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Physical Review A

Trapped planar three-boson system with spin 1 and with hard-core interactions

Bao Cheng-guang, T. Y. Shi

Published Sep 24, 2003• 9 citations
Publisher

Abstract

A two-dimensional spin 1 three-boson system trapped by a parabolic confinement and interacting with hard-core repulsion has been investigated. The spectrum has been analyzed in detail, in particular, the existence of breathing bands has been confirmed. Two density functions associated with the oscillations of breathing and deformation, respectively, have been defined to study the structure of low-lying states. The inherent nodal structure of wave functions is found to play a decisive role. The effect of rotation on the ground-state property has also been studied. Not only the angular momentum, the permutation symmetry will also transit in accord with the increase of the speed of rotation.

DOI
10.1103/physreva.68.032509

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A two-dimensional spin 1 three-boson system trapped by a parabolic confinement and interacting with hard-core repulsion has been investigated. The spectrum has been analyzed in detail, in particular, the existence of breathing bands has been confirmed. Two density functions associated with the oscillations of breathing and deformation, respectively, have been defined to study the structure of low-lying states. The inherent nodal structure of wave functions is found to play a decisive role. The effect of rotation on the ground-state property has also been studied. Not only the angular momentum, the permutation symmetry will also transit in accord with the increase of the speed of rotation.
A two-dimensional three-boson system interacting with hard-core repulsion and trapped by parabolic confinement has been investigated. Two density functions associated with breathing motion and deformation, respectively, have been defined. Based on these density functions, the wave functions of low-lying states have been analyzed in detailed. The states are found to have explicit geometric features caused by the hard-core repulsion, these features depend strongly on the constraints imposed by symmetry. Striking similarity exists in the density functions, so that breathing bands can be well defined. A classification scheme is thereby proposed.
A two-dimensional rotating six-boson system interacting with hard-core repulsion and trapped by parabolic confinement has been investigated. The emphasis is placed on the study of the effect of symmetry. The magic numbers are found to originate from the quantum constraints. The energy of an eigenstate and the spatial distribution of its wave function are found to be strongly affected by its inherent ability to get access to symmetric shapes. Some states with special inherent ability are found to be crystal-like, they have explicit geometric structures.
Abstract The ground and low-lying collective states of a rotating system of N = 3 bosons harmonically confined in quasi-two-dimension and interacting via repulsive finite-range Gaussian potential is studied in weakly to moderately interacting regime. The N-body Hamiltonian matrix is diagonalized in subspaces of quantized total angular momenta 0 ≥ L ≥ 4N to obtain the ground and low-lying eigenstates. Our numerical results show that breathing modes with N-body eigenenergy spacing of 2ħω⊥, known to exist in strictly 2D system with zero-range (δ-function) interaction potential, may as well exist in quasi-2D system with finite-range Gaussian interaction potential. To gain an insight into the many-body states, the von Neumann entropy is calculated as a measure of quantum correlation and the conditional probability distribution is analyzed for the internal structure of the eigenstates. In the rapidly rotating regime the ground state in angular momentum subspaces L = (q/2)N (N − 1) with q = 2, 4 is found to exhibit the anticorrelation structure suggesting that it may variationally be described by a Bose-Laughlin like state. We further observe that the first breathing mode exhibits features similar to the Bose-Laughlin state in having eigenenergy, von Neumann entropy and internal structure independent of interaction for the three-boson system considered here. On the contrary, for eigenstates lying between the Bose-Laughlin like ground state and the first breathing mode, values of eigenenergy, von Neumann entropy and internal structure are found to vary with interaction.
Four identical spinless bosons with purely attractive two-body short-range interactions and repulsive three-body interactions under external spherically symmetric harmonic confinement are considered. The repulsive three-body potential prevents the formation of deeply bound states with molecular character. The low-energy spectrum with vanishing orbital angular momentum and positive parity for infinitely large two-body sss-wave scattering length is analyzed in detail. Using the three-body contact, states are classified as universal, quasiuniversal, or strongly nonuniversal. Connections with the zero-range interaction model are discussed. The energy spectrum is mapped out as a function of the two-body sss-wave scattering length as,as>0{a}_{s}, {a}_{s}>0as​,as​>0. In the weakly to medium-strongly interacting regime, one of the states approaches the energy obtained for a hard-core interaction model. This state is identified as the energetically lowest-lying ``BEC state.'' Structural properties are also presented.
We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density limit in the lattice is studied systematically, and the results obtained compared with the ones known for the hard-core boson gas without the lattice.