  Entanglement preparation and signal accumulation are essential for quantum
parameter estimation, which pose significant challenges to both theories and
experiments. Here, we propose how to utilize chaotic dynamics in a periodically
driven Bose-Josephson system for achieving a high-precision measurement beyond
the standard quantum limit (SQL). Starting from an initial non-entangled state,
the chaotic dynamics generates quantum entanglement and simultaneously encodes
the parameter to be estimated. By using suitable chaotic dynamics, the ultimate
measurement precision of the estimated parameter can beat the SQL. The sub-SQL
measurement precision scaling can also be obtained via specific observables,
such as population measurements, which can be realized with state-of-art
techniques. Our study not only provides new insights for understanding quantum
chaos and quantum-classical correspondence, but also is of promising
applications in entanglement-enhanced quantum metrology.
