  We propose a novel method to generate non-classical states of a single-mode
microwave field, and to produce macroscopic cat states by virtue of a
three-level system with $\Delta$-shaped (or cyclic) transitions. This exotic
system can be implemented by a superconducting quantum circuit with a broken
symmetry in its effective potential. Using the cyclic population transfer,
controllable single-mode photon states can be created in the third transition
when two classical fields are applied to induce the other two transitions. This
is because, for large detuning, two classical fields are equivalent to an
effective external force, which derives the quantized single mode. Our approach
is valid not only for superconducting quantum circuits but also for any
three-level quantum system with $\Delta$-shaped transitions
