Figure 3. Broken sign-preserving selection rule.

(a) Spectrum of the qubit-resonator system at high driving power. Multi-photon transitions to higher-photon number dressed states are visible below the resonance at 8 GHz. Above 12 GHz, the blue sideband |0, g〉 ↔ |2, −〉 can be clearly observed, together with an additional weaker resonance. The latter corresponds to |1, −〉 ↔ |2, +〉, breaking the sign-preserving selection rule. The transition disappears away from the symmetry point due to the decrease of the coupling strength with the mixing angle in equation (16), and the increase of dephasing rate of the qubit⁴¹,⁴⁶,⁴⁷. (b) Spectroscopy trace at the symmetry point of (a). Above 12 GHz, the transition |1, −〉 ↔ |2, +〉 is visible as a peak in switching probability.