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arXiv:2106.03577 · Optica

Approaching optimum phase measurement in the presence of amplifier noise

Darko Zibar, Jens E. Pedersen, Poul Varming, Giovanni Brajato, Francesco Da Ros

Published Sep 6, 2021• 18 citations

Abstract

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.

DOI: 10.1364/optica.431668

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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.

Quantum mechanics imposes that any amplifier that works independently on the phase of the input signal has to introduce some excess noise. The impossibility of such a noiseless amplifier is rooted in the unitarity and linearity of quantum evolution. A possible way to circumvent this limitation is to interrupt such evolution via a measurement, providing a random outcome able to herald a successful-and noiseless-amplification event. Here we show a successful realization of such an approach; we perform a full characterization of an amplified coherent state using quantum homodyne tomography, and observe a strong heralded amplification, with about a 6 dB gain and a noise level significantly smaller than the minimal allowed for any ordinary phase-independent device.

We investigate amplification of optical images by means of a traveling-wave optical parametric amplifier. As shown recently by Kolobov and Lugiato [Phys. Rev. A 52, 4930 (1995)] for a cavity-based geometry, such a scheme can amplify images, without deteriorating their sign-to-noise ratio, thus working as a noiseless amplifier. Here we consider a configuration without cavity, which is more realistic for a possible experimental realization. We investigate in detail the quantum fluctuations of the amplifier and formulate criteria for its noiseless performance. The spatial resolution power, which guarantees noiseless amplification is estimated. We demonstrate how the optimum phase matching of a phase-sensitive wavefront of the image can improve the noise performance of the amplifier and bring it to the ultimate value achievable under given physical conditions. We discuss the effect of improvement of the signal-to-noise ratio in the case of observation of both the input and the amplified image, with an ideal photodetector of small area (i.e., much less than the coherence area of the amplifier). This improvement is due to the fact that the signal-to-noise ratio in the input is deteriorated by the observation with the photodetector of small area.

The standard technique for measuring the phase of a single-mode field is heterodyne detection. Such a measurement may have an uncertainty far above the intrinsic quantum phase uncertainty of the state. Recently it has been shown [H. M. Wiseman and R. B. Killip, Phys. Rev. A 57, 2169 (1998)] that an adaptive technique introduces far less excess noise. Here we quantify this difference by an exact numerical calculation of the minimum measured phase variance for the various schemes, optimized over states with a fixed mean photon number. We also analytically derive the asymptotics for these variances. For the case of heterodyne detection our results disagree with the power law claimed by D'Ariano and Paris [Phys. Rev. A 49, 3022 (1994)].

A scheme for detecting the phase of an incoming optical signal is systematically optimized and demonstrated experimentally. It makes use of four-wave mixing in a highly nonlinear fiber but differs from a phase-sensitive amplifier by its focus on phase detection, rather than on phase-dependent noise reduction. This experimental setup combines the signal with its phase-conjugated idler at the same frequency, before sending the combination to a photodetector. Experimental results show that the ratio of maximum and minimum currents can exceed 1000 even at a relatively low pump power of 10 mW. The proposed scheme may be useful for detecting the signal phase in coherent communication systems without the need of heterodyne detection.

We present calculations of the intensity smoothing of stochastic light by a semiconductor optical amplifier (SOA). We predict spectral changes of the light that are due to amplitude-to-phase coupling in the gain medium. The intensity smoothing of noisy optical signals with an SOA carries a penalty of spectral broadening (increased phase noise) that increases with increasing alpha parameter (linewidth enhancement factor). The spectral broadening also increases with increasing strength of the intensity fluctuations being smoothed.

Optical phase-sensitive amplifiers (PSAs) leverage nonlinear interactions to achieve noise figures below the conventional quantum limit. Dual-pump phase-insensitive amplification has been studied in wavelength conversion, phase conjugation and spectral inversion, but phase-sensitive amplification remains challenging due to stimulated Brillouin scattering (SBS) in optical fibers. While pump-phase modulation helps mitigate SBS, it broadens the idler spectrum, complicating practical implementation. We demonstrate a counter-phase pump modulation approach to suppress idler spectral broadening using optical coherent combining and delayed self-heterodyne techniques to achieve excellent noise figure (NF) performance in dual-pump PSAs. Our methods achieve over 30 dB suppression of residual phase modulation tones and significantly improve the idler spectrum. We obtained a 20 dB gain with an NF of 1.45 dB and a minimal NF penalty of 0.2 dB due to pump-phase modulation. This achievement enables PSAs to support optical communication, wavelength conversion, and deep-space communication applications.