Floquet topological system based on frequency-modulated classical coupled harmonic oscillators

Abstract

We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency-modulation of the different oscillators. We illustrate how the topologically-protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.

15 pages, 9 figures

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• Synthetic Dimensions for Cold Atoms from Shaking a Harmonic Trap
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• Spin-orbit coupling in a hexagonal ring of pendula
• Experimental demonstration of dynamical input isolation in nonadiabatically modulated photonic cavities
• Floquet engineering of optical nonlinearities: a quantum many-body approach
• Floquet-engineered nonlinearities and controllable pair-hopping processes: From optical Kerr cavities to correlated quantum matter
• Dynamical Detection of Topological Spectral Density
• Synthetic Mechanical Lattices with Synthetic Interactions
• Non-dispersive one-way signal amplification in sonic metamaterials
• Topological phonons in arrays of ultracold dipolar particles
• Omnidirectional spin Hall effect in a Weyl spin-orbit coupled atomic gas
• Oscillating states of periodically driven anharmonic Langevin systems
• Non-Bloch band theory for time-modulated discrete mechanical systems
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