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We study the microwave absorption of a driven three-level quantum system,which is realized by a superconducting flux quantum circuit (SFQC), with amagnetic driving field applied to the two upper levels. The interaction betweenthe three-level system and its environment is studied within the Born-Markovapproximation, and we take into account the effects of the driving field on thedamping rates of the three-level system. We study the linear response of thedriven three-level SFQC to a weak probe field. The linear magneticsusceptibility of the SFQC can be changed by both the driving field and thebias magnetic flux. When the bias magnetic flux is at the optimal point, thetransition from the ground state to the second excited state is forbidden andthe three-level SFQC has a ladder-type transition. Thus, the SFQC responds tothe probe field like natural atoms with ladder-type transitions. However, whenthe bias magnetic flux deviates from the optimal point, the three-level SFQChas a cyclic transition, thus it responds to the probe field like a combinationof natural atoms with ladder-type transitions and natural atoms with$\Lambda$-type transitions. In particular, we provide detailed discussions onthe conditions for realizing electromagnetically induced transparency andAutler-Townes splitting in three-level SFQCs.

Electromagnetically induced transparency and Autler-Townes splitting in superconducting flux quantum circuits