Probing short-range gravity using quantum reflection

TL;DR

This work addresses detecting anomalous short-range gravity-like forces near surfaces by exploiting quantum reflection of ultracold atoms in an interferometric geometry. It combines a simple analytical phase model with comprehensive numerical simulations (Schrödinger and Gross-Pitaevskii) to predict a measurable phase shift φ arising from a Yukawa-type perturbation, and identifies key parameters such as x0, vc, and the velocity regime for reliable measurements. The authors show that the analytical model agrees with numerics under realistic conditions and that atomic interactions can introduce phase noise, which can be mitigated; they propose a concrete experimental path using Casimir-Polder shielding and present sensitivity estimates suggesting substantial improvements over existing atomic limits. The approach offers a compact, micrometer-scale probe of short-range forces with broad applicability to beyond-standard-model scenarios and a path to differential measurements of Casimir-Polder and related surface interactions.

Abstract

Quantum reflection occurs when ultra-cold atoms are incident on a material surface with sufficiently low velocity. The reflecting matter wave can interfere with the incident wave to form a detectable pattern, and this pattern contains information about atom-surface interactions at micrometer scales. We discuss how such an interferometer could be used to probe for anomalous short-range forces that are predicted by some beyond-standard model theories. We compare a simple analytical model for the anomalous phase to numerical solution of both the linear and non-linear Schrodinger equations, finding good agreement. With interactions, the phase does depend on the atomic density, which can be a source of noise. We nonetheless predict that under realistic conditions, the reflection technique can reach sensitivities approaching those obtained with macroscopic objects, and significantly improve the limits on anomalous coupling to atoms.

Figures (5)

• Figure 1: Comparison between numerical results for a non-interacting gas (data points) and analytical model (curves). (a) The Yukawa perturbation phase $\phi$ as a function of the Yukawa length $\lambda$, for $^{87}$Rb atoms with incident speed $v_0 = 0.2$ mm/s and a perturber density $\rho = 3$ g/cm$^3$. (b) Phase $\phi$ vs. density $\rho$, for $v_0 = 0.2$ mm/s and $\lambda = 15$ µ m. (c) Phase $\phi$ vs. velocity $v_0$, for $\lambda = 15$ µ m and $\rho = 3$ g/cm$^3$. The vertical dashed line shows the velocity limit of Eq. \ref{['vlimit']}. For all curves, $\alpha = 10^7$.
• Figure 2: Atom density distribution after quantum reflection from a gold surface. The oscillations are due to interference between the incident and reflected wave functions. The solid curve is obtained with only the Casimir-Polder surface interaction, while the dashed curved is obtained when including a Yukawa potential with $\alpha = 10^7$ and $\lambda = 15$ µ m. Here we assume $^{87}$Rb atoms with $\sigma = 10^{10}$ atoms/cm$^2$.
• Figure 3: Numerical and analytical results for an interacting $^{87}$Rb gas reflecting from a gold surface. The Yukawa phase $\phi$ is shown as a function of the interaction length $\lambda$ for various values of interaction strength $\alpha$ and surface density $\rho$, as indicated. To collapse the data to a uniform range, the phase values are scaled by $1/\alpha\rho$, relative to reference values $\alpha_\bullet = 10^7$ and $\rho_\bullet = 19$ g/cm$^3$. Data points are numerical results from the Gross-Pitaevskii equation, and the curve is the analytical result of Eq. \ref{['phiresult']}. The analytical formula was evaluated using $v_0 = 0.225$ mm/s, obtained from the observed period of the interference pattern as seen in Fig. 2.
• Figure 4: (Color online) Schematic layout for quantum reflection interferometer. A Bose condensate (blue) in an elongated trap potential is allowed to expand into a conductive membrane. The membrane sits just in front of a test mass consisting of bonded gold and glass blocks. The test mass can be translated roughly 50 µ m parallel to the surface to vary the density which which the atoms interact. An absorption imaging laser beam (red) passes through the atoms at a small angle, reflects from the membrane, and is then imaged by a camera (not shown). A secondary imaging system perpendicular to the plane of the drawing is used to locate the atoms relative to the boundary between test-mass sections.
• Figure 5: (Color online) Constraints on the Yukawa $\alpha$ and $\lambda$ parameters from existing atomic (black), existing macroscopic (gray) and proposed atomic (blue) measurements. The Harber 2005 results Harber2005 are measurements based on the oscillation frequency of atoms trapped near a surface. The Bennett 2019 Bennett2019 curve is based on a proposed experiment using Bloch oscillations of trapped atoms near a surface. The Panda 2024 Panda2024 curve is based on a proposed measurement using a lattice-based interferometer near a surface. The Chen 2016 Chen2016, Lee 2020 Lee2020 and Tan 2020 Tan2020 curves are measurements using torsion pendula.