Fig. 2: The mechanical mode.
From: Continuous time crystal coupled to a mechanical mode as a cavity-optomechanics-like platform
a The frequency modulation amplitude \(G=g{\theta }_{\max }^{2}\) of the bulk time crystal measured as a function of the mechanical forcing frequency ωexc. The solid lines are fits to a driven and damped harmonic oscillator response, from which the resonance frequency and width of the mechanical surface wave mode are determined. The thermometer fork width Δf relative to the intrinsic width Δf0 of the device for the two data sets is given in the legend. In the shown temperature interval the on-resonance amplitude G remains approximately constant despite exponentially increasing resonance width, suggesting that coupling increases with the same exponent as a function of temperature. Here, unlike other measurements in this Article, the magnon number was kept constant by applying continuous pumping to an excited state in the confining trap10, as extremely long lifetime of bulk time crystal makes pulsed spectral measurements impractical. b Data measured for the surface time crystal are extracted from the end of the decay after an RF excitation pulse, where the time crystal’s frequency has stopped changing. c The extracted width of the surface wave resonance (points) scales linearly with the the thermometer fork resonance width (solid line). This confirms that the damping of the mechanical mode that is coupled to the time crystal mainly originates from scattering of thermal excitations in the superfluid. The y-axis intercept corresponds to the mechanical mode dissipation in the absence of superfluid thermal excitations, which may be caused by friction on the container walls or by the edge states bound to the free surface of the topological superfluid68.
