Probing Lambda-Gravity with Bose-Einstein Condensate

We propose a precise test of two fundamental gravitational constants using a detector concept that exploits the dynamics of quantum phononic excitations in a trapped Bose-Einstein condensate (BEC), operable at the scale of tabletop experiments. In this setup, the sensitivity is enhanced by approximately 2 orders of magnitude through the use of a tritter operation, which mixes phononic excitations with the BEC's ground state. The BEC exhibits unique sensitivity to the two key components of the gravitational potential in $\Lambda$-gravity: the Newtonian $GM/r$ term and the cosmological constant $\Lambda r^2$, both entering the most general function following from a Gurzadyan's theorem. Using state-of-the-art experimental design, we predict that the gravitational constant $G$ could be measured with an accuracy up to $10^{-17}$ N m$^2$/kg$^2$, representing an improvement by 2 orders of magnitude over current measurements. Moreover, this experiment aims to establish the best Earth-based upper limit on $\Lambda$ at $<10^{-31}$ m$^{-2}$, marking the first laboratory-based probe of the cosmological constant. Additionally, the setup allows for the measurement of the distance-dependent behavior of each term in the gravitational potential, providing a means to test modified gravity theories.