  Quantum statistics and symmetrization dictate that identical fermions do not
interact via s-wave collisions. However, in the presence of spin-orbit coupling
(SOC), fermions prepared in identical internal states with distinct momenta
become distinguishable. The resulting strongly interacting system can exhibit
exotic topological and pairing behaviors, many of which are yet to be observed
in condensed matter systems. Ultracold atomic gases offer a promising pathway
for simulating these rich phenomena. Two recent experiments reported the
observation of single atom SOC in optical lattice clocks (OLCs) based on
alkaline-earth atoms. In these works encoding the effective spin degree of
freedom in the long-lived electronic clock states significantly reduced the
detrimental effects of spontaneous emission and heating that have thus far
hindered the study of interacting SOC with alkali atoms. Beyond first studies
of interacting SOC with alkali atoms in a bulk gas and with two particles in a
lattice, here we enter a new regime of many-body interacting SOC in an OLC.
Using clock spectroscopy, we observe the precession of the collective
magnetization and the emergence of spin locking effects arising from an
interplay between p-wave and SOC-induced exchange interactions. The many-body
dynamics are well captured by a collective XXZ spin model, which describes a
broad class of condensed matter systems ranging from superconductors to quantum
magnets. Furthermore, our work will aid in the design of next-generation OLCs
by offering a route for avoiding the observed large density shifts caused by
SOC-induced exchange interactions.
