Atomic twin beams and violation of a motional-state Bell inequality from a phase-fluctuating quasicondensate source

We investigate the dynamics of atomic twin beams produced from a phase-fluctuating source, specifically a one-dimensional Bose gas in the quasicondensate regime, motivated by the experiment reported in Bucker et al. [Nat. Phys. 7, 608 (2011)]. A short-time analytic model is constructed, which is a modified version of the undepleted pump approximation widely used in quantum and atom optics, except that here we take into account the initial phase fluctuations of the pump source as opposed to assuming long-range phase coherence. We use this model to make quantitative and qualitative predictions of how phase fluctuations of the source impact the two-particle correlations of scattered atom pairs. The model is benchmarked against detailed numerical simulations using stochastic phase-space methods, and is shown to validate the intuitive notion that the broadening of momentum-space correlation functions between atoms scattered from a quasicondensate is driven by the broadened momentum width of the source compared to a true phase-coherent condensate. Finally, we combine these theoretical tools and results to investigate the effect phase fluctuations of the twin-beam source can have on a proposed demonstration of a violation of a Bell inequality, which intrinsically relies on phase-sensitive pair correlations