  The pursuit of quantum-enhanced parameter estimations without the need for
nonclassical initial states has long been driven by the goal of achieving
experimentally accessible quantum metrology. In this paper, employing a
coherent averaging mechanism, we prove that the prototypical cavity-quantum
electrodynamics (QED) system, such as the Tavis-Cummings (TC) model, enables us
to achieve not only the Heisenberg scaling (HS) precision in terms of the
average photon number but also the double-HS sensitivity concerning both the
average photon and atom numbers. Such a double sensibility can be
experimentally realized by introducing either photon- or atom-number
fluctuations through quantum squeezing. Furthermore, we discuss the methodology
to achieve this double-HS precision in a realistic experimental circumstance
where the squeezing is not perfect. Our results provide insights into
understanding the coherent averaging mechanism for evaluating quantum-enhanced
precision measurements and also present a usable metrological application of
the cavity QED systems.
