Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry
arXiv:1812.05977 · doi:10.1103/PhysRevA.99.013616
Abstract
Elucidating similarities and differences between quantum-optics biphoton interference phenomena and the quantum physics of quasi-one-dimensional double-well optically-trapped ultracold neutral bosonic or fermionic atoms, we show that the analog of the optical biphoton joint-coincidence spectral correlations, studied with massless non-interacting biphotons emanating from EPR-Bell-Bohm single-occupancy sources, corresponds to a distinct contribution in the total second-order momentum correlations of the massive, interacting, and time-evolving ultracold atoms. This single-occupancy contribution can be extracted from the total second-order momentum correlation function measured in time-of-flight experiments, which for the trapped atomic system contains, in general, a double-occupancy, NOON, component. The dynamics of the two-particle system are modeled by a Hubbard Hamiltonian. This partial coincidence spectrum is a cosine-square quantum beating dependent on the difference of the momenta of the two particles, while the corresponding coincidence probability proper, familiar from its role in describing the Hong-Ou-Mandel coincidence dip of overlapping photons, results from an integration over the particle momenta. Because the second-order momentum correlations are mirrored in the time-of-flight spectra in space, our theoretical findings provide impetus for time-of-flight experimental protocols for emulating with (massive) ultracold atoms venerable optical interferometries that use two space-time separated and entangled (massless) photons or double-slit optical sources. The implementation of such developments will facilitate testing of fundamental aspects and enable applications of quantum physics with trapped massive ultracold atoms, that is, investigations of nonlocality and violation of Bell inequalities, entanglement, and quantum information science.
Published version. 31 pages, 10 color figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/
References in corpus (20)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Spatial quantum noise interferometry in expanding ultracold atom clouds
- Quantum Phase Transitions and Bipartite Entanglement
- Non-standard Hubbard models in optical lattices: a review
- Coherence and Indistinguishability of Single Electrons Emitted by Independent Sources
- Quantum Beat of Two Single Photons
- Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
- An atomic Hong-Ou-Mandel experiment
- Quantum Information Processing in Optical Lattices and Magnetic Microtraps
- Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
- Spectral Correlation Measurements at the Hong-Ou-Mandel Interference Dip
- Compressibility of a fermionic Mott insulator of ultracold atoms
- Electron and hole Hong-Ou-Mandel interferometry
- Proposal for a motional-state Bell inequality test with ultracold atoms
- Two-particle interference of electron pairs on a molecular level
- Rapidly rotating boson molecules with long or short range repulsion: an exact diagonalization study
- Entanglement and intra-molecular cooling in biological systems? - A quantum thermodynamic perspective
- Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg and t-J models
- A continuous-variable approach to the spectral properties and quantum states of the two-component Bose-Hubbard dimer
- Two-point momentum correlations of few ultracold quasi-one-dimensional trapped fermions: Diffraction patterns