Theory of itinerant collisional spin dynamics in nondegenerate molecular gases

We study the fully itinerant dynamics of ultracold but nondegenerate polar molecules with a spin-$1/2$ degree of freedom encoded into two of their electric field dressed rotational states. Center-of-mass molecular motion is constrained to two dimensions via tight confinement with a one-dimensional optical lattice, but remains mostly unconstrained within the plane. The pseudospins can become entangled through ultracold dipolar collisions, for which the locality of interactions is greatly relaxed by free molecular motion. At the level of single-molecule observables, collision-induced entanglement manifests as spin decoherence, for which our theoretical calculations serve well to describe recent Ramsey contrast measurements of quasi-two-dimensional confined KRb molecules at JILA [A. Carroll et al., Science 388, 6745 (2025)]. In presenting a more detailed theoretical analysis of the KRb experiment, we highlight a key finding that molecular loss enhanced by particle exchange symmetry can lead to a suppression of collective spin decoherence, a mechanism we refer to as ``loss-induced quantum autoselection.'' We then show that, by utilizing bialkali species with sufficiently large dipole moments, loss can be near completely suppressed in all collision channels via electric field tunable confinement-induced collisional shielding. The afforded collisional stability permits fully coherent spin mixing dynamics, natively realizing unitary circuit dynamics with random all-to-all connectivity and U(1) charge conservation. This work establishes a bridge between the domains of ultracold molecular collisions and many-body spin physics, ultimately proposing the use of nondegenerate bulk molecular gases as a controllable platform for nonequilibrium explorations of itinerant quantum matter.