Two-point momentum correlations of few ultracold quasi-one-dimensional trapped fermions: Diffraction patterns

Abstract

Spatial and momentum correlations are important in the analysis of the quantum states and different phases of trapped ultracold atom systems as a function of the strength of interatomic interactions. Identification and understanding of spin-resolved patterns exhibited in two-point correlations, accessible directly by experiments, are key for uncovering the symmetry and structure of the many-body wave functions of the trapped system. Using the configuration interaction method for exact diagonalization of the many-body Hamiltonian of $N=2-4$ fermionic atoms trapped in single, double, triple, and quadruple wells, we analyze both two-point momentum and space correlations, as well as associated noise distributions, for a broad range of interparticle contact repulsion strengths and interwell separations, unveiling characteristics allowing insights into the transition, via an intermediate phase, from the non-interacting Bose-Einstein condensate to the weakly interacting quasi-Bose-Einstein regime, and from the latter to the strong-repulsion Tonks-Girardeau (TG) one. The ab-initio numerical predictions are shown to agree well with the results of a constructed analytical model employing localized displaced Gaussian functions to represent the $N$ fermions. The two-point momentum correlations are found to exhibit damped oscillatory diffraction behavior. This diffraction behavior develops fully for atoms trapped in a single well with strong interatomic repulsion in the TG regime, or for atoms in well-separated multi-well traps. Additionally, the two-body momentum correlation and noise distributions are found to exhibit "shortsightedness", with the main contribution coming from nearest-neighboring particles.

Published extended version. 19 pages, 14 color figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/

References in corpus (13)

• Experimental Observation of a Generalized Gibbs Ensemble
• Spatial quantum noise interferometry in expanding ultracold atom clouds
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Engineering the Dynamics of Effective Spin-Chain Models for Strongly Interacting Atomic Gases
• Ideal n-body correlations with massive particles
• Strongly Interacting Quantum Gases in One-Dimensional Traps
• Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures
• Two-body momentum correlations in a weakly interacting one-dimensional Bose gas
• Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement
• Rapidly rotating boson molecules with long or short range repulsion: an exact diagonalization study
• Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap
• 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
• Artificial quantum-dot Helium molecules: Electronic spectra, spin structures, and Heisenberg clusters

Cited by in corpus (2)

• Momentum correlations of a few ultra-cold bosons escaping from an open well
• Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry