  We study spectroscopy of artificial solid-state four-level quantum system.
This system is formed by two coupled superconducting flux qubits. When multiple
driving frequency of the applied microwaves matches the energy difference
between any two levels, the transition to the upper level is induced. We
demonstrate two types of the multi-photon transitions: direct transitions
between two levels and ladder-type transitions via an intermediate level. For
the latter transitions, in particular, the inverse population of the excited
state with respect to the ground one is realized. These processes can be useful
for the control of the level population for the multilevel scalable quantum
systems.
