Abstract
Finite fermion systems are known to exhibit shell structure in the weakly-interacting regime, as well known from atoms, nuclei, metallic clusters or even quantum dots in two dimensions. All these systems have in common that the particle interactions between electrons or nucleons are spatially isotropic. Dipolar quantum systems as they have been realized with ultra-cold gases, however, are governed by an intrinsic anisotropy of the two-body interaction that depends on the orientation of the dipoles relative to each other. Here we investigate how this interaction anisotropy modifies the shell structure in a weakly interacting two-dimensional anisotropic harmonic trap. Going beyond Hartree-Fock by applying the so-called "importance-truncated" configuration interaction (CI) method as well as quadratic CI with single- and double-substitutions, we show how the magnetostriction in the system may be counteracted upon by a deformation of the isotropic confinement, restoring the symmetry.
Highlights
Atomic alkali-metal clusters are one of the first experimentally realized man-made artificial quantum systems with mass spectra revealing pronounced electronic shells [1,2] analogous to the closed shells in atomic noble gases, or the “magic numbers” of increased stability well known from nuclear structure [3]
When the shell structure is strong, one expects a series of pronounced peaks in 2 at the shell fillings which for a system close to a two-dimensional isotropic harmonic oscillator should occur at N = 1, 3, 6, 10, 15, . . . , as we argued for above
We here investigated the effect of an anisotropic dipole-dipole interaction between fermions on the shell structure in a quasi-two-dimensional harmonic oscillator confinement
Summary
Atomic alkali-metal clusters are one of the first experimentally realized man-made artificial quantum systems with mass spectra revealing pronounced electronic shells [1,2] analogous to the closed shells in atomic noble gases, or the “magic numbers” of increased stability well known from nuclear structure [3]. In contrast, the dipole-dipole twobody interaction itself is spatially anisotropic and depends on the orientation of the dipoles relative to each other In this case an anisotropy of the effective mean field may originate rather from the intrinsic structure of the two-body force than from the trap, confining the gas by a potential with an externally determined shape. We here restrict our analysis to a quasi-two-dimensional harmonic trap, where the azimuthal symmetry yields a strong shell structure despite the reduced dimensionality [4], but where for moderate tilt angles the otherwise dominant head-to-tail attraction can be avoided [25,26] Studies of both energy- and density-shell structures in trapped Fermi gases were reported in Refs.
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