Communications in Theoretical Physics ›› 2016, Vol. 65 ›› Issue (04): 473-482.

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Ground and Low-Lying Collective States of Rotating Three-Boson System

Mohd. Imran, M. A. H. Ahsan   

  1. Department of Physics, Jamia Millia Islamia (Central University), New Delhi 110025, India
  • Received: 2015-11-02 Revised: 2016-01-27 Published: 2016-04-01

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 2?ω, 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.

Key words: Bose-Einstein condensation, exact diagonalization, breathing mode, Bose-Laughlin state, von Neumann entropy, conditional probability distribution

PACS numbers: 

  • 05.30.Jp