Emergent Schr\"{o}dinger cat states during superradiant phase transitions

Superradiant phase transitions (SPTs) are important for understanding light-matter interactions at the quantum level [1, 2], and play a central role in criticality-enhanced quantum sensing [3]. So far, SPTs have been observed in driven-dissipative systems [4-9], but the emergent light fields did not show any nonclassical characteristic due to the presence of strong dissipation. Here we report an experimental demonstration of the SPT featuring the emergence of a highly nonclassical photonic field, realized with a resonator coupled to a superconducting qubit, implementing the quantum Rabi model [10, 11]. We fully characterize the light-matter state by Wigner matrix tomography. The measured matrix elements exhibit quantum interference intrinsic of a photonic Schr\"{o}dinger cat state [12], and reveal light-matter entanglement. Besides their fundamental importance, these hitherto unobserved emergent quantum phenomena are useful for quantum metrology and fault-tolerant quantum computation.Comment: 19 pages, 14 figures, 2 table