  Noncentrosymmetric superconductors offer fascinating phenomena of quantum
transport and optics such as nonreciprocal and nonlinear responses.
Time-reversal symmetry breaking often plays an essential role in the emergence
and enhancement of nonreciprocal transport. In this paper, we show the
nonreciprocal optical responses in noncentrosymmetric superconductors arising
from time-reversal symmetry breaking by demonstrating them in $s$-wave
superconductors with a Rashba spin-orbit coupling and a magnetic field.
Numerical results reveal the superconductivity-induced bulk photocurrent and
second harmonic generation, which are forbidden at the zero magnetic field. We
discuss the properties and mechanisms of the superconducting nonlinear
responses emerging under the magnetic field. In particular, we investigate the
magnetic-field dependence of the photocurrent conductivity and clarify the
essential ingredients which give a contribution unique to superconductors under
the magnetic field. This contribution is dominant in the low carrier density
regime although the corresponding joint density of states is tiny. We attribute
the enhancement to the quantum geometry. Moreover, the nonlinear conductivity
shows peculiar sign reversal at the transition to the topological
superconducting state. We propose a bulk probe of topological transition and
quantum geometry in superconductors.
