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.

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

References in corpus (34)

• Experimental Observation of a Generalized Gibbs Ensemble
• Probing many-body states of ultra-cold atoms via noise correlations
• Spatial quantum noise interferometry in expanding ultracold atom clouds
• Deterministic Preparation of a Tunable Few-Fermion System
• The Mott insulator transition in two dimensions
• Probing Pair-Correlated Fermionic Atoms through Correlations in Atom Shot Noise
• Fermionization of two distinguishable fermions
• Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
• Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
• Strongly interacting confined quantum systems in one dimension
• Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases
• Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
• Engineering the Dynamics of Effective Spin-Chain Models for Strongly Interacting Atomic Gases
• Hanbury Brown and Twiss correlations across the Bose-Einstein condensation threshold
• Ideal n-body correlations with massive particles
• Strongly Interacting Quantum Gases in One-Dimensional Traps
• Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin
• Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures
• Magnetism in strongly interacting one-dimensional quantum mixtures
• Momentum-space correlations of a one-dimensional Bose gas
• Crystalline boson phases in harmonic traps: Beyond the Gross-Pitaevskii mean field
• Two-body momentum correlations in a weakly interacting one-dimensional Bose gas
• Strongly correlated wave functions for artificial atoms and molecules
• Noise Correlations in low-dimensional systems of ultracold atoms
• Solving the quantum many-body problem via correlations measured with a momentum microscope
• Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement
• Universality of nucleon-nucleon short-range correlations: two-nucleon momentum distributions in few-body systems
• Rapidly rotating boson molecules with long or short range repulsion: an exact diagonalization study
• Double-well ultracold-fermions computational microscopy: Wave-function anatomy of attractive-pairing and Wigner-molecule entanglement and natural orbitals
• 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 (13)

• One-dimensional mixtures of several ultracold atoms: a review
• Correlations of strongly interacting ultracold dipolar bosons in optical lattices
• Signatures of unconventional pairing in spin-imbalanced one-dimensional few-fermion systems
• Interatomic interaction effects on second-order momentum correlations and Hong-Ou-Mandel interference of double-well-trapped ultracold fermionic atoms
• Intercomponent correlations in attractive one-dimensional mass-imbalanced few-body mixtures
• 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
• Anyon optics with time-of-flight two-particle interference of double-well-trapped interacting ultracold atoms
• Fractional quantum Hall physics and higher-order momentum correlations in a few spinful fermionic contact-interacting ultracold atoms in rotating traps
• Unconventional pairing in few-fermion systems at finite temperature
• Few-body perspective on fermionic pairing in one spatial dimension
• Third-order momentum correlation interferometry maps for entangled quantal states of three singly trapped massive ultracold fermions
• All-order momentum correlations of three ultracold bosonic atoms confined in triple-well traps: Signatures of emergent many-body quantum phase transitions and analogies with three-photon quantum-optics interference