Coherent photons and macroscopic cat states generated by a cyclic artificial atom with broken symmetry

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