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 level
s, 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.
