2017/10/31 by Benedikt B. Brandt, Constantine Yannouleas, Uzi Landman
Computer Science · Physics and Astronomy · #Bose–Einstein condensate #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Diffraction #Fermion #Gaussian #Hamiltonian (control theory) #Momentum (technical analysis) #Physics #Position and momentum space #Quantum #Quantum Information and Cryptography #Quantum mechanics #Quantum, superfluid, helium dynamics #Ultracold atom #Wave function #cond-mat.quant-gas #nucl-th #quant-ph
paper · pdf · doi:10.1103/physreva.96.053632
published as Phys. Rev. A 96, 053632 (2017) · Published extended version. 19 pages, 14 color figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/
openalex publication_date 2017/11/30 · arxiv created 2017/12/07 · arxiv updated 2017/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 full 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 noninteracting 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 multiwell traps. Additionally, the two-body momentum correlation and noise distributions are found to exhibit ``shortsightedness,'' with the main contribution coming from nearest-neighboring particles.