Harnessing quantum chaos in spin-boson models for all-purpose quantum-enhanced sensing

Quantum chaotic systems have great potential for sensing since they can rapidly generate highly entangled states in time scales faster than typical decoherence and technique noise. In this spirit, we study the Dicke model -- a paradigmatic quantum model featuring chaos -- that describes a uniform coupling between an ensemble of qubits and a single bosonic mode. We systematically map out the quantum Fisher information (QFI) as a function of system parameters, and identify that the chaotic dynamics generated by the Dicke Hamiltonian generically leads to quantum states that are delocalized over the accessible phase space and are robust resources for sensing spin rotations or bosonic displacements without fine tuning of the associated axis or direction, respectively. To overcome the challenges associated with exploiting the complex entangled states generated by the chaotic evolution, such as requirements to measure high-order correlation functions or distribution functions, we develop a set of interferometric protocols based on interaction-based readout and time-reversal echoes. We identify optimal echoes and parameter regimes that enable us to nearly saturate the fundamental quantum Cramer-Rao bound on the sensitivity using only simple spin observables. Furthermore, we investigate the robustness of our approach to technical noise and imperfections that are associated with current state-of-the-art experimental setups. Our proposal opens new opportunities to exploit complex entangled states rapidly generated by chaotic nonlinear dynamics for the next-generation of quantum-enhanced sensors.