Analytical solutions for the dynamics of two trapped interacting ultracold atoms

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Zbigniew Idziaszek
CNR-INFM BEC Center, I-38050 Povo (TN), Italy and Centrum Fizyki Teoretycznej, Polska Akademia Nauk, 02-668 Warsaw, Poland

Tommaso Calarco
CNR-INFM BEC Center, I-38050 Povo (TN), Italy; ECT*, I-38050 Villazzano (TN), Italy; and ITAMP, Harvard Smithsonian Center for Astrophysics, and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

Received 3 May 2006; published 8 August 2006

Wediscuss exact solutions of the Schrödinger equation for the systemof two ultracold atoms confined in an axially symmetric harmonicpotential. We investigate different geometries of the trapping potential, inparticular we study the properties of eigenenergies and eigenfunctions forquasi-one-dimensional and quasi-two-dimensional traps. We show that the quasi-one-dimensional andthe quasi-two-dimensional regimes for two atoms can be already realizedin the traps with moderately large (or small) ratios ofthe trapping frequencies in the axial and the transverse directions.Finally, we apply our theory to Feshbach resonances for trappedatoms. Introducing in our description an energy-dependent scattering length wecalculate analytically the eigenenergies for two trapped atoms in thepresence of a Feshbach resonance.

URL:	http://link.aps.org/doi/10.1103/PhysRevA.74.022712
DOI:	10.1103/PhysRevA.74.022712
PACS:	34.50.-s; 32.80.Pj 34.50.-s Scattering of atoms and molecules 32.80.Pj Optical cooling of atoms; trapping YEAR: 2006
KEYWORDS:	radiation pressure, Schrodinger equation, eigenvalues and eigenfunctions

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