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arXiv:2007.15029 · Physical Review Research

Relative acceleration noise mitigation for nanocrystal matter-wave interferometry: Applications to entangling masses via quantum gravity

Marko Toroš, Thomas W. van de Kamp, Ryan J. Marshman, M. S. Kim, Anupam Mazumdar, Sougato Bose

Published Jun 4, 2021• 61 citations
arXivHTMLPDF

Abstract

The authors show that a nanocrystal matter-wave interferometer can be used to create a state-of-the-art quantum sensor to detect low accelerations and discuss how it can be used to probe quantum aspects of gravity in a laboratory.
DOI
10.1103/physrevresearch.3.023178

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•Jul 29, 2020•2 citations
Matter-wave interferometers have fundamental applications for gravity experiments such as testing the equivalence principle and the quantum nature of gravity. In addition, matter-wave interferometers can be used as quantum sensors to measure the local gravitational acceleration caused by external massive moving objects, thus lending itself for technological applications. In this paper, we will establish a three-dimensional model to describe the gravity gradient signal from an external moving object, and theoretically investigate the achievable sensitivities using the matter-wave interferometer based on the Stern-Gerlach setup. As an application we will consider the mesoscopic interference for metric and curvature and gravitational-wave detection scheme [R. J. Marshman et al., Mesoscopic interference for metric and curvature (MIMAC) & gravitational wave detection, New J. Phys. 22, 083012 (2020)] and quantify its sensitivity to gravity gradients using frequency-space analysis. We will consider objects near Earth-based experiments and space debris in proximity of satellites and estimate the minimum detectable mass of the object as a function of their distance, velocity, and orientation.
Large mass, large splitting and long duration matter wave interferometry in unprecedented regimes is necessary for revealing the quantum nature of gravity in the laboratory, as well as for extreme sensing. In this talk I first explain these two applications along with the domain required, namely, micron sized crystals in superposed states separated by 10 microns. Then we will show how one of two principal sources of noise in the system -- noninertial acceleration noise and gravity gradient noise (Newtonian noise) can be mitigated in such systems, to enable one to create and verify superpositions in the above mentioned scales.
The interference of matter waves is a direct consequence of wave-particle duality and lies at the heart of quantum mechanics. Today, with the validity of quantum theory being widely ascertained, we are beyond proof-of-principle demonstrations and are transforming this phenomenon into a measurement tool for practical applications via the development of quantum technologies. Atom interferometry is a special type of quantum technology, which is particularly suitable for the detection of gravity. Its potential for absolute, low-drift measurements with options for noise suppression could bring wide-ranging benefits for applications that are important across economies. This journey from the laboratory into the real world of applications requires the understanding and mitigation of the effects of external influences on the system.
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In this white paper, we highlight the importance of the (1−10 Hz1-10~{\rm Hz}1−10 Hz) frequency range for laboratory tests of the quantum nature of gravity using the quantum gravity-induced entanglement of masses (QGEM) protocol. QGEM requires matter-wave interferometers with masses (m∼10−15−10−14 kgm\sim10^{-15}-10^{-14}~{\rm kg}m∼10−15−10−14 kg), brought within separations (d∼30−50 μmd\sim30-50~μ{\rm m}d∼30−50 μm), while maintaining spatial superpositions of (1−20 μm1-20~μ{\rm m}1−20 μm) and coherence for (τ∼0.1−1 sτ\sim 0.1 - 1~{\rm s}τ∼0.1−1 s). These requirements make low-frequency environmental noise a central experimental challenge and place QGEM in a regime closely related to the low-frequency goals of the Einstein Telescope (ET) and the Cosmic Explorer (CE). In particular, QGEM is sensitive to relative acceleration noise (RAN) and to gravity-gradient noise (GGN) generated by seismic and other environmental mass-density fluctuations. For representative parameters m=10−14 kgm=10^{-14}~{\rm kg}m=10−14 kg, Δx=10 μmΔx=10~μ{\rm m}Δx=10 μm, and τ=1 sτ=1~{\rm s}τ=1 s, the differential acceleration-noise amplitude spectral density must be suppressed well below the 10−15 m s−2/Hz10^{-15}~{\rm m\,s^{-2}/\sqrt{Hz}}10−15 ms−2/Hz​ level to keep acceleration-induced dephasing below the relevant experimental scale. Achieving this level of low-frequency noise suppression is therefore a key requirement for QGEM and closely parallels the seismic and gravity-gradient noise challenges that ET and CE address.
Relative accelerations between a mass undergoing matter-wave interference and the associated apparatus, when not tracked, can appear as dephasing. It can be an important limiting factor in interferometry with large masses. Here we advocate taking conceptually the simplest solution: putting both the interfering mass and its associated apparatus in a freely falling capsule, so that the strongest inertial noise components vanish due to the equivalence principle. In this setting, we investigate two of the most important remaining noise sources: (a) the non-inertial jitter of the experimental setup which arises through gas collisions and photon scattering on the experimental apparatus as well as the walls of the enclosing capsule, and (b) the gravity-gradient noise, namely the fluctuating curvature change in a finite sized capsule arising from any untracked motion of external masses. We show that the former can be reduced below desired values by appropriate pressures and temperatures, while the latter can be fully mitigated in a controlled environment. We finally apply the analysis to a recent proposal for testing the quantum nature of gravity [S. Bose et. al. Phys. Rev. Lett 119, 240401 (2017)] through the entanglement of two masses undergoing interferometry. We show that the relevant entanglement witnessing is feasible in a freely falling capsule with achievable levels of relative acceleration noise.