  Quantum sensing improves the accuracy of measurements of relevant parameters
by exploiting the unique properties of quantum systems. The divergent
susceptibility of physical systems near a critical point for quantum phase
transition enables criticality-enhanced quantum sensing. The quantum Rabi model
(QRM), composed of a single qubit coupled to a single bosonic field, represents
a good candidate for realizing such critical enhancement for its simplicity,
but it is experimentally challenging to achieve the ultrastrong qubit-field
coupling required to realize the critical phenomena. In this work, we explore
an alternative to construct the analog of the QRM for the sensing, exploiting
the criticality appearing in the Jaynes-Cummings (JC) model whose bosonic field
is parametrically driven, not necessitating the ultrastrong coupling condition
thus to some extent relaxing the requirement for the practical implementation.
