Time-Reversal Symmetry-Protected Coherent Control of Ultracold Molecular Collisions

Coherent control of atomic and molecular scattering relies on the preparation of colliding particles in superpositions of internal states, establishing interfering pathways that can be used to tune the outcome of a scattering process. However, the incoherent addition of different partial wave contributions to the integral cross-sections, commonly encountered in systems with complex collisional dynamics, poses a significant challenge, often limiting the control. This work demonstrates that time-reversal symmetry can be used to overcome these limitations by constraining the relation between the S-matrix elements. For example, the preparation of a superposition of two states related by the time-reversal superposition can provide extensive control for transitions to a time-reversal invariant final state, such as the J = 0, M = 0. Using the example of ultracold O₂-O₂ scattering, we show that for such states coherent control is robust against short-range dynamical complexity. Furthermore, the time-reversal symmetry also protects the control against a distribution of collisional energies. Beyond the ultracold regime, we observe significant differences in the controllability of crossed-molecular beam vs trap experiments with complete control achievable in the former case at any temperature, emphasizing the cooperative role of time-reversal and permutation symmetries in maintaining control at any temperature. These results open new avenues for the coherent control of complex inelastic collisions and chemical reactions both in and outside of the ultracold regime.