- The paper classifies driven quantum systems into the Kapitza, Dirac, and Dunlap-Kenkre classes, highlighting distinct deviations from the time-averaged Hamiltonian.
- It employs Magnus and high-frequency expansions to derive the Floquet Hamiltonian along with finite-frequency corrections.
- Findings pave the way for engineered Hamiltonians in quantum simulations, potentially enabling synthetic matter phases and topological states.
Analyzing High-Frequency Behavior in Periodically Driven Systems
The paper explores the high-frequency dynamics of periodically driven quantum systems, exploring the universality of these dynamics and assessing the implications for practical and theoretical advancements in quantum simulations and engineering. The work distinguishes between three classes of driving protocols under which the infinite-frequency behavior deviates from the time-averaged Hamiltonian: the Kapitza class, the Dirac class, and the Dunlap-Kenkre (DK) class. These classes extend over varied systems, including the Kapitza pendulum, the Harper-Hofstadter model, and the Haldane Floquet Chern insulator, among others.
In all configurations discussed, both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian are examined. The paper provides an overview of the foundational aspects of Floquet theory while giving due attention to the gauge structures influenced by the choice of stroboscopic frames and the distinction between stroboscopic and non-stroboscopic dynamics. In particular, it identifies how observables and a dressed density matrix must be treated within the non-stroboscopic dynamical framework.
The primary contribution of the paper is the detailed classification of periodically driven systems based on their high-frequency responses. Specifically, the research outlines:
- The Kapitza Class: Associated with a quadratic dependence on momentum in non-relativistic systems where the interaction potential or external potential is time-varying. Notably, this includes scenarios such as the stabilization of the inverted position of a pendulum through rapid periodic driving.
- The Dirac Class: Centers on systems with linear kinetic energy in momentum, typically requiring a spin structure. The paper reveals unique phenomena like dynamically induced spin-orbit coupling upon periodic driving.
- The Dunlap-Kenkre Class: Characterized by particles exhibiting arbitrary dispersion relations under periodic driving, leading to phenomena such as dynamical localization and synthetic gauge fields.
Each class's dynamical behavior is elucidated using both classical and quantum frameworks. The paper uses the Magnus and High-Frequency expansions to derive expressions for the Floquet Hamiltonian and computes leading corrections that contribute to our understanding of how these systems evolve under rapid driving.
Implications for quantum simulations include the potential for using such driving protocols to engineer effective Hamiltonians with tailored properties not easily accessible in equilibrium conditions. Practically, this paper opens pathways for experimental realizations in cold atoms and condensed matter systems, as it suggests methods for generating synthetic matter phases, topological insulators, and other exotic states through controlled driving of quantum systems.
The nuanced separation between stroboscopic and non-stroboscopic dynamics fosters insights into how different experimental setups might impact observable phenomena and measurement outcomes. For instance, observable divergences and subtle phenomena arising from stroboscopic choices underscore the necessity of careful alignment between theoretical predictions and experimental configurations.
Future directions may explore the potential for finer-grained control of quantum states using such driving protocols and further examine applications in topological materials and other quantum technologies. Enhanced understanding of periodic driving effects could advance quantum computing, communication, and simulation platforms, unlocking new potentials rooted in the controlled dynamical stabilization of quantum systems.