  Engineered spin-orbit coupling (SOC) in cold atom systems can aid in the
study of novel synthetic materials and complex condensed matter phenomena.
Despite great advances, alkali atom SOC systems are hindered by heating from
spontaneous emission, which limits the observation of many-body effects,
motivating research into potential alternatives. Here we demonstrate that SOC
can be engineered to occur naturally in a one-dimensional fermionic 87Sr
optical lattice clock (OLC). In contrast to previous SOC experiments, in this
work the SOC is both generated and probed using a direct ultra-narrow optical
clock transition between two electronic orbital states. We use clock
spectroscopy to prepare lattice band populations, internal electronic states,
and quasimomenta, as well as to produce SOC dynamics. The exceptionally long
lifetime of the excited clock state (160 s) eliminates decoherence and atom
loss from spontaneous emission at all relevant experimental timescales,
allowing subsequent momentum- and spin-resolved in situ probing of the SOC band
structure and eigenstates. We utilize these capabilities to study Bloch
oscillations, spin-momentum locking, and Van Hove singularities in the
transition density of states. Our results lay the groundwork for the use of
OLCs to probe novel SOC phases of matter.
