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Physical Review A

Complex scaling calculation of the decaying quantum-propagation modes of neutral atoms in a magnetic guide

R. M. Potvliege, Véronique Zehnlé

Published Jan 3, 2001• 15 citations
Publisher

Abstract

It is shown that the energies and the lifetimes of unstable modes of quantum propagation of neutral atoms in a quadrupole magnetic guide can be calculated simply by diagonalizing the complex scaled Hamiltonian. The results reproduce those obtained for the same geometry, but by a different method, by E. A. Hinds and C. Eberlein [Phys. Rev. A 61, 033614 (2000)]. The destabilizing effect of a weak bias magnetic field on the $l=0$ propagation mode of $s=1/2$ atoms is illustrated.

DOI
10.1103/physreva.63.025601

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It is shown that the energies and the lifetimes of unstable modes of quantum propagation of neutral atoms in a quadrupole magnetic guide can be calculated simply by diagonalizing the complex scaled Hamiltonian. The results reproduce those obtained for the same geometry, but by a different method, by E. A. Hinds and C. Eberlein [Phys. Rev. A 61, 033614 (2000)]. The destabilizing effect of a weak bias magnetic field on the l=0l=0l=0 propagation mode of s=1/2s=1/2s=1/2 atoms is illustrated.
We consider the quantized motion of neutral atoms at very low temperature in a two-dimensional magnetic quadrupole structure formed, for example, by four current-carrying wires along the z direction. The magnetic field B\mathbf{B}B in the guide is proportional to the vector $(x,\ensuremath{-}y).$ We show that this field can be used to make a single-mode atomic de Broglie waveguide which has bound states of low angular momentum, even though the field at the center of the guide goes to zero. We investigate the spectrum and decay rate of the transverse modes for spin-1/2 and spin-1 atoms.
We investigate the resonant motion of neutral spin-12\frac{1}{2}21​-fermions in a magnetic guide. A wealth of unitary and antiunitary symmetries is revealed in particular giving rise to a twofold degeneracy of the energy levels. To compute the energies and decay widths of a large number of resonances the complex scaling method is employed. We discuss the dependence of the lifetimes on the angular momentum of the resonance states. In this context the existence of so-called quasibound states is shown. In order to approximately calculate the resonance energies of such states a radial Schr\"odinger equation is derived which improves the well-known adiabatic approximation. The effects of an additionally applied homogeneous Ioffe field on the resonance energies and decay widths are also considered. The results are applied to the case of the 6Li^{6}\mathrm{Li}6Li atom in the F=12F=\frac{1}{2}F=21​ hyperfine ground state.
We investigate the motion of neutral fermions and bosons in a three-dimensional magnetic quadrupole trap. Inspecting the underlying Hamiltonian a variety of symmetries is revealed which give rise to degeneracies of the resonance energies. Our numerical approach which involves the eigenvalue problem resulting from a Sturmian basis set together with the complex scaling method enables us to calculate several hundred resonance states. The distributions of the energies and decay widths of the resonances are analyzed for both spin-12\frac{1}{2}21​ fermions and spin-1 bosons. We also investigate under what conditions quasibound states with long lifetimes can be achieved. An effective scalar Schr\"odinger equation describing such states is derived. The results are applied to the cases of the alkali-metal atoms 87Rb^{87}\mathrm{Rb}87Rb and 6Li^{6}\mathrm{Li}6Li trapped in a hyperfine ground state.
We investigate the resonant quantum motion of spin-1 particles in a magnetic guide. A symmetry analysis is undertaken in order to reveal the complex symmetry properties of the system which lead to a twofold degeneracy in the energy-level spectrum. Lifetimes and energies of the resonance states are computed by employing the complex scaling method. By analyzing several hundreds of resonances we are able to make conclusions about the global properties of the resonance spectrum. The effect of an Ioffe field which is applied parallel to the guide is also discussed. We observe a global increase of the lifetimes with increasing Ioffe-field strength. For certain parameter regimes we find the ground-state resonance to exhibit a longer lifetime than the energetically neighbored excited states. The latter could have interesting implications on the time evolution of trapped ultracold atomic ensembles. Applications of our results to calculate the resonance energies andlifetimes of the trapped alkali-metal atoms 7Li^{7}\mathrm{Li}7Li and 87Rb^{87}\mathrm{Rb}87Rb are outlined.
We propose a novel magnetic guide for cold neutral atoms using some current-carring conductors,The spatial distributions of the magnetic fields from a V-shaped or U-shaped current-carrying coductor are calculated.and the relationship between the resulting magnetic field and the parametes of the current-carrying conductors is analysed in dtail,The result shows that these current-craaying conductors can be used to realize a single or a controllable double magnetic guide of cold atoms in the weak-field-seeking state,and to construct various atom-optical elements,and even to realize a single-mode atomic waveguiding under certain conditions.
We propose a novel magnetic guide for cold neutral atoms using some current-carrying conductors. The spatial distributions of the magnetic fields from a V-shaped or U-shaped current-carrying conductor are calculated, and the relationship between the resulting magnetic field and the parameters of the current-carrying conductors is analysed in detail. The result shows that these current-carrying conductors can be used to realize a single or a controllable double magnetic guide of cold atoms in the weak-field-seeking state, and to construct various atom-optical elements, and even to realize a single-mode atomic waveguiding under certain conditions.