  Quantum sensing is inevitably an elegant example of the supremacy of quantum
technologies over their classical counterparts. One of the desired endeavors of
quantum metrology is AC field sensing. Here, by means of analytical and
numerical analysis, we show that integrable many-body systems can be exploited
efficiently for detecting the amplitude of an AC field. Unlike the conventional
strategies in using the ground states in critical many-body probes for
parameter estimation, we only consider partial access to a subsystem. Due to
the periodicity of the dynamics, any local block of the system saturates to a
steady state which allows achieving sensing precision well beyond the classical
limit, almost reaching the Heisenberg bound. We associate the enhanced quantum
precision to closing of the Floquet gap, resembling the features of quantum
sensing in the ground state of critical systems. We show that the proposed
protocol can also be realized in near-term quantum simulators, e.g. ion-traps,
with a limited number of qubits. We show that in such systems a simple block
magnetization measurement and a Bayesian inference estimator can achieve very
high precision AC field sensing.
