Proposal for a Bose–Einstein Condensate Based Test of Born's Rule Using Light–Pulse Atom Interferometry

Light-pulse atom interferometry with ultra-cold quantum gases is proposed and numerically benchmarked as a platform to test the modulo-square hypothesis of Born's rule. The 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, the impact of experimental uncertainties is examined in accordance with conventional BEC interferometer to provide an upper bound of $5.7\times {10}^{-3}\left(1.8,\times ,{10}^{-3}\right)$ on the statistical deviation of $100\left(1000\right)$ iterations for a hypothetical third-order interference term.