Ultracold Atoms for Foundational Tests of Quantum Mechanics

Abstract

We investigate the generation, characterization and measurement of non-classical correlations and entanglement in ultracold atomic gases. Specifically, we propose new tests to demonstrate non-classical correlations, Einstein-Podolsky-Rosen (EPR) entanglement and Bell inequality violations, in systems involving dilute gas Bose-Einstein condensates (BECs). We focus on the challenges of generating and preserving these correlations in atom-optics schemes with massive particles and define appropriate operational measurements to demonstrate them experimentally. Further, we characterize how measures of EPR entanglement and violations of a Bell inequality evolve with time and scale with system size.To begin, we detail a theoretical proposal to demonstrate the well-known optical HongOu-Mandel (HOM) effect of destructive quantum interference with massive particles. Our proposed matter-wave experiment, realized recently in a related experimental setup [Lopes et. al., Nature 520, 66 (2015)], utilizes pair-correlated atoms produced via spontaneous fourwave mixing in colliding BECs. The atom pairs are then subjected to Bragg pulses -the atom-optics equivalent of optical mirrors and beam-splitters -to realize a HOM atom interferometer. By taking advantage of the multimode nature of the four-wave mixing process we formulate a measurement protocol which, unlike the optical case, does not require repeated measurements for different beam-splitter settings. We perform numerical simulations of a realistic experimental system and predict a HOM 'dip' visibility of ∼ 69%, indicating the correlations between atom pairs are stronger than classically allowed.In Chapter 5 we outline a theoretical proposal to demonstrate a violation of a motionalstate Bell inequality with massive particles. Identically to Chapter 4, the proposal uses pairs of momentum-entangled atoms produced via spontaneous four-wave mixing in colliding BECs. However, this scheme requires two pairs of atoms which are used as the input state of an atom-optics analog of the Rarity-Tapster interferometer, constructed via a sequence of Bragg pulses. We formulate a measurable form of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality taking into account experimental limitations, and perform numerical simulations of a realistic experimental system for a range of parameters. We predict values of the CHSH-Bell parameter up to S 2.5, demonstrating a violation of the CHSH-Bell inequality which is bounded by S ≤ 2 for local hidden-variable theories.In Chapter 6 we investigate the prospect of demonstrating EPR entanglement between massive particles via spin-changing collisions in a spinor BEC. This investigation is motivated by recent experimental work of Gross et al. [Nature 480, 219 (2011)] who reported inconclusive results in an attempt to measure EPR entanglement. In the experiment, spinchanging collisions between atoms in the (F, m F ) = (2, 0) state lead to pairs of strongly correlated atoms being created in opposing (F, m F ) = (2, ±1) states. For m F = ±1 states in...

Initial states for quantum field simulations in phase space

“…Later applications included large-scale truncated Wigner simulations of BEC collisions [31], simulated quantum transport in a BEC in an optical lattice [32], detailed comparison of experiment and theory for optical fiber quantum correlations, to below the quantum noise level [33], comparisons of 3D positive-P and Wigner simulations of BEC collisions with 150 000 atoms from first principles [15], proposals for atomic Hong-Ou-Mandel correlations from BEC collisions [34], violations of Bell inequalities [35,36], and many other applications [12] including Boson sampling quantum computers [17,18]. Other applications include representations of parity operators, with existence and boundedness theorems summarized in recent literature [37].…”

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

“…(4) describes the widely studied phenomena of spontaneous optical parametric down-conversion. This process is known to produce the two-mode squeezed vacuum state [39,40], which exibits strong correlations between the down-converted particles. Whilst this simplification is not valid in the system under investigation, due to the absence of a true condensate in 1D, we still expect strong, non-trivial correlations in the downconverted field due to the pair-wise nature of the scattering process.…”

A matter wave Rarity-Tapster interferometer to demonstrate non-locality

“…Such a platform would allow us to investigate a number of important research areas in the intersection of quantum mechanics and gravity. For instance, why are non-local correlations between massive objects in general uncommon and difficult to observe [1,12]; how do we properly quantify entanglement in massive systems [22][23][24]; and how does the size of a Bell violation scale with the size of the system [25,26]. Furthermore, pushing our understanding of quantum theory into realms which are increasingly more strongly coupled to gravity may enable the formulation and verification of a complete theory of quantum gravity [22,23,[26][27][28][29].…”

“…II, and builds on the ideas proposed in Refs. [25,43]. This represents an atomic realization of a Rarity-Tapster type interferometer [9] (see Fig.…”