Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap

Abstract

We investigate the ground state of the system of N bosons enclosed in a hard-wall trap interacting via a repulsive or attractive $\delta$-function potential. Based on the Bethe ansatz method, the explicit ground state wave function is derived and the corresponding Bethe ansatz equations are solved numerically for the full physical regime from the Tonks limit to the strongly attractive limit. It is shown that the solution takes different form in different regime. We also evaluate the one body density matrix and second-order correlation function of the ground state for finite systems. In the Tonks limit the density profiles display the Fermi-like behavior, while in the strongly attractive limit the Bosons form a bound state of N atoms corresponding to the N-string solution. The density profiles show the continuous crossover behavior in the entire regime. Further the correlation function indicates that the Bose atoms bunch closer as the interaction constant decreases.

7 pages, 6 figures, version published in Phys. Rev. A

Cited by in corpus (38)

• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Exact solution for infinitely strongly interacting Fermi gases in tight waveguides
• Ultracold Few-Boson Systems in a Double-Well Trap
• Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
• Composite fermionization of 1-D Bose-Bose mixtures
• Correlations in Ultracold Trapped Few-Boson Systems: Transition from Condensation to Fermionization
• Ground-state properties of one-dimensional anyon gases
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions
• Decay by tunneling of Bosonic and Fermionic Tonks-Girardeau Gases
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Excitations of Few-Boson Systems in 1-D Harmonic and Double Wells
• Pairing of few Fermi atoms in one dimension
• Ground-state properties of interacting two-component Bose gases in a one-dimensional harmonic trap
• Density-functional theory of two-component Bose gases in one-dimensional harmonic traps
• Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz
• Magnetic ordering and quantum statistical effects in strongly repulsive Fermi-Fermi and Bose-Fermi mixtures
• Ground-state properties of few-Boson system in a one-dimensional hard wall potential with split
• Excitations of attractive 1-D bosons: Binding vs. fermionization
• Ground-state properties of interacting two-component Bose gases in a hard-wall trap
• One-dimensional fermionic gases with attractive p-wave interaction in a hard-wall trap
• Comparative study of one-dimensional Bose and Fermi gases with contact interactions from the viewpoint of universal relations for correlation functions
• Momentum distribution of a freely expanding Lieb-Liniger gas
• Half-space stationary Kardar-Parisi-Zhang equation
• Interaction Driven Interband Tunneling of Bosons in the Triple Well
• Yang-Yang thermodynamics of Bose-Fermi Mixture
• Binding between two-component bosons in one dimension
• Atom Fock state preparation by trap reduction
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Fermionization via cavity-assisted infinite-range interactions
• Two Atoms in a Double Well: An Exact Solution
• Hard-core Bose-Fermi mixture in one-dimensional split traps
• Universality of internal correlations of strongly interacting p-wave fermions in one-dimensional geometry
• Symplectic tomography of ultracold gases in tight-waveguides
• Density-Matrix Renormalization Group for Continuous Quantum Systems
• Lieb-Liniger gas in a constant force potential
• Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity
• The granularity of weakly occupied bosonic fields beyond the local density approximation