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arXiv:2010.04943 · The European Physical Journal C

Testing weakest force with coldest spot

Rong-Gen Cai, Shao-Jiang Wang, Su Yi, Jiang-Hao Yu

Published Apr 1, 2021• 1 citation
arXivHTMLPDF

Abstract

Abstract Ultra-cold atom experiment in space with microgravity allows for realization of dilute atomic-gas Bose-Einstein condensate (BEC) with macroscopically large occupation number and significantly long condensate lifetime, which allows for a precise measurement on the shape oscillation frequency by calibrating itself over numerous oscillation periods. In this paper, we propose to measure the Newtonian gravitational constant via ultra-cold atom BEC with shape oscillation, although it is experimentally challenging. We also make a preliminary perspective on constraining the modified Newtonian potential such as the power-law potential, Yukawa interaction, and fat graviton. A resolution of frequency measurement of $$(1-100)\,\mathrm {nHz}$$ ( 1 - 100 ) nHz at most for the occupation number $$10^9$$ 10 9 , just one order above experimentally achievable number $$N\sim 10^6{-}10^8$$ N ∼ 10 6 - 10 8 , is feasible to constrain the modified Newtonian potential with Yukawa interaction greatly beyond the current exclusion limits.

DOI
10.1140/epjc/s10052-021-09102-y

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Abstract Ultra-cold atom experiment in space with microgravity allows for realization of dilute atomic-gas Bose-Einstein condensate (BEC) with macroscopically large occupation number and significantly long condensate lifetime, which allows for a precise measurement on the shape oscillation frequency by calibrating itself over numerous oscillation periods. In this paper, we propose to measure the Newtonian gravitational constant via ultra-cold atom BEC with shape oscillation, although it is experimentally challenging. We also make a preliminary perspective on constraining the modified Newtonian potential such as the power-law potential, Yukawa interaction, and fat graviton. A resolution of frequency measurement of (1−100) nHz(1-100)\,\mathrm {nHz}(1−100)nHz ( 1 - 100 ) nHz at most for the occupation number 10910^9109 10 9 , just one order above experimentally achievable number N∼106−108N\sim 10^6{-}10^8N∼106−108 N ∼ 10 6 - 10 8 , is feasible to constrain the modified Newtonian potential with Yukawa interaction greatly beyond the current exclusion limits.
Extending the understanding of Bose-Einstein condensate (BEC) physics to new geometries and topologies has a long and varied history in ultracold atomic physics. One such new geometry is that of a bubble, where a condensate would be confined to the surface of an ellipsoidal shell. Study of this geometry would give insight into new collective modes, self-interference effects, topology-dependent vortex behavior, dimensionality crossovers from thick to thin shells, and the properties of condensates pushed into the ultradilute limit. Here we propose to implement a realistic experimental framework for generating shell-geometry BEC using radiofrequency dressing of magnetically trapped samples. Such a tantalizing state of matter is inaccessible terrestrially due to the distorting effect of gravity on experimentally feasible shell potentials. The debut of an orbital BEC machine (NASA Cold Atom Laboratory, aboard the International Space Station) has enabled the operation of quantum-gas experiments in a regime of perpetual freefall, and thus has permitted the planning of microgravity shell-geometry BEC experiments. We discuss specific experimental configurations, applicable inhomogeneities and other experimental challenges, and outline potential experiments.
We explore the effect of mutual gravitational interaction between ultra-cold gas atoms on the dynamics of Bose-Einstein condensates (BEC). Small amplitude oscillation of BEC is studied by applying variational technique to reduce the Gross-Pitaevskii equation, with gravity included, to the equation of motion of a particle moving in a potential. According to our analysis, if the s-wave scattering length can be tuned to zero using Feshbach resonance for future BEC with occupation numbers as high as ≈1020\approx 10^{20}≈1020, there exists a critical ground state occupation number above which the BEC is unstable, provided that its constituents interact with a $1/r^3 $ gravity at short scales.
We explore the effect of mutual gravitational interaction between ultra-cold gas atoms on the dynamics of Bose-Einstein condensates (BEC). Small-amplitude oscillation of BEC is studied by applying variational technique to reduce the Gross-Pitaevskii equation, with gravity included, to the equation of motion of a particle moving in a potential. According to our analysis, if the s-wave scattering length can be tuned to zero using Feshbach resonance for future BEC with occupation numbers as high as ≈10 20 , there exists a critical ground state occupation number above which the BEC is unstable, provided that its constituents interact with a 1/r 3 gravity at short scales.
In this work, we study low-lying collective excitations of a Bose-Einstein condensate with Newtonian and Yukawa-like two-particle interaction and derive boundaries for both Yukawa parameters. Using a variational approach, we explicitly show for spherical condensate that the corresponding frequencies depend on the gravitational interaction strength. The acquired results are presented in contour plots and compared to experimentally verified data from other tests. Furthermore, we discuss experimental requirements to test our theoretical model as well as possibilities to improve the boundaries. In addition, we consider axisymmetric condensates, where it turns out that disk-shaped BECs lead to better constraints. We also show that in theory we can determine the values for both Yukawa parameters independently by a measurement of at least two collective frequencies.
We describe two experiments where atom interferometry is applied for precision measurements of gravitational effects. In the first, we measure the Newtonian gravitational constant G using an atom interferometry gravity-gradiometer which combines a rubidium fountain, a juggling scheme for fast launch of two atomic clouds, and Raman interferometry. We show that the sensor is able to detect the gravitational field produced by source masses and G is measured with better than 10-2 accuracy. In the second experiment, using ultra-cold strontium atoms in a vertical optical lattice and observing persistent Bloch oscillations for several seconds, we measure gravity acceleration with micromet-ric spatial resolution. We discuss the prospects for the study of gravitational forces at short distances and show that unexplored regions can be investigated in the search for deviations from Newtonian gravity.
The Cold Atom Laboratory is a multipurpose ultracold gas experiment currently being developed for operation on the international space station. It will have the ability to demonstrate proof-of-principle atom interferometry experiments in space. By using microgravity, atom interferometry has the potential to achieve extremely good performance in sensing and navigation applications. Terrestrial experiments can be used to explore potential challenges and prior to launch. One issue of concern is the release of cold atoms from a magnetic trap into free space. Although the atoms will not fall, they can acquire relatively large velocities due to technical limitations such as stray magnetic fields. This can limit the time available for measurements and thus the atom interferometer performance.