Bonn 2010 – wissenschaftliches Programm
HK 18.5: Vortrag
Dienstag, 16. März 2010, 15:00–15:15, HG V
Spectrum of particles with short-ranged interactions in a harmonic potential — •Simon Tölle, Hans-Werner Hammer, and Bernard Metsch — Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), Universität Bonn
The possibility to control short-ranged interactions of cold gases in optical traps by Feshbach-resonances makes these systems ideal candidates to study universal scale properties and Efimov physics. For A particles with equal mass m the energy spectrum in a trap, idealised by an harmonic potential, in the zero-range limit in leading order is determined by the Hamiltonian H=∑i=1A(|p^→_i|^2/2m+1/2mω^2|x_i|^2)+∑i<jAV_ij+∑i<j<kAW_ijk , where ω is the trapping frequency and Vij and Wijk are 2- and 3-particle contact interactions. In Jacobi-coordinates the centre-of-mass motion is separated. The Hamiltonian is regularised by restricting the coupled oscillator basis with a cutoff N. For a given N the corresponding Hamilton matrix is diagonalised numerically. The effective coupling constants are renormalised by the requirement that for each N the ground state energies of the 2- and 3-body sector match the exact results. The excitation spectrum can in general be extrapolated reliably for N→∞. Appropriate symmetries for identical bosons and fermions can be considered. Results for 2-, 3- and 4-particle systems will presented. First applications to physical systems like 6Li will be discussed.