Proposal for a Motional-State Bell Inequality Test with Ultracold Atoms

Abstract

We propose and theoretically simulate an experiment for demonstrating a motional-state Bell inequality violation for pairs of momentum-entangled atoms produced in Bose-Einstein condensate collisions. The proposal is based on realizing an atom-optics analog of the Rarity-Tapster optical scheme: it uses laser-induced Bragg pulses to implement two-particle interferometry on the underlying Bell state for two pairs of atomic scattering modes with equal but opposite momenta. The collision dynamics and the sequence of Bragg pulses are simulated using the stochastic Bogoliubov approach in the positive-P representation. We predict values of the ClauserHorne-Shimony-Holt (CHSH) parameter up to S 2.5 for experimentally realistic parameter regimes, showing a strong violation of the CSHS-Bell inequality bounded classically by S 2.

Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry

“…Unlike Ref. [11], our proposal here to use the partial coincidence p soc (k 1 , k 2 ) instead of the total G(k 1 , k 2 ) is particularly advantageous, because the maximum quantal value of S = 2 √ 2 decreases rapidly when higheroccupancy components are considered in the two-particle wave function, and can even become smaller than the classical value of 2 [91].…”

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

“…As a larger-sized example, consider the same Hamiltonian and master equation as (95) and (96) (take N = 0), but with a longer chain of 32 sites, which is already beyond or at the limit of the capabilities of alternative methods such as brute force or corner space renormalisation [24,59]. The tunnelling term in (95) now becomes −J 31 j=1 a † j a j+1 + a † j+1 a j , and a driving of F = 3 remains only at the j = 1 site. While the stationary state does not show any time-dependent change in expectation values, we should expect to still see signatures of transport in its multi-time correlations as a function of distance and delay time if the method is good.…”

“…It has been used for solving and simulating a multitude of problems in various physical fields: e.g. quantum optics [21,28,30,32,52,54,84,91,110], ultracold atoms [22,39,40,49,74,82,94,95,101,102,108,125,131,134,144], fermionic systems [6,7,27,29], spin systems [11,106,107], nuclear physics [137], dissipative systems in condensed matter [26,45,143], or cosmology [111]. The vast majority of such calculations so far have considered only equal time correlations and observables.…”

A tractable prescription for large-scale free flight expansion of wavefunctions

“…The algorithm is readily adapted to cases where several complex-valued fields are present. One such case that may be aided with the algorithm presented here are positive-P simulations of supersonic BEC collisions [6,[34][35][36]. Here, two independent complex-valued fields ψ(x) and ψ + (x) that correspond to the Ψ(x) and Ψ † (x) Bose fields are used, and allow for the exact treatment of quantum fluctuations.…”