Coherent control of ultracold molecular collisions: Generalized Optical theorem

Coherent control of ultracold collisions relies on coherent superpositions of initial states of the collision partners to tune the scattering amplitudes to a final state via quantum interference of indistinguishable pathways. This method does not require external magnetic (or electric) fields and is complementary to current control methods based on external fields. In our previous work, we demonstrated highly efficient coherent control of state-to-state cross sections for spin exchange in ultracold molecule-molecule collisions in the s-wave regime for both the incident and final collision channels.

However, coherent control could be more easily observed by measuring the total (as opposed to state-to-state) scattering cross sections. In quantum scattering theory, the total cross section is related to the imaginary part of the elastic forward scattering amplitude via the optical theorem. We present a generalization of the multichannel optical theorem to include the scattering of molecules in coherent superpositions of their internal states.  Using the generalized optical theorem, we show extensive control of the total cross-section for O₂-O₂ and ⁸⁵Rb-⁸⁵Rb collisions.