Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study

Abstract

We study ground state properties of spinless, quasi one-dimensional bosons which are confined in a harmonic trap and interact via repulsive delta-potentials. We use the exact diagonalization method to analyze the pair correlation function, as well as the density, the momentum distribution, different contributions to the energy and the population of single-particle orbitals in the whole interaction regime. In particular, we are able to trace the fascinating transition from bosonic to fermi-like behavior in characteristic features of the momentum distribution which is accessible to experiments. Our calculations yield quantitative measures for the interaction strength limiting the mean-field regime on one side and the Tonks-Girardeau regime on the other side of an intermediate regime.

5 pages, 5 figures

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• Correlations of strongly interacting ultracold dipolar bosons in optical lattices
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• Density-functional theory of two-component Bose gases in one-dimensional harmonic traps
• Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures
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• Ground-state properties of few-Boson system in a one-dimensional hard wall potential with split
• Three interacting atoms in a one-dimensional trap: A benchmark system for computational approaches
• Exploring the few- to many-body crossover using cold atoms in one dimension
• Ground-state properties of interacting two-component Bose gases in a hard-wall trap
• Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction
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• Binding between two-component bosons in one dimension
• Efficient construction of many-body Fock states having the lowest energies
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• Repulsive to attractive interaction quenches of 1D Bose gas in a harmonic trap
• Mesoscopic superpositions of Tonks-Girardeau states and the Bose-Fermi mapping
• Fermionization via cavity-assisted infinite-range interactions
• Quantum dynamics of two bosons in an anharmonic trap: Collective vs internal excitations
• Few-boson localization in a continuum with speckle disorder
• Optimized Configuration Interaction Approach for Trapped Multiparticle Systems Interacting Via Contact Forces
• Modulated trapping of interacting bosons in one dimension
• Density-functional theory for 1D harmonically trapped Bose-Fermi mixture
• Static and dynamic phases of a Tonks-Girardeau gas in an optical lattice
• Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
• Are smooth pseudopotentials a good choice for representing short-range interactions?
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• Quantum correlations and spatial localization in trapped one-dimensional ultra-cold Bose-Bose-Bose mixtures
• Dipolar particles in a double-trap confinement: Response to tilting the dipolar orientation
• The lowest scattering state of one-dimensional Bose gas with attractive interactions
• The weakening of fermionization of one dimensional spinor Bose gases induced by spin-exchange interaction
• Fundamental limitations of the eigenvalue continuation approach
• Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential
• Ground State Properties of Anti-Ferromagnetic Spinor Bose gases in One Dimension
• Ultracold bosons in one-dimensional harmonic and multi-well traps: a Quantum Monte Carlo vs a correlated pair approach
• The granularity of weakly occupied bosonic fields beyond the local density approximation
• Comparative study of quantum dynamics of a few bosons in a one-dimensional split hard-wall trap: exact results versus Bose-Hubbard-model approximations
• Few particles with an impurity in a one-dimensional harmonic trap
• Spatial correlations and entanglement in a hybrid system of N fermion pairs with harmonic interaction
• On the direct diagonalization method for a few particles trapped in harmonic potentials