A protocol to create a multi-particle entangled state for quantum-enhanced sensing

We propose a protocol for generating multi-particle entangled states using coherent manipulation of atoms trapped in an optical cavity. We show how entanglement can be adiabatically produced with two control beams and by exploiting cavity-mediated interactions between the atoms. Our methods will allow for optimal generation of entanglement for the measurement protocol we propose. We discuss a possible experimental implementation and compare the performance of the states produced with those of classical states and ideal maximally-entangled Dicke states. We find that our states always feature metrological gain and even outperform ideal Dicke states in the measurement of magnetic field gradients. Due to the easy scalability, our entanglement protocol is a promising tool for quantum state engineering.