  It is well known that a nontrivial Chern number results in quantized Hall
conductance. What is less known is that, generically, the Hall response can be
dramatically different from its quantized value in materials with broken
inversion symmetry. This stems from the leading Hall contribution beyond the
linear order, known as the Berry curvature dipole (BCD). While the BCD is in
principle always present, it is typically very small outside of a narrow window
close to a topological transition and is thus experimentally elusive without
careful tuning of external fields, temperature, or impurities. In this work, we
transcend this challenge by devising optical driving and quench protocols that
enable practical and direct access to large BCD and nonlinear Hall responses.
Varying the amplitude of an incident circularly polarized laser drives a
topological transition between normal and Chern insulator phases, and
importantly allows the precise unlocking of nonlinear Hall currents comparable
to or larger than the linear Hall contributions. This strong BCD engineering is
even more versatile with our two-parameter quench protocol, as demonstrated in
our experimental proposal. Our predictions are expected to hold qualitatively
across a broad range of Hall materials, thereby paving the way for the
controlled engineering of nonlinear electronic properties in diverse media.
