Ultracold Atoms for Foundational Tests of Quantum Mechanics
This 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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2 Proposal for Demonstrating the HongOuMandel Effect with Matter Waves
3 Proposal for a MotionalState Bell Inequality Test with Ultracold Atoms
4 Sensitivity to Thermal Noise of Atomic EinsteinPodolskyRosen Entanglement
5 An Atomic SU1 1 Interferometer via SpinChanging Collisions
6 On the Relation of the Particle Number Distribution of Stochastic Wigner Trajectories and Experimental Realizations
Appendix AAnalytic Models of Condensate Collisions
Appendix BMeanField Theory of Bragg Scattering
Appendix CSupplementary Material for Chapter 2
Appendix DSupplementary Material for Chapter 3
Appendix ESupplementary Material for Chapter 4
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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