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ABSTRACT: The microscopic properties of few interacting cold fermionic atoms confined in a two-dimensional (2D) harmonic trap are studied by numerical diagonalization. For repulsive interactions, a strong shell structure dominates, with Hund's rule acting at its extreme for the midshell configurations. In the attractive case, odd-even oscillations due to pairing occur simultaneously with deformations in the internal structure of the ground states, as seen from pair correlation functions.
Physical Review Letters 03/2009; 102(6):060401. · 7.37 Impact Factor
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ABSTRACT: A rotating, two-component Bose–Einstein condensate is shown to exhibit vortices of multiple quantization, which are possible due to the interatomic interactions between the two species. Also, persistent currents are absent in this system. Finally, the order parameter has a very simple structure for a range of angular momenta.
New Journal of Physics 03/2008; 10(3):033029. · 4.18 Impact Factor
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ABSTRACT: A rotating, two-component Bose-Einstein condensate is shown to exhibit vortices of multiple quantization, which are possible due to the interatomic interactions between the two species. Also, persistent currents are absent in this system. Finally, the order parameter has a very simple structure for a range of angular momenta.
05/2007;
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ABSTRACT: We examine the spin asymmetry of ground states for two-dimensional, harmonically trapped two-component gases of fermionic atoms at zero temperature with weakly repulsive short range interactions. Our main result is that, in contrast to the three-dimensional case, in two dimensions a non-trivial spin-asymmetric phase can only be caused by shell structure. A simple, qualitative description is given in terms of an approximate single particle model, comparing well to the standard results of Hartree-Fock or direct diagonalization methods.
03/2007;
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ABSTRACT: 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 $\propto r^4$ 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. Comment: Final version of procedings for the 'Nilsson conference'
12/2006;
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ABSTRACT: We use the configuration interaction technique to study vortex formation in rotating systems of interacting spinless fermions and bosons trapped in a two-dimensional harmonic potential. In the fermionic case, the vortices appear as holes in the Fermi sea and localize in rings. The yrast spectrum is dominated by rigid rotation of the vortex ring, showing periodic oscillations. The Bose system shows a similar yrast spectrum and vortex formation. This can be explained by a one-to-one correspondence of the fermion and boson many-particle configurations. A simple mean-field model can reproduce the oscillations in the yrast spectrum, but fails to explain the localization of vortices.
Physica Scripta 06/2006; 2006(T125):31. · 1.20 Impact Factor
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ABSTRACT: Vortices can form when finite quantal systems are set rotating. In the limit of small particle numbers, the vortex formation in a harmonically trapped fermion system, with repulsively interacting particles, shows similarities to the corresponding boson system, with vortices entering the rotating cloud for increasing rotation. For a larger number of fermions, N 15, the fermion vortices compete and co-exist with (Chamon–Wen) edge-reconstructed ground states, forcing some ground states, as for example the central single vortex, into the spectrum of excited states. Experimentally, the fermion system could, for instance, be electrons in a semiconductor heterostructure, a quantum dot, and the corresponding boson system, a Bose–Einstein condensate in a magneto optical trap.
Journal of Physics B Atomic Molecular and Optical Physics 05/2006; 39(12):2721. · 1.88 Impact Factor
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ABSTRACT: Finite quantal systems at high angular momenta may exhibit vortex formation and localization. These phenomena occur independent of the statistics of the repulsively interacting particles, which may be of bosonic or fermionic nature. We analyze the relation between vortex localization and formation of stable Wigner molecules at high angular momenta in the view of particle-hole duality.Trial wave functions for the vortex states and the corresponding fermion-boson relations are discussed. Comment: 12 pages, 12 figures
05/2006;
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ABSTRACT: Small crystallites form when finite quantal systems are set highly rotating. This crystallization is independent of the statistics of the particles, and occurs for both trapped bosons and fermions. The spin degree of freedom does not change the tendency for localization. In a highly rotating state, the strongly correlated bosonic and fermionic systems approach to that of classical particles. Comment: 14 pages 6 figures
02/2006;
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ABSTRACT: We consider small systems of bosonic atoms rotating in a toroidal trap. Using the method of exact numerical diagonalization of the many-body Hamiltonian, we examine the transition from the Bose-Einstein condensed state to the Tonks-Girardeau state. The system supports persistent currents in a wide range between the two limits, even in the absence of Bose-Einstein condensation. Comment: 7 pages, 3 figures, revised version, to appear in Europh. Lett
10/2005;
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ABSTRACT: We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term $\propto r^4$. This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbits over the manifold $\mathbb{C}$P$^2$ which characterizes their 4-fold degeneracy. Then we obtain an analytical uniform trace formula which in the limit of strong perturbations (or high energy) asymptotically goes over into the correct trace formula of the full anharmonic system with SO(3) symmetry, and in the limit $\epsilon$ (or energy) $\to 0$ restores the HO trace formula with U(3) symmetry. We demonstrate that the gross-shell structure of this anharmonically perturbed system is dominated by the two-fold degenerate diameter and circular orbits, and {\it not} by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios $\omega_r:\omega_\phi=N:M$ of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential $V(r)\propto r^4$. Comment: LaTeX (revtex4), 26pp., 5 figures, 1 table; final version to be published in J. Phys. A (without appendices C and D)
05/2005;
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ABSTRACT: In a quantum-mechanical system, particle-hole duality implies that instead of studying particles, we can get equivalent information by studying the missing particles, the so-called holes. Using this duality picture for fermions in a rotating trap the vortices appear as holes in the Fermi sea. Here we predict that the formation of vortices in quantum dots at high magnetic fields causes oscillations in the energy spectrum which can be experimentally observed using accurate tunneling spectroscopy. We use the duality picture to show that these oscillations are caused by the localization of vortices in rings.
Physical Review Letters 04/2005; 94(10):106405. · 7.37 Impact Factor
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ABSTRACT: 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 U(3) --> SO(3). Comment: 4 pages, 4 figures; In version 2, references added. The semiclassical explanation of super-shell structure is refined. Version 3, as appeared in Phys. Rev. A
02/2005;
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ABSTRACT: Vortices can form when finite quantal systems are set to rotate. In the limit of small particle numbers the vortex formation in a harmonically trapped fermion system, with repulsively interacting particles, shows similarities to the corresponding boson system, with vortices entering the rotating cloud for increasing rotation. We show that for a larger number of fermions, $N\gtrsim15$, the fermion vortices compete and co-exist with (Chamon-Wen) edge-reconstructed ground states, forcing some ground states, for instance the central single vortex, into the spectrum of excited states. Experimentally, the fermion system could for instance be a semiconductor heterostructure, a quantum dot, and the corresponding boson system a magneto optical trap (MOT).
01/2005;
