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.
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