Imperfect driven Dicke model in extended systems

The driven Dicke model, with interesting quantum phases induced by parameterized driving, has been intensively studied in cavities. The confined cavity mode enables the simplification of the state space using permutation symmetry. However, such simplification might not hold in an extended system, where the system size is greater than the wavelength of the emitted photons, rendering each qubit distinguishable. Although Dicke superradiance in extended systems has been investigated recently, the driven Dicke model in extended systems has not been fully explored. Superconducting qubits coupled to a 1D waveguide, as a good example of extended systems, can simulate a perfect driven Dicke model when qubits are separated by an integer number of the wavelength of the waveguide mode. Its flexibility in addressing individual qubits facilitates a series of degrees of freedom: local dephasing, individual driving phases, separation between adjacent qubits, and individual detunings. We will present results about how these degrees of freedom affect the steady-state behavior of the driven Dicke model.