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arXiv:1911.08697

Linear quantum measurement theory of matter-wave interferometry

Yiqiu Ma, Xiang Li, Sheng-Jun Yang, Yanbei Chen

Published Nov 20, 2019• 0 citations
arXivHTMLPDF

Abstract

The theory of linear quantum measurement has been developed for analysing the sensitivities of experimental devices that measure extremely weak signals, such as gravitational waves. It has successfully contributed to the theoretical understanding of laser interferometer gravitational-wave detectors (used by LIGO, VIRGO and KaGRA) and helped many important experimental upgrades. In this work, we establish a linear quantum measurement theory for another kind of measurement device--- matter wave interferometers, which has been widely discussed as an important platform for many high-precision experiments. This theory allows us to account for both atom and light fluctuations, and leads to a detailed analysis of back-action in matter-wave interferometry (action of light back onto the atoms) and its effect on dynamics and measurement noise. From this analysis, we obtain a Standard Quantum Limit (SQL) for matter-wave interferometry. A comparison between the LIGO detector and matter wave interferometer is also given from the perspective of quantum measurement.

DOI
10.48550/arxiv.1911.08697

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Abstract Heisenberg’s back action and Robertson’s intrinsic uncertainty are presented. von Neumann’s analysis of quantum measurement is recounted. Advanced LIGO is used as an example of quantum measurement: giant Michelson interferometers achieve sensitivity to motion of 1 part in 1021. The discovery at LIGO of gravitational waves is outlined. Then the standard quantum limit is deduced. The use of cavities in the interferometer arms to increase the photon flux is described. The potential for improvement by squeezing the vacuum at the blank input port is discussed. Prospects for speed interferometry are outlined.
The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting.
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Quantum fluctuations in the phase and amplitude quadratures of light set limitations on the sensitivity of modern optical instruments. The sensitivity of the interferometric gravitational-wave detectors, such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), is limited by quantum shot noise, quantum radiation pressure noise, and a set of classical noises. We show how the quantum properties of light can be used to distinguish these noises using correlation techniques. Particularly, in the first part of the paper we show estimations of the coating thermal noise and gas phase noise, hidden below the quantum shot noise in the Advanced LIGO sensitivity curve. We also make projections on the observatory sensitivity during the next science runs. In the second part of the paper we discuss the correlation technique that reveals the quantum radiation pressure noise from the background of classical noises and shot noise. We apply this technique to the Advanced LIGO data, collected during the first science run, and experimentally estimate the quantum correlations and quantum radiation pressure noise in the interferometer.