Generating synthetic magnetism via Floquet engineering auxiliary qubits in phonon-cavity-based lattice

Gauge magnetic fields have a close relation to breaking time-reversal symmetry in condensed matter. In the presence of the gauge fields, we might observe nonreciprocal and topological transport. Inspired by these, there is a growing effort to realize exotic transport phenomena in optical and acoustic systems. However, due to charge neutrality, realizing analog magnetic flux for phonons in nanoscale systems is still challenging in both theoretical and experimental studies. Here we propose a novel mechanism to generate synthetic magnetic field for phonon lattice by Floquet engineering auxiliary qubits. We find that, a longitudinal Floquet drive on the qubit will produce a resonant coupling between two detuned acoustic cavities. Specially, the phase encoded into the longitudinal drive can exactly be transformed into the phonon-phonon hopping. Our proposal is general and can be realized in various types of artificial hybrid quantum systems. Moreover, by taking surface-acoustic-wave (SAW) cavities for example, we propose how to generate synthetic magnetic flux for phonon transport. In the presence of synthetic magnetic flux, the time-reversal symmetry will be broken, which allows one to realize the circulator transport and analog Aharonov-Bohm effects for acoustic waves. Last, we demonstrate that our proposal can be scaled to simulate topological states of matter in quantum acoustodynamics system.