Analytical solutions for the dynamics of two trapped interacting ultracold atoms

Journal Article · Tue Aug 15 04:00:00 EDT 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.74.022712· OSTI ID:20853073

Idziaszek, Zbigniew; Calarco, Tommaso ^[1]; ECT, I-38050 Villazzano ^[2]

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1. CNR-INFM BEC Center, I-38050 Povo (Tunisia) (Italy) and Centrum Fizyki Teoretycznej, Polska Akademia Nauk, 02-668 Warsaw (Poland)
2. Tunisia; Italy

We discuss exact solutions of the Schroedinger 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.

• OSTI ID: 20853073
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 74; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ANALYTICAL SOLUTION
ATOMS
AXIAL SYMMETRY
EIGENFUNCTIONS
EIGENVALUES
ENERGY DEPENDENCE
EXACT SOLUTIONS
HARMONIC POTENTIAL
ONE-DIMENSIONAL CALCULATIONS
RADIATION PRESSURE
RESONANCE
SCATTERING LENGTHS
SCHROEDINGER EQUATION
TRAPPING
TRAPS
TWO-DIMENSIONAL CALCULATIONS