Ground-state properties of few dipolar bosons in a quasi-one-dimensional harmonic trap

Abstract

We study the ground state of few bosons with repulsive dipole-dipole interaction in a quasi-one-dimensional harmonic trap by means of the exact diagonalization method. Up to three interaction regimes are found, depending on the strength of the dipolar interaction and the ratio of transverse to axial oscillator lengths: a regime where the dipolar Bose gas resembles a system of weakly δ-interacting bosons, a second regime where the bosons are fermionized, and a third regime where the bosons form a Wigner crystal. In the first two regimes, the dipole-dipole potential can be replaced by a δ potential. In the crystalline state, the overlap between the localized wave packets is strongly reduced and all the properties of the boson system equal those of its fermionic counterpart. The transition from the Tonks-Girardeau gas to the solidlike state is accompanied by a rapid increase of the interaction energy and a considerable change of the momentum distribution, which we trace back to the different short-range correlations in the two interaction regimes.

Quantum Entanglement of Two Harmonically Trapped Dipolar Particles

“…In the limit as → ∞ (the strictly 1D case) the system of bosons gets fermionized for any g = 0 [2,7], which is due to the singular behavior of the interaction potential |x 2 − x 1 | −3 at x 1 = x 2 . In this limit, the two bosonic ground-state wavefunctions approach, as g → 0, the modulus of the Slater determinant ψ g→0…”

“…The theoretical description of such quasi-1D systems can be simplified, since one can assume that the particles stay in the lowest transverse confinement mode and the single-mode approximation (SMA) can be applied. Within this approximation, the system of four dipolar bosons in a trap of anisotropy of = 50 has recently been considered in [7], wherein the effects of the interaction strength on various characteristics (such as the density, the momentum distribution, and the occupation number distribution) have been determined. For the two-particle system under consideration here, the Hamiltonian in the SMA is…”

“…The recent technological developments have also opened up perspectives for the experimental realization of systems of spatially confined particles with long-range dipole-dipole interactions (DDI) [3][4][5], providing, among other things, new possibilities for studying quantum correlation effects in many-body systems. Since then, there has been a remarkable increase of interest in understanding the properties of such systems [6][7][8][9][10][11][12][13]. For recent developments in studies of Dipolar Quantum Gases, see the overview [14].…”

“…where we have omitted the short-range contact interaction in order to explore only the pure dipolar effects (for details on this point, see, for example, Deuretzbacher et al [7]). The coordinates and the energies are measured in terms of √ mω/h,hω, respectively, and the dimensionless coupling g is related to the control parameters of the system by g = d 2 √ ωm 3 2 (1 + 3cos2θ)/8h 5 2 .…”

Fermionized Dipolar Bosons Trapped in a Harmonic Trap

“…In particular, recent experimental progress has opened up perspectives for achieving systems with particles interacting through the dipole-dipole interaction (DDI) [1,2], which has inspired great interest in understanding their properties [3][4][5][6]. There has also been a growing interest in studying entanglement properties of quantum composite systems, since their entangled states are an essential ingredient for quantum computation.…”