## Ultracold Atoms for Foundational Tests of Quantum MechanicsThis thesis presents a theoretical investigation into the creation and exploitation of quantum correlations and entanglement among ultracold atoms. Specifically, it focuses on these non-classical effects in two contexts: (i) tests of local realism with massive particles, e.g., violations of a Bell inequality and the EPR paradox, and (ii) realization of quantum technology by exploitation of entanglement, for example quantum-enhanced metrology. In particular, the work presented in this thesis emphasizes the possibility of demonstrating and characterizing entanglement in realistic experiments, beyond the simple “toy-models” often discussed in the literature. The importance and relevance of this thesis are reflected in a spate of recent publications regarding experimental demonstrations of the atomic Hong-Ou-Mandel effect, observation of EPR entanglement with massive particles and a demonstration of an atomic SU(1,1) interferometer. With a separate chapter on each of these systems, this thesis is at the forefront of current research in ultracold atomic physics. |

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### Contents

1 | |

2 Proposal for Demonstrating the HongOuMandel Effect with Matter Waves | 45 |

3 Proposal for a MotionalState Bell Inequality Test with Ultracold Atoms | 56 |

4 Sensitivity to Thermal Noise of Atomic EinsteinPodolskyRosen Entanglement | 71 |

5 An Atomic SU1 1 Interferometer via SpinChanging Collisions | 82 |

6 On the Relation of the Particle Number Distribution of Stochastic Wigner Trajectories and Experimental Realizations | 95 |

7 Conclusion | 113 |

Appendix AAnalytic Models of Condensate Collisions | 116 |

Appendix BMeanField Theory of Bragg Scattering | 131 |

Appendix CSupplementary Material for Chapter 2 | 137 |

Appendix DSupplementary Material for Chapter 3 | 147 |

Appendix ESupplementary Material for Chapter 4 | 154 |

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Ultracold Atoms for Foundational Tests of Quantum Mechanics Robert J. Lewis-Swan No preview available - 2016 |

### Common terms and phrases

amplitude analytic atom-optics beam-splitter Bell inequality Bell’s Bose-Einstein condensates Bragg pulses calculation Cauchy–Schwarz inequality CHSH-Bell classical collision halo condensate collisions correlation function corresponds coupling defined demonstrate density dynamics EPR entanglement EPR paradox equation experimental fluctuations Fock Foundational Tests four-wave mixing Gaussian Hamiltonian Heisenberg HOM dip HOM effect initial interferometer Kheruntsyan lattice Lett massive particles matter waves mean-field measurement momenta momentum modes number distribution off-resonant optical lattice oscillations pair parameter parametric down-conversion phase shift phase-space photons Phys positive-P representation pump mode quantum mechanics quantum optics R.J. Lewis-Swan regime rms width s-wave scattered atoms scattering halo source condensate spatial spin-changing collisions spinor spinor BEC spinor condensate spontaneous four-wave mixing Springer squeezed coherent Tests of Quantum theory trajectories two-mode squeezed vacuum Ultracold Atoms undepleted pump approximation variables violation Wigner distribution Wigner function Zeeman shift