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Physical Review A

Interacting atoms under strong quantum confinement

Eite Tiesinga, Carl J. Williams, Frederick H. Mies, Paul S. Julienne

Published May 17, 2000• 81 citations
Publisher

Abstract

We calculate the energy-level shifts of a tightly confined trapped alkali-metal atom in the presence of a second trapped atom. A complete microscopic description of the interaction energy between the two atoms is used. This allows us to study tightly confined atoms near a Feshbach resonance and to evaluate the usefulness of the regularized $\ensuremath{\delta}$-function potential approximation. We present results for sodium and cesium when confined in a spherically symmetric harmonic optical trap. Possible implications of the level shifts and collisional decoherence for quantum computing with atomic systems are given.

DOI
10.1103/physreva.61.063416

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We calculate the energy-level shifts of a tightly confined trapped alkali-metal atom in the presence of a second trapped atom. A complete microscopic description of the interaction energy between the two atoms is used. This allows us to study tightly confined atoms near a Feshbach resonance and to evaluate the usefulness of the regularized \ensuremathδ\ensuremath{\delta}\ensuremathδ-function potential approximation. We present results for sodium and cesium when confined in a spherically symmetric harmonic optical trap. Possible implications of the level shifts and collisional decoherence for quantum computing with atomic systems are given.
We discuss exact solutions of the Schr\"odinger equation for the system of two ultracold atoms confined in an axially symmetric harmonic potential. We investigate different geometries of the trapping potential, in particular we study the properties of eigenenergies and eigenfunctions for quasi-one-dimensional and quasi-two-dimensional traps. We show that the quasi-one-dimensional and the quasi-two-dimensional regimes for two atoms can be already realized in the traps with moderately large (or small) ratios of the trapping frequencies in the axial and the transverse directions. Finally, we apply our theory to Feshbach resonances for trapped atoms. Introducing in our description an energy-dependent scattering length we calculate analytically the eigenenergies for two trapped atoms in the presence of a Feshbach resonance.
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We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in ppp wave and confined in an axially symmetric harmonic trap. To this end we utilize ppp-wave pseudopotential with an energy-dependent scattering volume. This allows to describe the scattering in tight trapping potentials in the presence of scattering resonances. We verify predictions of the pseudopotential treatment for some model interaction potential obtaining an excellent agreement with exact energy levels. Then we turn to the experimentally relevant case of neutral atom interactions in the vicinity of a ppp-wave Feshbach resonance. In the framework of the multichannel quantum-defect theory we derive relatively simple formula for an energy-dependent scattering volume, and later we apply it to investigate the energy spectrum of trapped atoms close to the ppp-wave Feshbach resonance.
The energy spectrum and corresponding wave functions of two bosonic particles confined in a spherically symmetric shell trap and interacting via a three-dimensional zero-range potential are computed. Confinement-induced resonances, originating entirely from the strong coupling of the relative and center-of-mass motions of the two particles, are identified as avoided crossings for certain values of the shell radius. By working close to the found resonances, these results offer a new way to control the atom-atom interaction in an atomic gas by tuning only the geometrical parameters of the shell.
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