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

We derive the two-channel (TC) description of the photoassociation (PA) process in the presence of a magnetic Feshbach resonance and compare to full coupled multi-channel calculations for the scattering of $^{6}$Li-$^{87}$Rb. Previously derived results [P. Pellegrini et al., Phys. Rev. Lett. 101, 053201 (2008)] are corrected. The PA process is shown to be fully described by two parameters: the maximal transition rate and the point of vanishing transition rate. The TC approximation reproduces excellently the PA transition rates of the full multi-channel calculation and reveals, e.g., that the enhancement of the rate at a resonance is directly connected to the position of vanishing rate. For the description of two independent resonances it was found that only three parameters completely characterize the PA process.

💡 Research Summary

The paper presents a rigorous two‑channel (TC) formulation of photoassociation (PA) in the presence of a magnetic Feshbach resonance and validates it against full coupled multi‑channel (MC) calculations for the heteronuclear system $^{6}$Li–$^{87}$Rb. The authors begin by reviewing the importance of PA for creating ultracold molecules and the dramatic influence that a nearby Feshbach resonance has on the scattering length and phase shift of the colliding atom pair. While MC approaches can treat all spin‑dependent channels explicitly, they are computationally intensive and obscure the underlying physics. To overcome this, the authors reduce the problem to an effective two‑channel picture: an open channel describing the free‑atom scattering state and a closed channel representing a bound molecular state that couples to the open channel via the inter‑channel coupling responsible for the Feshbach resonance.

In the TC model the magnetic‑field‑dependent scattering length follows the familiar formula
(a(B)=a_{\rm bg}\bigl