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

Influence of kinetic energy on the metrology of Rabi frequency