Electromagnetically induced transparency with amplification in superconducting circuits.

We show that controlling relative phases of electromagnetic fields driving an atom with a Δ-configuration energy-level structure enables optical susceptibility to be engineered in novel ways. In particular, relative-phase control can yield electromagnetically induced transparency but with the benefit that the transparency window is sandwiched between an absorption and an amplification band rather than between two absorption bands in typical electromagnetically induced transparency. We show that this new phenomenon is achievable for a microwave field interacting with a fluxonium superconducting circuit.