Energy-dependent scattering lengths and Feshbach resonances

S. Jonsell

A model for the system of three identical bosons with interactions containing a Feshbach resonance is developed. The model assumes short-range interactions, but includes the energy dependence of the interaction due to the finite width of the resonance. The model is applied to the system of three bosons trapped in a harmonic potential. In particular we study the energy in the limit of infinite scattering length. In this limit the energy does not depend on the scattering length, but it does depend on the other parameters of the resonance.

Raffaele Carlone, M. Correggi, D. Finco +1 more

Ryan M. Kalas, Eddy Timmermans

Y. Avishai, Y. B. Band, Marek Trippenbach

The physics of Feshbach resonance is analyzed using an analytic expression for the s-wave scattering phase shift and the scattering length a which we derive within a two-channel tight-binding model. Employing a unified treatment of bound states and resonances in terms of the Jost function, it is shown that, for strong interchannel coupling, Feshbach resonance can occur even when the closed channel does not have a bound state. This may extend the range of ultracold atomic systems that can be manipulated by Feshbach resonance. The dependence of the sign of a on the coupling strength in the unitary limit is elucidated. As a by-product, analytic expressions are derived for the background scattering length, the external magnetic field at which resonance occurs, and the energy shift ε-ε(B), where ε is the scattering energy and ε(B) is the bound-state energy in the closed channel (when there is one).

Haibin Wu, John E. Thomas

We describe two-field optical techniques to control interactions in Feshbach resonances for two-body scattering in ultracold gases. These techniques create a molecular dark state in the closed channel of a magnetically tunable Feshbach resonance, greatly suppressing optical scattering compared to single optical field methods. The dark-state method enables control of the effective range, by creating narrow features that modify the energy dependence of the scattering phase shift, as well as control of the elastic and inelastic parts of the zero-energy $s$-wave scattering amplitude. We determine the scattering length and the effective range from an effective range expansion, by calculating the momentum-dependent scattering phase shift from the two-body scattering state.

Rajat K. Bhaduri, Michael Seidl, Avinash Khare