Mimicking multichannel scattering with single-channel approaches

Abstract

The collision of two atoms is an intrinsic multi-channel (MC) problem as becomes especially obvious in the presence of Feshbach resonances. Due to its complexity, however, single-channel (SC) approximations, which reproduce the long-range behavior of the open channel, are often applied in calculations. In this work the complete MC problem is solved numerically for the magnetic Feshbach resonances (MFRs) in collisions between generic ultracold 6 Li and 87 Rb atoms in the ground state and in the presence of a static magnetic field B. The obtained MC solutions are used to test various existing as well as presently developed SC approaches. It was found that many aspects even at short internuclear distances are qualitatively well reflected. This can be used to investigate molecular processes in the presence of an external trap or in many-body systems that can be feasibly treated only within the framework of the SC approximation. The applicability of various SC approximations is tested for a transition to the absolute vibrational ground state around an MFR. The conformance of the SC approaches is explained by the two-channel approximation for the MFR.

Theoretical description of two ultracold atoms in finite three-dimensional optical lattices using realistic interatomic interaction potentials

“…Whenever the manipulation leads to a shift of a very weakly bound state into the dissociation continuum, resonant behavior (divergence of a sc ) is observed. Examples for such artificially obtained single-channel resonances include the variation of van der Waals coefficients [50], the reduced mass [23], the innerwall of the molecular interaction potential [26], or the local modification of the Born-Oppenheimer curve at intermediate distances [51]. A comparison of these different procedures and the full multi-channel treatment is provided in [51].…”

“…Examples for such artificially obtained single-channel resonances include the variation of van der Waals coefficients [50], the reduced mass [23], the innerwall of the molecular interaction potential [26], or the local modification of the Born-Oppenheimer curve at intermediate distances [51]. A comparison of these different procedures and the full multi-channel treatment is provided in [51]. As is shown in [28] a better and in fact almost perfect model for a multi-channel Feshbach resonance can be obtained with a two-channel model which appears more realistic with respect to a possible implementation within the present approach than the full multi-channel Hamiltonian.…”

Two-channel model of photoassociation in the vicinity of a Feshbach resonance

“…In order to verify the TC description of the PA process, we consider the exemplary case of an elastic collision of 6 Li-87 Rb ( 6 Li is atom 1, 87 Rb is atom 2) in the initial atomic basis state |α 0 = |1/2, 1/2 |1, 1 . For an energy 50 Hz above the threshold of the entrance channel which is well in the s-wave scattering regime the MC solution was calculated for different magnetic fields B in [16]. For B < 1500 G two s-wave resonances occur, a broad one at B = 1066, 917 G which was also observed experimentally [17], and a narrow one at B = 1282.576 G. The dependence of the scattering length a sc on the magnetic field strength is shown in Fig.…”

“…These transitions take place at internuclear distances where the coupling between all atomic channels is strong such that any deficiency of the TC description would become obvious. The MC rate was calculated in [16] for an electronic dipole moment Additionally a fit to the behavior…”

“…We thank Y. V. Vanne for fruitful discussions and for providing us with the differential MC transition rates of [16]. The authors are grateful to the Deutsche Forschungsgemeinschaft (SFB 450 C6) for financial support.…”