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Semiclassical interpretation of super-shells in trapped fermionic gases

Magnus Ögren

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

We give an analysis, based on periodic orbit theory, of the super-shell structure observed in numerical Hartree-Fock calculations for trapped fermions.

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We show that a dilute harmonically trapped two-component gas of fermionic atoms with a weak repulsive interaction has a pronounced super-shell structure: The shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the ``magic numbers'' occurring between the beat nodes by half a period. The length and amplitude of this beating mode depend on the strength of the interaction. We give a simple interpretation of the beat structure in terms of a semiclassical trace formula for the symmetry breaking $\mathrm{U}(3)\ensuremath{\rightarrow}\mathrm{SO}(3)$.

arXiv:cond-mat/0502096•Physical Review A•Nov 11, 2005•8 citations
It was recently shown in self-consistent Hartree-Fock calculations that a harmonically trapped dilute gas of fermionic atoms with a repulsive two-body interaction exhibits a pronounced {\it super-shell} structure: the shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the ``magic numbers'' occurring between the beat nodes by half a period. The length and amplitude of the beating mode depends on the strength of the interaction. We give a qualitative interpretation of the beat structure in terms of a semiclassical trace formula that uniformly describes the symmetry breaking U(3) →\to→ SO(3) in a 3D harmonic oscillator potential perturbed by an anharmonic term ∝r4\propto r^4∝r4 with arbitrary strength. We show that at low Fermi energies (or particle numbers), the beating gross-shell structure of this system is dominated solely by the two-fold degenerate circular and (diametrically) pendulating orbits.
We show that a dilute harmonically trapped two-component gas of fermionic atoms with a weak repulsive interaction has a pronounced super-shell structure: The shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the ``magic numbers'' occurring between the beat nodes by half a period. The length and amplitude of this beating mode depend on the strength of the interaction. We give a simple interpretation of the beat structure in terms of a semiclassical trace formula for the symmetry breaking $\mathrm{U}(3)\ensuremath{\rightarrow}\mathrm{SO}(3)$.