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Nature Communications

Enhanced on-chip phase measurement by inverse weak value amplification

Meiting Song, John Steinmetz, Yi Zhang, Juniyali Nauriyal, Kevin Lyons, Andrew N. Jordan, Jaime Cárdenas

Published Oct 29, 2021• 30 citations
Publisher

Abstract

Optical interferometry plays an essential role in precision metrology such as in gravitational wave detection, gyroscopes, and environmental sensing. Weak value amplification enables reaching the shot-noise-limit of sensitivity, which is difficult for most optical sensors, by amplifying the interferometric signal without amplifying certain technical noises. We implement a generalized form of weak value amplification on an integrated photonic platform with a multi-mode interferometer. Our results pave the way for a more sensitive, robust, and compact platform for measuring phase, which can be adapted to fields such as coherent communications and the quantum domain. In this work, we show a 7 dB signal enhancement in our weak value device over a standard Mach-Zehnder interferometer with equal detected optical power, as well as frequency measurements with 2 kHz sensitivity by adding a ring resonator.

DOI
10.1038/s41467-021-26522-2

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Optical interferometry plays an essential role in precision metrology such as in gravitational wave detection, gyroscopes, and environmental sensing. Weak value amplification enables reaching the shot-noise-limit of sensitivity, which is difficult for most optical sensors, by amplifying the interferometric signal without amplifying certain technical noises. We implement a generalized form of weak value amplification on an integrated photonic platform with a multi-mode interferometer. Our results pave the way for a more sensitive, robust, and compact platform for measuring phase, which can be adapted to fields such as coherent communications and the quantum domain. In this work, we show a 7 dB signal enhancement in our weak value device over a standard Mach-Zehnder interferometer with equal detected optical power, as well as frequency measurements with 2 kHz sensitivity by adding a ring resonator.
Weak value amplification (WVA) has emerged as a powerful technique that enhances measurement precision. However, traditional table-top WVA setups and on-chip demonstrations have not achieved an amplification over 20 dB. The practical limit of the amplification is the fidelity of photon post-selection. To address this limit, we design a weak value device with an over 30 dB interferometer extinction ratio, where the stray light in the dark port is minimized with thermally tunable phase shifters. As a result, the device successfully shows 30 dB WVA, termed ultra-high WVA. This WVA optimization strategy by improving interferometer extinction is extensible to a wide range of WVA-based detections, paving the way for their broader application in practical precision measurements.
We present an inverse weak value amplification (IWVA) scheme to perform precision frequency measurements in an integrated optics environment. The IWVA technique allows us to amplify small signals by introducing a weak perturbation to the system and performing a post-selection on the data. A Bragg grating with two band gaps is used to convert the optical frequency into a phase, and a perturbation is applied to the mode coefficients. We demonstrate the advantages of a Bragg grating with two band gaps for obtaining high transmission and low group velocity. We numerically model the interferometer, and demonstrate that we obtain the desired amplification effect. By using an on-chip device instead of a free space implementation, precision measurements can be carried out in a small volume with reliable performance.
An important part of optical sensing is interferometry, where direct or homodyne detection at the output of an interferometer yields information about small phase shifts. Classical interferometry operates at the shot-noise limit (SNL), caused by the photon structure of light and reached when an interferometer is fed with coherent light. The use of nonclassical light at the input of an interferometer enables overcoming the SNL. In particular, squeezed light is known to be less noisy than coherent light. An interferometer fed with strongly squeezed light can, in principle, provide the phase sensitivity at the Heisenberg limit, the ultimate limit allowed by the laws of physics. However, this supersensitive operation is strongly degraded by loss – both inside the interferometer and outside it, at the stage of detection. While the former (internal loss) seems to be inevitable, the latter (detection loss) can be overcome, and we demonstrate it in our recent experiment. The clue is to amplify light at the interferometer output using a phase-sensitive optical parametric amplifier. This device does not introduce additional noise, but it amplifies the fragile quantum signal and thus makes it tolerant to loss at the detection stage. In a proof-of-principle experiment, we build a polarization Mach-Zehnder interferometer and feed it with coherent light in one port and a squeezed vacuum in another port. At one output port, we amplify light with an optical parametric amplifier and measure a phase sensitivity of 13 mrad for 1500 photons in the interferometer. This result, achieved with 50% detection efficiency, overcomes the SNL by 3 dB. Moreover, by using stronger amplification, we can overcome the SNL under detection efficiency as low as 13%. Our results outline a way to use squeezed light for real-life sensing, where the detection efficiency cannot be very high, especially in spectral ranges like middle-infrared or terahertz.
In a weak measurement with postselection, a measurement value, called the weak value, can be amplified beyond the eigenvalues of an observable. However, there are some controversies whether weak-value amplification is practically useful in increasing the sensitivity of the measurement, in which fundamental quantum noise dominates. In this paper, we investigate the sensitivity limit of an optical interferometer when weak-value amplification is implemented, properly accounting for quantum shot noise and radiation-pressure noise. To do so, we formulate weak-value amplification in the Heisenberg picture instead of in the Schr\"odinger picture, which is conventionally used. This formulation enables us to understand intuitively what happens when the measurement outcome is postselected and the weak value is amplified. As a result, we find that the sensitivity limit is given by the standard quantum limit that is the same as in a standard interferometry. We also discuss a way to circumvent the standard quantum limit.