Tunable $\mathrm{\Lambda }$-type system made of a superconducting qubit pair

Two transversely coupled and resonant qubits form symmetric and antisymmetric states as their eigenstates. In this paper, we show that parametric modulation of an individual qubit enables direct Rabi swapping between the two states. Its application to setup a $\mathrm{\Lambda }$-type system with a pair of strongly coupled superconducting transmon qubits is discussed. The excited state is made of the symmetric state and the metastable state is the antisymmetric state. The coherence of the metastable state is only limited by the pure dephasing mechanism. Based on this scheme, $\mathrm{\Lambda }$-type electromagnetically induced transparency, Autler-Townes splitting and stimulated Raman adiabatic passage are numerically demonstrated. We highlight the large frequency tunability in such superconducting $\mathrm{\Lambda }$-type systems.