Approaching the double-Heisenberg scaling sensitivity in the Tavis-Cummings model

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 work, employing a coherent averaging mechanism, we prove that the prototypical cavity quantum electrodynamics (QED) system, such as the Tavis-Cummings 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 and superconducting circuits.