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arXiv:2005.09082

Quantum Noise of Kramers-Kronig Receiver

Fan Zhang, Jiayu Zheng, Haijun Kang, Sun, Fengxiao, Qiongyi He, Su, Xiaolong

Published May 18, 2020• 0 citations
arXivHTMLPDF

Abstract

The Kramers-Kronig (KK) receiver provides an efficient method to reconstruct the complex-valued optical field by means of intensity detection given a minimum-phase signal. In this paper, we analytically show that for detecting coherent states through measuring the minimum-phase signal, while keeping the radial quantum fluctuation the same as the balanced heterodyne detection does, the KK receiver can indirectly recover the tangential component with fluctuation equivalently reduced to 1/3 times the radial one at the decision time, by adopting the KK relations to utilize the information of the physically measured radial component of other time of the symbol period. In consequence, the KK receiver achieves 3/2 times the signal-to-noise ratio of balanced heterodyne detection, while presenting an asymmetric quantum fluctuation distribution depending on the time-varying phase. Therefore, the KK receiver provides a feasible scheme to reduce the quantum fluctuation for obtaining the selected component to 2/ 3 times that of physically measuring the same component of the coherent state. This work provides a physical insight of the KK receiver and should enrich the knowledge of electromagnetic noise in quantum optical measurement.

DOI
10.48550/arxiv.2005.09082

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The Kramers-Kronig (KK) receiver provides an efficient method to reconstruct the complex-valued optical field by means of intensity detection given a minimum-phase signal. In this paper, we analytically show that for detecting coherent states through measuring the minimum-phase signal, while keeping the radial quantum fluctuation the same as the balanced heterodyne detection does, the KK receiver can indirectly recover the tangential component with fluctuation equivalently reduced to 1/3 times the radial one at the decision time, by adopting the KK relations to utilize the information of the physically measured radial component of other time of the symbol period. In consequence, the KK receiver achieves 3/2 times the signal-to-noise ratio of balanced heterodyne detection, while presenting an asymmetric quantum fluctuation distribution depending on the time-varying phase. Therefore, the KK receiver provides a feasible scheme to reduce the quantum fluctuation for obtaining the selected component to 2/ 3 times that of physically measuring the same component of the coherent state. This work provides a physical insight of the KK receiver and should enrich the knowledge of electromagnetic noise in quantum optical measurement.
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In fundamental papers from 1962, Heffener and Haus showed that it is not possible to construct a linear noiseless amplifier [ Proc. IRE 50 , 1604 ( 1962 ) PIREAE 0096-8390 10.1109/JRPROC.1962.288130 ; Phys. Rev. Lett. 128 , 2407 ( 1962 ) PHRVAO 0031-899X 10.1103/PhysRev.128.2407 ]. This implies that amplifier intrinsic noise sources induce random perturbations on the phase of the incoming optical signal, which translates into spectral broadening. Achieving the minimum induced phase fluctuation requires a phase measurement method that introduces minimum uncertainty, i.e., optimum phase measurement. We demonstrate that a measurement method based on heterodyne detection and extended Kalman filtering approaches optimum phase measurement in the presence of amplifier noise. A penalty of 5 dB (numerical) and 15 dB (experimental) compared to quantum limited spectral broadening is achieved. Spectral broadening reduction of 44 dB is achieved, compared to when using the widely employed phase measurement method, based purely on the argument of the signal field. Our results reveal new scientific insights by demonstrating a phase measurement method that enables to approach minimum phase fluctuation, induced by amplifier noise. An impact is envisioned for phase-based optical sensing systems, as optical amplification could increase sensing distance with minimum impact on the phase.