Phonon-based quantum testing schemes using BECs for gravity modifications in light of dark matter exploration

Abstract

The nature of dark matter and dark energy remains an open question in modern physics. While dark matter is inferred from astrophysical observations and dark energy accounts for the accelerated expansion of the universe, their fundamental origins remain unknown. This motivates alternative approaches to explain the observed behaviour of the universe by modifying our current theory of gravity. This thesis proposes a novel method for testing such modified theories of gravity by exploiting the dynamics of quantum phononic excitations present in Bose-Einstein Condensates (BECs), which can be realized in tabletop experiments with current technology. Our proposal implements quantum metrology within the physics of the BEC and its phononic excitations, taking advantage of Gaussian states and the tritter operation to prepare highly sensitive phonon states for estimating gravitational parameters. Specifically, we aim to measure the gravitational potential of an oscillating massive sphere by estimating the exerted acceleration on a BEC, inferred through phonon dynamics. We predict an acceleration precision of approximately $10^{-17}$ m/s$^{2}$, allowing us to test deviations from Newtonian gravity. We examine two modified-gravity models: Modified Newtonian Dynamics (MOND) and Lambda-gravity. The precision of our method enables the distinction between MOND and Newtonian gravity under experimentally feasible conditions. For Lambda-gravity, our setup allows us to measure Newton’s gravitational constant $G$ with a relative precision of 10$^{-7}$, improving current measurements by two orders of magnitude. Additionally, it provides an upper bound on the cosmological constant of $\Lambda < 10^{-31}$ m$^{-2}$, representing the first laboratory-based experimental constraint on $\Lambda$. In conclusion, this thesis presents a novel, high-precision method for probing Newtonian gravity while paving the road for future research focused on probing relativistic effects.

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Identifiers

ORCID for Hector Antonio Fernandez Melendez: orcid.org/0000-0003-3224-1282

ORCID for Alexander Belyaev: orcid.org/0000-0002-1733-4408

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