  The topology of two-dimensional materials traditionally manifests itself
through the quantization of the Hall conductance, which is revealed in
transport measurements. Recently, it was predicted that topology can also give
rise to a quantized spectroscopic response upon subjecting a Chern insulator to
a circular drive: Comparing the frequency-integrated depletion rates associated
with drives of opposite orientations leads to a quantized response dictated by
the topological Chern number of the populated Bloch band. Here we
experimentally demonstrate this intriguing topological effect for the first
time, using ultracold fermionic atoms in topological Floquet bands. In
addition, our depletion-rate measurements also provide a first experimental
estimation of the Wannier-spread functional, a fundamental geometric property
of Bloch bands. Our results establish topological spectroscopic responses as a
versatile probe, which could be applied to access the geometry and topology of
many-body quantum systems, such as fractional Chern insulators.
