Identical-Particle Symmetry-Enabled Complete Coherent Control of Ultracold Atomic and Molecular Collisions

We show that exchange symmetry in collisions of identical particles enables symmetry-protected coherent control of the total scattering cross section. For identical fermions, antisymmetrization enforces complete phase synchronization of the contributing scattering channels, yielding maximal control visibility. For identical bosons, synchronization persists but with reduced visibility due to additional exchange (satellite) contributions. Collisions of distinguishable particles lack this symmetry-imposed phase locking, leading to lower controllability and visibility. We elucidate these principles through coupled-channel quantum-scattering calculations for lithium-lithium collisions, comparing the $^{6}\mathrm{Li}$-$^{6}\mathrm{Li}$ (identical fermions), $^{7}\mathrm{Li}$-$^{7}\mathrm{Li}$ (identical bosons), and $^{6}\mathrm{Li}$-$^{7}\mathrm{Li}$ (distinguishable) systems. Furthermore, in the identical particle cases, symmetry-enforced synchronization enables full control over the parity of the final state at any collisional energy. This mechanism is broadly applicable to identical-particle collisions, including homonuclear molecules for which established approaches -- DC electric fields, or microwave shielding -- are ineffective or unavailable.