A Background-Free Search for Physics Beyond the Standard Model Using Atom Interferometry

Atom interferometry provides a unique platform for testing fundamental physics. Building on the successful realization of the gravitational Aharonov-Bohm (gAB) effect, I propose a next-generation experiment that integrates a macroscopic electrostatic potential into a compact, geometrically shielded dual-isotope setup. This architecture enables a background-free search for Beyond Standard Model (BSM) physics manifesting as a phenomenological composition-dependent coupling to both gravitational and electric potentials ($L_{BSM} \propto q \phi_g \phi_e$). Because the atomic ground state possesses strictly even parity, the analogous Standard Model linear Stark effect vanishes identically, providing a pristine null test framework. However, because the physical spatial separation of the wavepackets is generated by laser photon recoil ($\Delta z \propto k_{eff}$), the target BSM signal is structurally k-odd. This creates a fundamental kinematic degeneracy with the spatial gradients of the residual quadratic Stark shift. To break this degeneracy and isolate the μrad-scale target from gigaradian-scale inertial backgrounds, non-linear transients, and massive vibration noise, the design integrates a tripartite error-rejection architecture: (1) Physical Isolation: Geometric exponential suppression inside a deep Faraday tube extinguishes the Stark gradient, while kinematic thermal baffles isolate the system from Blackbody Radiation (BBR) shifts; (2) Algorithmic Veto: A Physics-Informed Bayesian Neural Network (PI-BNN) evaluates live multidomain telemetry to actively flag and veto non-linear magnetic and thermodynamic transients; and (3) Algebraic Extraction: A double-difference lock-in quadrature algebraically annihilates gravity and linear drift, while simultaneous dual-isotope ${}^{85}Rb /{}^{87}Rb$ mid-fringe phase sweeping of optimal spin-squeezed states (N = 10^6) extracts the signal at the fundamental quantum limit without estimator bias. An ab initio Split-Step Fourier Method (SSFM) physics engine coupled with a statistical Monte Carlo simulator validates the post-veto signal extraction. Computational results demonstrate that a 17-day integration (25,000 cycles) algebraically cancels severe macroscopic drifts exceeding ~357 μrad to extract a theoretical ~28.2 μrad parity signal. A true-seed Monte Carlo validation over 120 independent ensembles confirms an unbiased, normally distributed signal extraction (p > 0.55) with a mean statistical significance of 12.6σ, providing a rigorous, error-resilient blueprint for probing screened scalar fields.