We calculate transition amplitudes and probabilities between the coherent and Fock states of a quantum harmonic oscillator with a moving center for an arbitrary law of motion. These quantities are determined by the Fourier transform of the moving center acceleration. In the case of a constant acceleration, the probabilities oscillate with the oscillator frequency, so that no excitation occurs after every period. Examples of oscillating and rotating motion of the harmonic trap center are considered too. Estimations show that the effect of excitation of vibration states due to the motion of the harmonic trap center can be observed in available atomic traps.

中文翻译：

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激励运动的振荡器

对于任意运动定律，我们计算了一个具有移动中心的量子谐波振荡器的相干和福克状态之间的跃迁幅度和概率。这些量由运动中心加速度的傅立叶变换确定。在恒定加速度的情况下，概率随振荡器频率振荡，因此在每个周期之后都不会发生激励。还考虑了谐波陷波器中心的振荡和旋转运动的示例。估计表明，在可用的原子陷阱中，可以观察到由于谐波陷阱中心的运动而引起的振动状态激发的影响。