The multifrequency resonance has been widely explored in the context of single-particle models, of which the modulating Rabi model has been the most widely investigated. It has been found that with diagonal periodic modulation, steady dynamics can be realized in some well-defined discrete frequencies. These frequencies are independent of off-diagonal couplings. In this work, we generalize this physics to the many-body seesaw realized using the tilted Bose–Hubbard model. We find that the wave function will recover to its initial condition when the modulation frequency is commensurate with the initial energy level spacing between the ground and the first excited levels. The period is determined by the driving frequency and commensurate ratio. In this case, the wave function will be almost exclusively restricted to the lowest two instantaneous energy levels. By projecting the wave function to these two relevant states, the dynamics is exactly the same as that for the spin precession dynamics and nutation dynamics around an oscillating axis. We map out the corresponding phase diagram, and show that, in the low-frequency regime, the state is thermalized, and in the strong modulation limit, the dynamics is determined by the effective Floquet Hamiltonian. The measurement of these dynamics from the mean position and mean momentum in phase space are also discussed. Our results provide new insights into multifrequency resonance in the many-body system.

在单粒子模型的背景下，对多频共振进行了广泛的探索，其中对调制Rabi模型的研究最为广泛。已经发现，利用对角线周期性调制，可以在一些明确定义的离散频率中实现稳定的动态。这些频率与非对角线耦合无关。在这项工作中，我们将这种物理学推广到使用倾斜的Bose-Hubbard模型实现的多体跷跷板。我们发现，当调制频率与地面和第一激发能级之间的初始能级间隔相称时，波函数将恢复到其初始状态。周期由驱动频率和相称比率确定。在这种情况下，波动函数将几乎只限于最低的两个瞬时能级。通过将波动函数投影到这两个相关状态，其动力学特性与围绕旋转轴的自旋进动动力学和章动动力学完全相同。我们绘制了相应的相位图，并显示出，在低频状态下，状态被热化，在强调制极限下，动力学由有效的Floquet哈密顿量决定。还讨论了根据相空间中的平均位置和平均动量来测量这些动力学的方法。我们的结果为多体系统中的多频共振提供了新的见解。动力学与旋转轴上的自旋进动动力学和章动动力学完全相同。我们绘制了相应的相位图，并显示出，在低频状态下，状态被热化，在强调制极限下，动力学由有效的Floquet哈密顿量决定。还讨论了根据相空间中的平均位置和平均动量来测量这些动力学的方法。我们的结果为多体系统中的多频共振提供了新的见解。动力学与旋转轴上的自旋进动动力学和章动动力学完全相同。我们绘制了相应的相位图，并显示出，在低频状态下，状态被热化，在强调制极限下，动力学由有效的Floquet哈密顿量决定。还讨论了根据相空间中的平均位置和平均动量来测量这些动力学的方法。我们的结果为多体系统中的多频共振提供了新的见解。还讨论了根据相空间中的平均位置和平均动量来测量这些动力学的方法。我们的结果为多体系统中的多频共振提供了新的见解。还讨论了根据相空间中的平均位置和平均动量来测量这些动力学的方法。我们的结果为多体系统中的多频共振提供了新的见解。