Fig. 1: Time crystal with optomechanics-like coupling.
From: Continuous time crystal coupled to a mechanical mode as a cavity-optomechanics-like platform
a The CTC is formed of magnons (represented by operator \(\hat{a}\)) that are spatially trapped by the combined effect of the spin-orbit energy related to order parameter distribution (radial direction) and Zeeman energy controlled by the magnetic field profile (axial direction). The magnetic field profile H is used to move the CTC against the free surface (red blob inside the container) or within the bulk liquid (blue blob inside the container). The CTC couples to externally driven surface wave mode (represented by the position operator \(\hat{x}\)). b The precession of magnetisation within the time crystal is observed as an induced, decaying sinusoidal voltage in the pick-up coils, recorded with downconversion in frequency. c A sliding windowed fast Fourier transform (FFT) of the signal with on-resonance mechanical forcing reveals that the CTC signal is accompanied by sidebands. The sidebands result from the frequency modulation of the time crystal signal, caused by the motion of the free surface. The red dash line indicates the mean frequency of the time crystal in the limit of vanishing magnon number \({\omega }_{{{\rm{TC}}}}^{\infty }=\langle {\omega }_{{{\rm{TC}}}}(t\to \infty )\rangle\). The measurements of the optomechanical coupling are carried out in this limit. The large inset shows a snapshot of the signal (blue points), including the fitted spectrum shape (red line) and parameter values in the region where the time crystal’s frequency has ceased changing. The fit details are explained in Methods. The fundamental surface wave mode driven in this Article is depicted in the small inset.
