  The absorption of a single photon that excites a quantum system from a low to
a high energy level is an elementary process of light-matter interaction, and a
route towards realizing pure single-photon absorption has both fundamental and
practical implications in quantum technology. Due to nonlinear optical effects,
however, the probability of pure single-photon absorption is usually very low,
which is particularly pertinent in the case of strong ultrafast laser pulses
with broad bandwidth. Here we demonstrate theoretically a counterintuitive
coherent single-photon absorption scheme by eliminating nonlinear interactions
of ultrafast laser pulses with quantum systems. That is, a completely linear
response of the system with respect to the spectral energy density of the
incident light at the transition frequency can be obtained for all transition
probabilities between 0 and 100% in a multi-level quantum systems. To that end,
a new multi-objective optimization algorithm is developed to find an optimal
spectral phase of an ultrafast laser pulse, which is capable of eliminating all
possible nonlinear optical responses while maximizing the probability of
single-photon absorption between quantum states. This work not only deepens our
understanding of light-matter interactions, but also offers a new way to study
photophysical and photochemical processes in the "absence" of nonlinear optical
effects.
