Ramsey interferometry with atoms and molecules: two-body versus many-body phenomena

We discuss the frequency and visibility of atom-molecule Ramsey fringes observed in recent experiments by Claussen [Phys. Rev. A 67, 060701 (2003)]. In these experiments a Rb-85 Bose-Einstein condensate was exposed to a sequence of magnetic field pulses on the high-field side of the 155 G Feshbach resonance. The observed oscillation frequencies largely agree with the theoretically predicted magnetic field dependence of the binding energy of the highest excited diatomic vibrational state, except for a small region very close to the singularity of the scattering length. Our analytic treatment of the experiment, as well as our dynamical simulations, follow the magnitude of the measured oscillation frequencies as well as the visibilities of the Ramsey fringes. We show that significant deviations from a purely binary dynamics, with an associated binding frequency, occur when the spatial extent of the molecular wave function becomes comparable with the mean distance between the atoms in the dilute gas. The experiments thus clearly identify the conditions under which diatomic molecules may be identified as a separate entity of the gas or, conversely, when the concept of binary physics in a many-body environment is bound to break down.