Fig. 4 | Nature Communications

Fig. 4

From: Above-threshold scattering about a Feshbach resonance for ultracold atoms in an optical collider

Fig. 4

Collisions between ballistically expanding projectile and target clouds. Phase-space representations of an ensemble of projectile atoms transiting a stationary target cloud subject to resonant Feshbach loss. Resonant interactions between groups of particles in the projectile and targets clouds are indicated by wavy blue lines and happen whenever a projectile particle arrives at the position of a target particle and their momentum difference is p p − p t = Δp res. The actual value for the resonant momentum difference depends on B as \(\Delta {p_{{\rm{res}}}}(B) = \sqrt {4m{E_{{\rm{res}}}}(B)} \); in particular, B res defines the field for which \(\Delta {p_{{\rm{res}}}} = {\bar p_{\rm{p}}}\)—the mean momentum of the projectile cloud. a Target and projectile atoms are initially confined by two harmonic potentials; the projectile cloud moves with a mean momentum \({\bar p_{\rm{p}}}\) toward the target. By switching off the harmonic confinement, the atomic clouds expand ballistically before colliding. b For a magnetic field B = B + > B res, \(\Delta {p_{{\rm{res}}}} \, >\, {\bar p_{\rm{p}}}\) and loss is resonantly enhanced at early times of the transit and occurs at the head-end of the projectile cloud and the z < 0 part of the target. c For B = B res, \(\Delta {p_{{\rm{res}}}} = {\bar p_{\rm{p}}}\) (by definition) and atoms with momentum difference equal to \({\bar p_{\rm{p}}}\) will undergo resonant loss. This condition is fulfilled uniformly throughout the clouds at the point in time where they coincide. d For B = B  < B res, \(\Delta {p_{{\rm{res}}}} < {\bar p_{\rm{p}}}\) and resonant collisions predominantly happen toward the end of the transit and lead to loss at the tail-end of the projectile cloud and the z > 0 part of the target. The rightmost frame of bd shows how the marginal spatial density distributions n t(z) and n p(z) of the target cloud (blue line) and the projectile cloud (red line), respectively, distort from their shape in absence of resonant loss (orange line)