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IEEE Journal of Quantum Electronics

Quantum-limited operation of balanced mixer homodyne and heterodyne receivers

S. Machida, Y. Yamamoto

Published May 1, 1986• 47 citations
Publisher

Abstract

The quantum-limited operation of balanced mixer optical homodyne and heterodyne receiver using a 50-50 percent beam splitter and two identical photodetectors is experimentally confirmed. The absolute quantum noise levels are calibrated with an incoherent GaAs light-emitting diode output. The photoelectron statistics, obtained through the analog photon counting experiment, are reduced to the quantum limit. The photocurrent fluctuation spectral density measured with a spectrum analyzer also agrees with the quantum noise spectral density. Furthermore, the deviations from the absolute quantum noise level are within ±0.02 dB. Finally, complete suppression of local oscillator excess noise is demonstrated in the 0-1.5 GHz frequency region.

DOI
10.1109/jqe.1986.1073022

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The quantum-limited operation of balanced mixer optical homodyne and heterodyne receiver using a 50-50 percent beam splitter and two identical photodetectors is experimentally confirmed. The absolute quantum noise levels are calibrated with an incoherent GaAs light-emitting diode output. The photoelectron statistics, obtained through the analog photon counting experiment, are reduced to the quantum limit. The photocurrent fluctuation spectral density measured with a spectrum analyzer also agrees with the quantum noise spectral density. Furthermore, the deviations from the absolute quantum noise level are within ±0.02 dB. Finally, complete suppression of local oscillator excess noise is demonstrated in the 0-1.5 GHz frequency region.
Quantum-mechanical calculations of the mean-square fluctuation spectra in optical homodyning and heterodyning are made for arbitrary input and local-oscillator quantum states. In addition to the unavoidable quantum fluctuations, it is shown that excess noise from the local oscillator always affects homodyning and, when it is broadband, also heterodyning. Both the quantum and the excess noise of the local oscillator can be eliminated by coherent subtraction of the two outputs of a 50-50 beam splitter. This result also demonstrates the fact that the basic quantum noise in homodyning and heterodyning is signal quantum fluctuation, not local-oscillator shot noise.
We experimentally study optical homodyne and heterodyne detections with the same setup, which is flexible to manipulate the signal sideband modulation. When the modulation only generates a single signal sideband, the light field measurement by mixing the single sideband at ω0 ±? with a strong local oscillator at the carrier frequency ω0on a beam splitter becomes balanced heterodyne detection. When two signal sidebands at ω0 ±? are generated and the relative phase of the two sidebands is locked, this measurement corresponds to optical balanced homodyne detection. With this setup, we may confirm directly that the signal-to-noise ratio with heterodyne detection is two-fold worse than that with homodyne detection. This work will have important applications in quantum state measurement and quantum information.
Quantum noise in optical heterodyning and homodyning, usually analyzed under the assumption that the photodetector output is conditionally Poisson,1,2 is frequently supposed to arise from local oscillator (LO) shot noise. However, a fully quantum mechanical analysis from Yuen and Shapiro3 has shown that it actually arises from the signal quantum fluctuation; in particular homodyning and heterodyning are realizations of abstract quantum measurements of the field quadratures. We analyze the effect of LO noise, both quantum and excess noise, on homodyne and heterodyne detection. For conventional input light, i.e., fields in coherent states or their random superpositions, we demonstrate how a conditionally Poisson calculation would yield the correct answer but incorrect interpretation for the detection quantum noise.
The rapid development of continuous-variable quantum communication has driven an increasing demand for high-performance quantum signal processing modules. Among these, the balanced homodyne detector (BHD) has emerged as a leading solution for practical quantum state measurement due to its capability to provide complete quantum mechanical characterization. However, its performance is often constrained by limited bandwidth and high noise levels, primarily due to the reliance on bulk optical components and discrete receiver electronics. The dominant noise source in these systems typically stems from electronic noise, while imbalances in the optical path further degrade the signal-to-noise ratio (SNR) of the BHD. In this work, we present an adjustable integrated optical path to enhance the balance within the BHD system, along with a low-noise transimpedance amplifier (TIA) by employing optoelectronic co-design. Our design achieves a bandwidth of 2.5 GHz, an input-referred noise current of only 2 pA/√Hz in 180 nm CMOS technology, and a measured quantum shot noise clearance of 15 dB generated from a 700 μA photocurrent. This is the maximum quantum shot noise clearance at the same BHD photocurrent reported to date above the GHz bandwidth.
The cross-correlation sensitivity of two identical balanced photodiode heterodyne receivers is characterized. Both the balanced photodiodes receive the same weak signal split up equally, a situation equivalent to an astronomical spatial interferometer. A common local oscillator is also split up equally and its phase difference between both the receivers is stabilized. We show by a semi-classical photon deletion theory that the post-detection laser shot noise contributions on both the receivers must be completely uncorrelated in this case of passing three power splitters. We measured the auto- and cross-correlation outputs as a function of the weak signal power (system noise temperature measurement) and obtained a cross-correlation system noise temperature up to 20 times lower than for the auto-correlation system noise temperature of each receiver separately. This is supported by Allan plot measurements showing cross-correlation standard deviations 30 times lower than in auto-correlation. Careful calibration of the source power shows that the auto-correlation (regular) noise temperature of the single balanced receivers is already very near to the quantum limit as expected, which suggests a cross-correlation system noise temperature below the quantum limit. If validated further, this experimentally clear finding will not only be relevant for astronomical instrumentation but also for other fields, such as telecommunications and medical imaging.
A broadband quantum noise source based on detection of shot noise of a balanced photodetector is demonstrated. Precise electro-optical tuning of the balanced photodetector circuit was carried out by an integrated optical beam splitter constructed in the form of the dual output Mach-Zehnder interferometer on a lithium niobate substrate. The classical component of the detected noise related to the relative intensity noise of a laser diode was suppressed by more than 15 dB. At the maximum laser power of 100 mW, the power spectral density of detected shot noise was 12 dB higher than the level of technical noise of the measuring system in the frequency band above 3 GHz. Keywords: quantum random number generator, vacuum fluctuations, shot noise measurements, integrated optics, lithium niobate