We present a deterministic protocol for the preparation of entangled states in the symmetric Dicke subspace of $N$ spins coupled to a common cavity mode that prepares entangled states useful for quantum sensing, achieving a precision significantly better than the standard quantum limit in the presence of photon cavity loss, spontaneous emission and dephasing. The protocol combines a new geometric phase gate which can be utilized for exact unitary synthesis on the Dicke subspace, an analytic solution of the noisy quantum channel dynamics and optimal control methods. This Letter opens the way to entanglement-enhanced sensing with cold trapped atoms in cavities and is extendable to other spin systems coupled to a bosonic mode.

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• Cavity quantum electrodynamics
• Coherent control
• Quantum optics
• Quantum sensing
• Quantum state engineering
• Quantum cavities
• Trapped atoms