Optical Selection Rules and Phase-Dependent Adiabatic State Control in a Superconducting Quantum Circuit

We analyze the optical selection rules of the microwave-assisted transitions in a flux qubit superconducting quantum circuit (SQC). We show that the parities of the states relevant to the superconducting phase in the SQC are well defined when the external magnetic flux Φe=Φ0/2; then the selection rules are the same as the ones for the electric-dipole transitions in usual atoms. When Φe≠Φ0/2, the symmetry of the potential of the artificial 'atom' is broken, a so-called Δ-type 'cyclic' three-level atom is formed, where one- and two-photon processes can coexist. We study how the population of these three states can be selectively transferred by adiabatically controlling the electromagnetic field pulses. Different from Λ-type atoms, the adiabatic population transfer in our three-level Δ atom can be controlled not only by the amplitudes but also by the phases of the pluses