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 Heisenberg scaling (HS) precision in terms of the average photon number but also double-HS sensitivity concerning both the average photon and atom numbers. Such 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.