Non-Gaussianity as a Signature of a Quantum Theory of Gravity

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Non-Gaussianity as a Signature of a Quantum Theory of Gravity

Richard Howl, Vlatko Vedral, Devang Naik, Marios Christodoulou, Carlo Rovelli, and Aditya Iyer

PRX Quantum 2, 010325 – Published 17 February 2021

Abstract

Tabletop tests of quantum gravity (QG) have long been thought to be practically impossible. However, remarkably, because of rapid progress in quantum information science (QIS), such tests may soon be achievable. Here we uncover an exciting new theoretical link between QG and QIS that also leads to a radical new way of testing QG with QIS experiments. Specifically, we find that only a quantum, not classical, theory of gravity can create non-Gaussianity, a QIS resource that is necessary for universal quantum computation, in the quantum field state of matter. This allows tests based on QIS in which non-Gaussianity in matter is used as a signature of QG. In comparison with previous studies testing QG with QIS where entanglement is used to witness QG when all other quantum interactions are excluded, our non-Gaussianity witness cannot be created by direct classical gravity interactions, facilitating tests that are not constrained by the existence of such processes. Our new signature of QG also enables tests that are based on just a single quantum system rather than a multipartite quantum system, simplifying previously considered experimental setups. We describe a tabletop test of QG that uses our non-Gaussianity signature and that is based on just a single quantum system, a Bose-Einstein condensate, in a single location. In contrast to proposals based on optomechanical setups, Bose-Einstein condensates have already been manipulated into massive nonclassical states, aiding the prospect of testing QG soon.

Received 30 April 2020
Accepted 21 January 2021

DOI:https://doi.org/10.1103/PRXQuantum.2.010325

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Bose-Einstein condensates Experimental studies of gravity Laboratory studies of gravity Quantum computation Quantum gravity Quantum information processing with continuous variables

Gravitation, Cosmology & AstrophysicsQuantum Information, Science & TechnologyInterdisciplinary PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Richard Howl ^1,2,3,*, Vlatko Vedral^4,5, Devang Naik⁶, Marios Christodoulou ^2,4, Carlo Rovelli^7,8,9, and Aditya Iyer⁴

¹School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
²QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
³Quantum Group, Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom
⁴Clarendon Laboratory, Department of Physics, University of Oxford, Oxford, OX1 3PU, United Kingdom
⁵Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, Singapore 117543
⁶LP2N, Laboratoire Photonique, Numérique et Nanosciences, Université Bordeaux–IOGS–CNRS:UMR 5298, 33400 Talence, France
⁷CPT, Aix-Marseille Université, Université de Toulon, CNRS, F-13288 Marseille, France
⁸Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada
⁹The Rotman Institute of Philosophy, Western University, 1151 Richmond Street North, London, Ontario, N6A5B7, Canada

^*rjhowl@gmail.com

Popular Summary

We have used recent findings in the field of quantum information science to develop a new approach to determining how our Universe works at its most fundamental level. For more than a hundred years, physicists have struggled to understand how the two foundational theories of science, quantum theory and general relativity, which respectively describe microscopic and macroscopic phenomena, are unified into a single overarching theory of nature. During this time, two fundamentally contrasting approaches have been developed, called ‘quantum gravity’ and ‘classical gravity’. However, a complete lack of experimental evidence means that we do not know which approach the overarching theory actually takes.

Now, a collaboration between researchers in quantum information, quantum gravity, and quantum technology, demonstrates that only quantum and not classical gravity could bring a signature (called non-Gaussianity) that is typically discussed in the context of quantum computation, connecting the fields of quantum gravity, quantum information, and computing.

In particular, we propose a way to test experimentally the quantum character of gravity in a scientific laboratory: billions of atoms are cooled to very low temperatures in a spherical trap such that they enter a new phase of matter, called a Bose-Einstein condensate, and act like a single ‘wave of matter’ inside the trap. This single wave is massive enough to feel its own gravitational pull, and if after a certain period of time it demonstrates non-Gaussianity, then this proves that nature must take the quantum gravity approach. The proposed experiment involves just a single quantum system and does not rely on assumptions concerning the locality of the interaction, making it simpler than previous approaches and potentially expediting the delivery of the first experimental test of quantum gravity. After more than a hundred years of research, having information on the unified theory of nature may be closer.

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Vol. 2, Iss. 1 — February - April 2021

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Figure 1
(a) Basic Feynman diagram for matter interacting with QG where matter emits a graviton, which is associated with ${\hat{h}}_{μ ν}$ . For simplicity, we represent matter by a real scalar field such that ${\hat{a}}^{†}$ and $\hat{a}$ are the creation and annihilation operators of matter. The interaction is then associated with three quantum operators and, therefore, can induce non-Gaussianity. (b) We can illustrate the analogous interaction between matter and classical gravity with a similar diagram except that now the gravitational leg represents a classical gravitational wave $h_{μ ν}$ rather than a graviton. Since this CG interaction is associated with just two quantum operators ${\hat{a}}^{†}$ and $\hat{a}$ , it cannot, in contrast to the QG interaction, induce non-Gaussianity. Although these diagrams represent weak-field, perturbative gravitational interactions, the fact that CG cannot create non-Gaussianity also applies to the strong-field, nonperturbative regime of gravity, as shown in Sec. 2.
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Figure 2
Illustration of the proposal for a tabletop test of QG. (a) A single spherical BEC of $10^{9}$ atoms and radius $R = 200 μ m$ is left to self-interact gravitationally for around $t = 2 s$ . If QG acts, non-Gaussianity is induced in its quantum state, whereas if CG acts, Gaussianity is preserved. Each atom is equally delocalized across the extent of the BEC but, since the BEC is in a spherical harmonic trap, the density of the BEC is greatest at its center and drops off to zero asymptomatically, as illustrated. The BEC is initially in a Gaussian state, and its Wigner function $W$ is displayed in (b). Here, for simplicity, a coherent state $| α ⟩$ is assumed, but this can also be squeezed to increase the signal-to-noise ratio, as discussed in the main text. If QG acts, and the interaction time were long enough, then gravity could even force the coherent state to a Yurke-Stoler cat state $(| α ⟩ + i | - α ⟩) / \sqrt{2}$ . The Wigner function for such a non-Gaussian state is illustrated in (c). If, however, CG acts, then the state will remain Gaussian. In the nonrelativistic CG limit, the state will remain a coherent state, whereas relativistic CG effects would, in principle, squeeze the state but keep it Gaussian. In practice, the interaction time would not be long enough for such a dramatic effect as a coherent state changing to a Yurke-Stoler state, and instead smaller deviations from a Gaussian distribution are sought (see the main text). $α = 2$ is used in the plots, whereas in practice the BEC will have an amplitude of around $| α | = 10^{4.5}$ , the square root of the number of atoms.
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