The interplay between crystal symmetry and its optical responses is at the heart of tremendous recent advances in light-matter interactions and applications. Nonlinear optical processes that produce electric currents, for example bulk photovoltaic (BPV) effect, require inversion symmetry broken materials, such as ferroelectrics. In the current work, we demonstrate that such BPV current could be generated in centrosymmetric materials with excitation of out-of-equilibrium coherent phonons. This is much different from the generally studied static or thermally excited states. We show that depending on the oscillating phase factor of the coherent phonon, uni-directional static electric current can be observed, in addition to some terahertz alternating currents. We also generalize the conventional injection charge current into angular momentum (spin and orbital) degrees of freedom, and demonstrate spin and orbital BPV photocurrents under coherent phonons. Our findings open the pathway to exploring the exotic phonon-photon-electron coherent interactions in quantum materials.
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