Proposal for a Bose-Einstein condensate based test of Born's rule using light-pulse atom interferometry

TL;DR

This paper proposes a light-pulse atom interferometry method using Bose-Einstein condensates to test Born's rule, employing optical diffraction lattices for high control and benchmarking its sensitivity to potential deviations.

Contribution

It introduces a novel interferometric protocol combining double Bragg and single Raman diffraction with BECs to test the modulo-square hypothesis of Born's rule with high precision.

Findings

Achieved high diffraction fidelities suitable for sensitive tests.

Numerical simulations account for atom-atom interactions and systematic errors.

Established an upper bound on deviations from Born's rule based on simulated experimental uncertainties.

Abstract

We propose and numerically benchmark light-pulse atom interferometry with ultra-cold quantum gases as a platform to test the modulo-square hypothesis of Born's rule. Our interferometric protocol is based on a combination of double Bragg and single Raman diffraction to induce multipath interference in Bose-Einstein condensates (BECs) and block selected interferometer paths, respectively. In contrast to previous tests employing macroscopic material slits and blocking masks, optical diffraction lattices provide a high degree of control and avoid possible systematic errors like geometrical inaccuracies from manufacturing processes. In addition, sub-recoil expansion rates of delta-kick collimated BECs allow to prepare, distinguish and selectively address the external momentum states of the atoms. This further displays in close-to-unity diffraction fidelities favorable for both high-contrast interferometry and high extinction of the blocking masks. In return, non-linear phase shifts caused by repulsive atom-atom interactions need to be taken into account, which we fully reflect in our numerical simulations of the multipath interferometer. Assuming that the modulo-square rule holds, we examine the impact of experimental uncertainties in accordance with conventional BEC interferometer to provide an upper bound of $5.7\times10^{-3}$ $\left(1.8\times10^{-3}\right)$ on the statistical deviation of $100$ $\left(1000\right)$ iterations for a hypothetical third-order interference term.