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Register a new userNutation dynamics and multifrequency resonance in a many-body seesaw
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The multifrequency resonance has been widely explored in some of the single-particle models, in which the modulating Rabi model has been most widely investigated. It has been found that with the diagonal periodic modulation, a steady dynamics can be realized in some well-defined discrete frequencies. These frequencies are independent of the 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 almost be 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 a new thought about the multifrequency resonance in the many-body system.
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Periodic driving has emerged as a powerful experimental tool to engineer physical properties of isolated, synthetic quantum systems. However, due to the lack of energy conservation and heating effects, non-trivial (e.g., topological) many-body states in periodically driven (Floquet) systems are generally metastable. Therefore it is necessary to find strategies for preparing long-lived many-body states in Floquet systems. We develop a theoretical framework for describing the dynamical preparation of states in Floquet systems by a slow turn-on of the drive. We find that the dynamics of the system is well approximated by the initial state evolving under a slowly varying effective Hamiltonian $H_{rm eff}^{(s)}(t)$, provided the ramp speed $s gg t_*^{-1} sim e^{-{mathcal{C} frac{omega}{J}}}$, the inverse of the characteristic heating time-scale in the Floquet system. At such ramp speeds, the heating effects due to the drive are exponentially suppressed. We compute the slowly varying effective Hamiltonian $H_{rm eff}^{(s)}(t)$, and show that at the end of the ramp it is identical to the effective Hamiltonian of the unramped Floquet system, up to small corrections of the order $O(s)$. Therefore, the system effectively undergoes a slow quench from $H_0$ to $H_{rm eff}$. As an application, we consider the passage of the slow quench through a quantum critical point (QCP), and estimate the energy absorbed due to the non-adiabatic passage through the QCP via a Kibble-Zurek mechanism. By minimizing the energy absorbed due to both the drive and the ramp, we find an optimal ramp speed $s_* sim t_*^{-z/({d+2z})}$ for which both heating effects are exponentially suppressed. Our results bridge the gap between the numerous proposals to obtain interesting systems via Floquet engineering, and the actual preparation of such systems in their effective ground states.
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