Probing lambda-gravity with Bose-Einstein condensates

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi mathvariant="normal">Λ</a:mi> </a:math> -gravity: the Newtonian <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>G</c:mi> <c:mi>M</c:mi> <c:mo>/</c:mo> <c:mi>r</c:mi> </c:mrow> </c:math> term and the cosmological constant <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi mathvariant="normal">Λ</d:mi> <d:msup> <d:mi>r</d:mi> <d:mn>2</d:mn> </d:msup> </d:mrow> </d:math> , 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>G</f:mi> </f:math> could be measured with an accuracy up to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:msup> <g:mn>10</g:mn> <g:mrow> <g:mo>−</g:mo> <g:mn>17</g:mn> </g:mrow> </g:msup> <g:mspace width="0.16em"/> <g:mi mathvariant="normal">N</g:mi> </g:mrow> <g:mo> </g:mo> <g:mrow> <g:msup> <g:mrow> <g:mi mathvariant="normal">m</g:mi> </g:mrow> <g:mn>2</g:mn> </g:msup> <g:msup> <g:mrow> <g:mo>/</g:mo> <g:mi>kg</g:mi> </g:mrow> <g:mn>2</g:mn> </g:msup> </g:mrow> </g:math> , representing an improvement by 2 orders of magnitude over current measurements. Moreover, this experiment aims to establish the best Earth-based upper limit on <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mi mathvariant="normal">Λ</k:mi> </k:math> at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>&lt;</m:mo> <m:msup> <m:mn>10</m:mn> <m:mrow> <m:mo>−</m:mo> <m:mn>31</m:mn> </m:mrow> </m:msup> </m:mrow> <m:mo> </m:mo> <m:msup> <m:mrow> <m:mi mathvariant="normal">m</m:mi> </m:mrow> <m:mrow> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> , 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.