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Journal of Physics B Atomic Molecular and Optical Physics

Internal motions in three-body bosonic Thomson atoms

Y. Z. He, Bao Cheng-guang

Published Apr 12, 2001• 7 citations
Publisher

Abstract

A three-body bosonic Thomson atom, namely a system of three charged bosons in a harmonic trap, with a very large Wigner parameter, has been studied. The states with zero angular momentum and even parity denoted as 0 n + have been calculated and analysed; the basic modes of excitation of this system have been revealed. It was found that each lower 0 n + state ( n is from 1 to 5) has its own means of internal motion. Although the size of the system is very sensitive to the strength of the trap, the other features are found to be insensitive to the strength if the system remains in the Wigner regime. The breathing mode was found to be the easiest to excite.

DOI
10.1088/0953-4075/34/9/304

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A three-body bosonic Thomson atom, namely a system of three charged bosons in a harmonic trap, with a very large Wigner parameter, has been studied. The states with zero angular momentum and even parity denoted as 0 n + have been calculated and analysed; the basic modes of excitation of this system have been revealed. It was found that each lower 0 n + state ( n is from 1 to 5) has its own means of internal motion. Although the size of the system is very sensitive to the strength of the trap, the other features are found to be insensitive to the strength if the system remains in the Wigner regime. The breathing mode was found to be the easiest to excite.
A system of charged particles in a harmonic trap is a realization of Thomson's raisin cake model. Therefore, we call it a Thomson atom. Bosonic, fermionic and mixed Thomson atoms exist. In this paper we focus on bosonic Thomson atoms in isotropic traps. Approximating the exact ground state by a condensate we investigate ground-state properties at temperature T = 0 using the Hartree-Fock theory for bosons. In order to assess the quality of our mean-field approach we compare the Hartree-Fock results for bosonic Thomson helium with an exact diagonalization. In contrast to the weakly interacting Bose gas (alkali vapours) mean-field calculations are reliable in the limit of large particle density. The Wigner regime (low particle density) is discussed.
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.
We investigate a few-body mixture of two bosonic components, each consisting of two particles confined in a quasi one-dimensional harmonic trap. By means of exact diagonalization with a correlated basis approach we obtain the low-energy spectrum and eigenstates for the whole range of repulsive intra- and inter-component interaction strengths. We analyse the eigenvalues as a function of the inter-component coupling, covering hereby all the limiting regimes, and characterize the behaviour in-between these regimes by exploiting the symmetries of the Hamiltonian. Provided with this knowledge we study the breathing dynamics in the linear-response regime by slightly quenching the trap frequency symmetrically for both components. Depending on the choice of interactions strengths, we identify 1 to 3 monopole modes besides the breathing mode of the centre of mass coordinate. For the uncoupled mixture each monopole mode corresponds to the breathing oscillation of a specific relative coordinate. Increasing the inter-component coupling first leads to multi-mode oscillations in each relative coordinate, which turn into single-mode oscillations of the same frequency in the composite-fermionization regime.