We consider a two-level quantum system interacting with two classical time-periodic electromagnetic fields. The frequency of one of the fields far exceeds that of the other. The effect of the high-frequency field can be averaged out of the dynamics to realize an effective transition frequency of the field-dressed two-level system. We examine the linear response, second harmonic response and Stokes and anti-Stokes Raman response of the dressed two-level system, to the weak frequency field. The vibrational resonance enhancement in each case is demonstrated for optimal strength of the high-frequency field. Our theoretical scheme is corroborated by full numerical simulation of the two-level, two-field dynamics governed by loss-free Bloch equations. We suggest that quantum optics can offer an interesting arena for the study of the vibrational resonance. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

中文翻译：

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驱动两能级量子系统中的振动共振，线性和非线性响应

我们考虑与两个经典时间周期电磁场相互作用的两级量子系统。其中一个场的频率远远超过另一个。高频场的影响可以从动力学中平均出来，以实现场修整两能级系统的有效跃迁频率。我们检查了修整的双能级系统对弱频率场的线性响应、二次谐波响应以及斯托克斯和反斯托克斯拉曼响应。每种情况下的振动共振增强都证明了高频场的最佳强度。我们的理论方案得到了由无损 Bloch 方程控制的两级、两场动力学的完整数值模拟的证实。我们建议量子光学可以为研究振动共振提供一个有趣的领域。