Evaluation of the influence of neighboring resonance on spectroscopy measurements

The quantum interference arising from neighboring resonance is investigated in a four-level system. This effect is evaluated through two methods: one is the direct numerical solution of the optical Bloch equation, and the other considers the impact of neighboring resonances as perturbations on other equations, i.e., using a simplified approximate optical Bloch equation for simulation. The results show that the energy shift caused by quantum interference is correlated with the spectral separation of two resonances, and is most significant when the interval is comparable to the spontaneous emission rate [Formula: see text]. For spectral separation that is sufficiently large, with spacing greater than [Formula: see text], the approximate optical Bloch equation method proves to be a straightforward and efficient approach. In addition, two formulas are given, which can be used to evaluate the contributions of neighboring resonances at other positions once the contribution of one is determined. According to the formulas, we evaluated the result of 4 He atom as about [Formula: see text] kHz, which is consistent with the value given in the paper [Phys. Rev. A 86 (2012) 040501(R)]. Utilizing these methods can streamline intricate energy level structures, and thus facilitate the evaluation of quantum interference in high-precision spectroscopic measurements.