  We investigate the bulk photovoltaic effect, which rectifies light into
electric current, in a collective quantum state with correlation driven
electronic ferroelectricity. We show via explicit real-time dynamical
calculations that the effect of the applied electric field on the electronic
order parameter leads to a strong enhancement of the bulk photovoltaic effect
relative to the values obtained in a conventional insulator. The enhancements
include both resonant enhancements at sub-bandgap frequencies, arising from
excitation of optically active collective modes, and broad-band enhancements
arising from non-resonant deformations of the electronic order. The deformable
electronic order parameter produces an injection current contribution to the
bulk photovoltaic effect which is entirely absent in a rigid-band approximation
to a time-reversal symmetric material. Our findings establish that correlation
effects can lead to the bulk photovoltaic effect and demonstrate that the
collective behavior of ordered states can yield large nonlinear optical
responses.
