Deterministic preparation of entangled Dicke states
Dicke states $|J=N/2,m\rangle$ of a collection of $N$ atoms were central to Dicke's theory of superradiance. Except for the fully polarized end states, they are entangled many-body states; in particular, the single-excitation Dicke state is the W state well known in quantum information science. However, deterministic preparation of Dicke states with a prescribed spin projection remains challenging, especially without relying on postselection or heralding. Here we present a detuning-programmed Hamiltonian protocol using atoms or qubits in a dispersive cavity subject to a coherent transverse drive. In the absence of the drive, the off-resonant cavity produces an effective collective-spin interaction. By combining this cavity-mediated interaction with the coherent drive, tuning the atom--drive detuning enables the protocol, in principle, to target any allowed Dicke state along the symmetric Dicke ladder. Starting from the transverse-drive ground state, adiabatic ground-state interpolation prepares the selected Dicke state by ramping down the drive strength while ramping up the cavity-mediated interaction. After preparation, tuning the cavity into resonance with the atoms or qubits provides a direct way to probe the collective-emission response of the prepared Dicke state. We discuss implementation with superconducting circuit QED and show that the prepared states, especially the central Dicke state with $m=0$, provide resources for quantum sensing with Heisenberg-limited scaling.