm{prot}}$ versus calibrated attenuation. The independent prediction is scaled by the measured transmission. In both cases the protocol and independent estimates agree within uncertainties.
• Figure 4: Traceable calibration of the lumped heterodyne detection efficiency for the fiber-coupled receiver. The heterodyne efficiencies derived from the protocol are shown for three intermediate frequencies (IF) (20;50;80). Within the stated uncertainties, the measured efficiencies are consistent across the investigated IF range and signal powers, yielding a representative value of $\eta = 0.386 \pm 0.012$ ($k=2$).
• Figure S1: Radiometric chain of traceability. Measurement of optical power is made traceable to the primary radiometric standard, the cryogenic radiometer, by a chain of inter-detector calibrations. Using the flat response (in wavelength) of the metrology-grade thermopile detector, traceability of optical power is transferred from the visible (silicon trap detectors) to the near infrared (integrating spheres with germanium detectors or cooled InGaAs detectors).