As an important tool for quantum optical measurement, the balanced homodyne detector (BHD) is highly sensitive to the amplitude and phase of the incident light. It can reliably extract quantum fluctuations, suppress classical common-mode noise, and amplify quantum fluctuations to the macro level. Additionally, it has been widely employed in quantum noise measurement, gravitational wave detection, high-sensitivity interferometric timing measurement, continuous variable quantum key distribution, and quantum random number generator. The common-mode rejection ratio (CMRR), operating bandwidth, and signal-to-noise ratio (SNR) of the detector have been the research focuses. The optical frequency comb contains a large number of equally spaced longitudinal modes, which is a good multi-mode resource. The spectrum width of the optical frequency comb is in the order of nanometers. The quantum optical frequency comb which breaks the limit of shot noise can be generated by nonlinear processes. Quantum optical frequency comb has a great application prospect in quantum precision measurement. Spectrally resolved balanced homodyne detection is an important detection method of quantum optical frequency comb. We analyze the noise source of the balanced homodyne detector theoretically and design the multi-pixel balanced homodyne detector (MBHD) based on photodiode array and multi-channel inductance-capacitance (L-C) coupled transimpedance amplifier (TIA) circuit. These designs enable MBHD to meet multi-channel parallel and high-SNR quantum noise measurements.
The MBHD consists of two highly symmetrical multi-pixel photodetectors (MPDs) and a multi-channel subtracter (Fig. 1). Each MPD includes a photodiode array, a multi-channel L-C coupled structure, AC amplification, and DC amplification. The photocurrent generated by the corresponding pair of pixels in the two MPD flows through their respective AC amplification outputs, and the common-mode signal in the detection result is eliminated by the subtracter to complete the multi-pixel parallel balanced homodyne detection. Multi-channel DC output monitors the optical power of all pixels by a multi-function data acquisition card (DAQ). In the amplification circuit structure of the single pixel in MPD, the generated photocurrent signal is divided into DC signal and AC signal through the L-C coupled circuit. The AC signal is converted into a voltage signal by a TIA and is further adopted to measure the intensity noise power of the incident light. The DC signal is converted into a voltage signal by a load resistor and a isolation amplifier. Additionally, an equivalent noise model is built to analyze the electronic noise. Due to the multi-channel parallel structure of the MBHD, each channel is similar to each other and independent. The electronic noise of the single-pixel channel includes the noise generated by the dark current of the photodiode, the thermal noise generated by the feedback resistance in the transimpedance amplifier circuit, the noise generated by the input voltage noise of the transimpedance amplifier, and the noise generated by the input current noise of the transimpedance amplifier. Theoretical analysis shows that a reasonable selection of feedback resistance and inductance, photodiode with low dark current and low junction capacitance, and the TIA with low input noise can reduce the electronic noise of the detector. Meanwhile, the L-C coupled structure is better than the R-C coupled structure in experimental conditions (Fig. 2).
The device is constructed to test the performance of MBHD (Fig. 3). AC output of MBHD is connected to a spectrometer to measure the bandwidth and SNR. The DC signals of each pixel are measured by a DAQ to monitor the optical powers of each pixel. When the optical power is distributed on all pixel channels, the distribution of the shot noise power in each channel is proportional to the distribution of the incident optical power, which verifies that the multi-pixel BHD can achieve spectrally resolved multi-channel parallel balanced homodyne detection (Fig. 4). When the incident optical power is 1.660 mW, 0.834 mW, 0.418 mW, 0.208 mW, and 0.102 mW respectively, the shot noise spectrum and electronic noise spectrum of one pixel are measured at different analysis frequencies (Fig. 5). The test results show that the 3 dB bandwidth of MBHD is 5 MHz. The resolution bandwidth is set to 100 kHz, the video bandwidth is 100 Hz, and the number of averaging times is 10. When the incident optical power is 1.660 mW, the shot noise power is 23 dB higher than the electronic noise power at the analysis frequency of 2 MHz. By comparing the shot noise power under different incident optical power, the shot noise power decreases by 3 dB when the incident optical power decreases by half, which indicates that the detector has a good linear gain within 0.102 mW to 1.660 mW of the optical power.
Based on the noise model of the BHD, the electronic noise source is analyzed theoretically. The results indicate that the L-C coupled structure is better. By adopting the multi-pixel photodiode array and L-C coupled structure, a high-performance multi-pixel BHD is developed. In each pixel channel, when the 815 nm laser with optical power of 1.660 mW is incident, the shot noise power is 23 dB higher than the electronic noise at the analysis frequency of 2 MHz. By employing the grating to scatter the incident light horizontally, the shot noise power in each channel is proportional to the incident optical power. It is verified that the multi-pixel BHD can realize the spectrally resolved multi-channel parallel balanced homodyne detection. The detector provides a high-performance detection tool for quantum precision measurement based on quantum optical frequency comb.
