Influence of kinetic energy on the metrology of Rabi frequency

The interacting model describing the Rabi transition is essential in studying atom-photon interactions, where the kinetic energy term is often neglected for the convenience of analysis. We first study the approximation through the fidelity approach and verify its valid region in the parameter space of detuning and momentum. We find that as the radiation field's momentum and the absolute value of detuning decrease, the approximation becomes valid. We further discover that the omission of the kinetic energy term will overestimate the measuring accuracy of the Rabi frequency in some parameter regions and underestimate the precision in other regimes with Fisher information tools' help. Notably, a specific choice of the initial Gaussian state's variance in position space will improve the measuring accuracy when we take the kinetic energy term into account. We also study the realistic measurement of the Rabi frequency for cases with and without the kinetic energy.