Deterministic preparation of entangled Dicke states

Deterministic preparation of entangled many-body states is a fundamental challenge in quantum information and precision metrology. While Dicke states—permutation-symmetric states with a fixed number of excitations—are valuable resources for quantum sensing, existing methods often rely on probabilistic postselection or heralding. This paper addresses the need for a deterministic, Hamiltonian-based approach to generate these states without postselection.

The authors propose a protocol using an ensemble of atoms or qubits coupled to a dispersive cavity. By applying a coherent transverse drive and utilizing the off-resonant cavity to mediate an effective collective-spin interaction, the system's Hamiltonian can be tuned. The protocol uses adiabatic ground-state interpolation: starting from a spin-coherent product state (the ground state of the transverse drive), the drive strength is ramped down while the cavity-mediated interaction is ramped up. By programming the atom-drive detuning, the researchers can target any specific Dicke state along the symmetric Dicke ladder.

The study demonstrates that this detuning-programmed approach successfully prepares target Dicke states, including the central Dicke state (m=0). Numerical simulations confirm that the system follows the instantaneous ground-state branch, approaching the target state with high fidelity as the ramp time increases. The authors show that the prepared central Dicke state is particularly useful for quantum-enhanced rotation sensing, achieving Heisenberg-limited scaling (delta-theta proportional to 1/N). This protocol is well-suited for implementation in superconducting circuit QED architectures, where such collective interactions and control have already been experimentally realized.

This work provides a robust, deterministic pathway to engineer multipartite entanglement in many-body systems. By converting the Dicke ladder from a passive decay pathway into a programmable manifold, the protocol enables the creation of pure entangled states that are ready for use in quantum metrology. This integration of state engineering and collective quantum optics offers a scalable route to improving the precision of quantum sensors.