Abstract
We present a numerical procedure allowing one to extract Feshbach resonance parameters from numerical calculations without relying on approximate fitting procedures. Our approach is based on a simple decomposition of the reactance matrix in terms of poles and residual background contribution, and can be applied to the general situation of inelastic overlapping resonances. A simple lineshape for overlapping inelastic resonances, equivalent to known results in the particular cases of isolated and overlapping elastic features, is also rigorously derived.
Highlights
Feshbach resonances are an ubiquitous phenomenon taking place when the energy of colliding particles is nearly degenerate with a quasi-bound level of the system
It has been long realized that resonances occurring at extremely low energies can be induced by tuning an external magnetic field [1], allowing one to vary in a controlled way the effective interatomic interaction
As a by-product of the formalism, we demonstrate that the complex scattering length can always be parametrized in a simple and intuitive way in terms of complex magnetic field locations and magnetic widths
Summary
Feshbach resonances are an ubiquitous phenomenon taking place when the energy of colliding particles is nearly degenerate with a quasi-bound level of the system. A more general lineshape describing a pair and an arbitrary number of elastic overlapping resonances has been derived using formal scattering theory and quantum defect analysis in the supplemental material of [4] and in [5], respectively In this case, the scattering length is still a purely real quantity showing a pair or a series of nearby divergences. The analytical lineshape for overlapping resonances in the presence of inelastic processes is not yet available This situation which occurs frequently for collisions in excited states [11] is still missing a systematic procedure allowing one to summarize the numerical data in few theoretical parameters.
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