Ground-state properties of hard core bosons in one-dimensional harmonic traps

Abstract

The one-particle density matrices for hard core bosons in a one-dimensional harmonic trap are computed numerically for systems with up to 160 bosons. Diagonalization of the density matrix shows that the many-body ground state is not Bose-Einstein condensed. The ground state occupation, the amplitude of the lowest natural orbital, and the zero momentum peak height scale as powers of the particle number, and the corresponding exponents are related to each other. Close to its diagonal, the density matrix for hard core bosons is similar to the one of noninteracting fermions.

arXiv comment4 pages, 4 EPS-figures, one reference added

References in corpus (13)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Realization of Bose-Einstein condensates in lower dimensions
• A quasi-pure Bose-Einstein condensate immersed in a Fermi sea
• Regimes of quantum degeneracy in trapped 1D gases
• Exploring phase coherence in a 2D lattice of Bose-Einstein condensates
• Bosons in cigar-shape traps: Thomas-Fermi regime, Tonks-Girardeau regime, and between
• Low-dimensional Bose liquids: beyond the Gross-Pitaevskii approximation
• Stability and phase coherence of trapped 1D Bose gases
• Ground state properties of a one-dimensional condensate of hard core bosons in a harmonic trap
• High-momentum tail in the Tonks gas under harmonic confinement
• Momentum distribution for a one-dimensional trapped gas of hard-core bosons
• Universal solutions for interacting bosons in one-dimensional harmonic traps

Cited by in corpus (52)

• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Bosonizing one-dimensional cold atomic gases
• Fragmentation of Bose-Einstein Condensates
• Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
• Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• One-dimensional Bosons in Three-dimensional Traps
• One-particle dynamical correlations in the one-dimensional Bose gas
• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Emergence of quasi-condensates of hard-core bosons at finite momentum
• Universal properties of hard-core bosons confined on one-dimensional lattices
• Ground-state properties of hard-core bosons confined on one-dimensional optical lattices
• Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
• Universal correlations of trapped one-dimensional impenetrable bosons
• Correlations in Ultracold Trapped Few-Boson Systems: Transition from Condensation to Fermionization
• Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wavepacket
• Applications and generalizations of Fisher-Hartwig asymptotics
• Interacting Bose gases in quasi-one dimensional optical lattices
• Universal scaling of density and momentum distributions in Lieb-Liniger gases
• Free expansion of impenetrable bosons on one-dimensional optical lattices
• Equilibrium and off-equilibrium trap-size scaling in 1D ultracold bosonic gases
• One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
• Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
• Interacting bosons in an optical lattice
• Excitations of Few-Boson Systems in 1-D Harmonic and Double Wells
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• One-dimensional fermionic gases with attractive p-wave interaction in a hard-wall trap
• Anderson localization of a Tonks-Girardeau gas in potentials with controlled disorder
• Ground state properties of hard-core anyons in a harmonic potential
• Scaling of noise correlations in one-dimensional-lattice-hard-core-boson systems
• Exact spectral function of a Tonks-Girardeau gas in a lattice
• On the asymptotics of some large Hankel determinants generated by Fisher-Hartwig symbols defined on the real line
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Levy distribution in many-particle quantum systems
• Ground state properties of a one-dimensional strongly-interacting Bose-Fermi mixture in a double-well potential
• Spin-incoherent Luttinger liquid of one-dimensional spin-1 Tonks-Girardeau Bose gas: Spin-dependent properties
• Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• Density fluctuations of a hard-core Bose gas in a one-dimensional lattice
• Strongly interacting one-dimensional bosons in arbitrary-strength optical lattices: from Bose-Hubbard to sine-Gordon and beyond
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas
• Ground state properties of a Tonks-Girardeau Gas in a periodic potential
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Statistical properties of the momentum occupation numbers of the Tonks-Girardeau gas in a harmonic trap
• Wavelet representation of hardcore bosons
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Long Range Interactions in Quantum Many Body Problem in One-Dimension:Ground State
• $n$-body Correlation of Tonks-Girardeau Gas
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain
• Stochastic method for calculating the ground state reduced density matrix of trapped Bose particles in one dimension
• Fate of the Quasi-condensed State for Bias-driven Hard-Core Bosons in one Dimension