  While the search for topological triplet-pairing superconductivity has
remained a challenge, recent developments in optically stabilizing metastable
superconducting states suggest a new route to realizing this elusive phase.
Here, we devise a testable theory of competing superconducting orders that
permits ultrafast switching to an opposite-parity superconducting phase in
centrosymmetric crystals with strong spin-orbit coupling. Using both
microscopic and phenomenological models, we show that dynamical inversion
symmetry breaking with a tailored light pulse can induce odd-parity (spin
triplet) order parameter oscillations in a conventional even-parity (spin
singlet) superconductor, which when driven strongly can send the system to a
competing minimum in its free energy landscape. Our results provide new guiding
principles for engineering unconventional electronic phases using light,
suggesting a fundamentally non-equilibrium route toward realizing topological
superconductivity.
