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

Abstract

We investigate the dynamics of atomic twin beams produced from a phase-fluctuating source, specifically a 1D Bose gas in the quasi-condensate regime, motivated by the experiment reported in Nature Physics 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 quasi-condensate 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. arXiv:2002.01998v1 [cond-mat.quant-gas]

Two-Particle Interference with Double Twin-Atom Beams

“…A binary collision between two atoms in the source state can lead to the emission of a pair of twin atoms (for an extensive study of the emission process, see Ref. [32]). Because of momentum conservation, the atoms are emitted with opposite momenta along the shallow longitudinal direction (x axis), which constitutes the first pair of modes available to each indistinguishable atom.…”

Phase-space stochastic quantum hydrodynamics for interacting Bose gases

“…which differs from the LSQHD expression (64) in that the term i 2 δρ(r )δS(r ) ρ 0 (r ) − δS(r)δρ(r) ρ 0 (r) (F2) is absent here in Eq. (F1).…”

“…An equivalent stochastic approach, like the one derived in this work, provides a means of avoiding this. Whilst we restrict ourselves to zero temperature here, we note that it is also possible to consider finite temperature situations by stochastically sampling the appropriate thermal P -distribution in order to construct the initial state [63,64].…”

“…As mentioned previously in Sec. III C regarding the real-space density, a similar discrepancy exists between the normalized reduced one-body density matrices (64) and (69). These expressions are not equivalent under the transformations (34) and (35) due to the inconsistency of maintaining second order terms in these expressions (which are needed to obtain leading order corrections to the mean-field results) while the equations of motion themselves have been truncated at linear order.…”