  We study electromagnetically induced interference at superconducting qubits.
The interaction between qubits and electromagnetic fields can provide
additional coupling channels to qubit states, leading to quantum interference
in a microwave driven qubit. In particular, the interwell relaxation or Rabi
oscillation, resulting respectively from the multi- or single-mode interaction,
can induce effective crossovers. The environment is modeled by a multi-mode
thermal bath, generating the interwell relaxation. Relaxation induced
interference, independent of the tunnel coupling, provides deeper understanding
to the interaction between the qubits and their environment. It also supplies a
useful tool to characterize the relaxation strength as well as the
characteristic frequency of the bath. In addition, we demonstrate the
relaxation can generate population inversion in a strongly driving two-level
system. On the other hand, different from Rabi oscillation, Rabi oscillation
induced interference involves more complicated and modulated photon exchange
thus offers an alternative means to manipulate the qubit, with more
controllable parameters including the strength and position of the tunnel
coupling. It also provides a testing ground for exploring nonlinear quantum
phenomena and quantum state manipulation, in not only the flux qubit but also
the systems with no crossover structure, e.g. phase qubits.
