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arXiv:2101.05533 · IEEE Access

On the Possibility of Breaking the Heterodyne Detection Quantum Noise Limit With Cross-Correlation

Ernest A. Michael, Felipe E. Besser

Published Jan 1, 2018• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/access.2018.2855405

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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.
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.
Recent results for the cross-correlation signal of a newly proposed balanced correlation receiver at 1.5 μm pointed towards a possible bypassing of the standard quantum limit for the receiver noise-temperature hν⁄k in cross-correlation by a factor of 4-6. The only radiation source strong enough for a clear hot-cold measurement was a heavily attenuated fiber-coupled superluminant LED (SLED), because a multi-mode fiber-coupled thermal halogen lamp was difficult to control in polarization due to its weakness when coupled to a single-mode fiber. This peculiarity left some doubts regarding a possible “strange” quantum-mechanical behavior of the signal light from the SLED. Here we want to present the concept for more convincing measurements using a true thermal signal source.
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.
The phase noise affecting the beat photocurrent produced by coherent detection of a single-frequency laser field with a time-delayed and frequency-shifted image of itself in a heterodyne two-wave interferometric system using a single-mode optical fiber is investigated as a function of source spectrum and phase-decorrelation time under the assumptions of quantum laser phase noise and high-local-oscillation level. The influence on the photocurrent spectrum of partial correlation between detected fields is pointed out. These calculations are an extension of a previously reported high-resolution spectroscopic method and account for the phase-noise limitation in unbalanced heterodyne fiber sensors and heterodyne-transmission receivers with an optical reference wave generated from the received signal. An experimental study is reported consisting of a Mach–Zender-type interferometer employing a single-frequency amplitude-stabilized laser, an acousto-optical single-side-band modulator for frequency shifting one of the arms, and several lengths of single-mode optical fiber to decorrelate the detected fields partially. Results are found to be in good agreement with theory.
A parallel development of the semiclassical and quantum statistics of multispatiotemporal mode direct, homodyne, and heterodyne detection using an ideal (except for its subunity quantum efficiency) photon detector is presented. Particular emphasis is placed on the latter two coherent detection Configurations. The primary intent is to delineate the semiclassical theory's regime of validity and to show, within this regime of validity, how the quantum theory's signal quantum noise, local oscillator quantum noise, the quantum noise incurred because of subunity detector quantum efficiency, plus (for heterodyning only) image band quantum noise produce the quantitative equivalent of the semiclassical theory's local oscillator shot noise. The effects of classical fluctuations on the local oscillator, and the recently suggested dual-detector arrangement for suppressing these fluctuations, are treated. It is Shown that previous studies of this arrangement have neglected a potentially significant noise contribution.
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.