Damping in a superconducting mechanical resonator

We study a mechanical resonator made of aluminum near the normal-tosuperconducting phase transition. A sharp drop in the rate of mechanical damping is observed below the critical temperature. The experimental results are compared with predictions based on the Bardeen Cooper Schrieffer theory of superconductivity and a fair agreement is obtained. Copyright c © EPLA, 2017 Mechanical resonators having low damping rate are widely employed for sensing and timing applications [1]. At sufficiently low temperatures such devices may allow the experimental exploration of the crossover from classical to quantum mechanics [2–8]. Commonly, the observation of non-classical effects in such experiments is possible only when the damping rate [9] of the mechanical resonator is sufficiently low. Mechanical resonators made of superconductors are widely employed in such lowtemperature experiments. In this study we experimentally investigate the effect of superconductivity on the damping rate of a mechanical resonator made of aluminum near its normal-to-superconducting phase transition. The damping rate can be measured by coupling the mechanical resonator under study to a displacement detector. In general, a variety of different mechanisms may contribute to the total mechanical damping rate. In order to isolate the effect of superconductivity it is important to employ a method of displacement detection that is unaffected by the normal-to-superconducting phase transition. In addition, systematic errors in the measured damping rate due to back-reaction effects originating from the coupling between the mechanical resonator and the displacement detector have to be kept at a sufficiently low level. In our setup (see fig. 1) we employ the so-called optomechanical cavity configuration [10–12], in which displacement detection is performed by coupling the mechanical resonator to an electromagnetic cavity. While many of the previous studies of superconducting mechanical resonators have employed such a configuration with a superconducting microwave cavity [4,6,7,13–21], our setup, which is based on a cavity in the optical band, allows displacement detection that is unaffected by the phase transition Fig. 1: (Colour online) The experimental setup. (a) A sketch of the mechanical resonator and the fiber-based optical cavity. (b) Electron micrograph of the trampoline. (c) The resonance lineshape of the fundamental mechanical mode. occurring in the mechanical resonator under study, which, in-turn, allows isolating the effect of superconductivity on the mechanical damping. Moreover, back-reaction effects are suppressed by employing a relatively low driving power to the optical cavity (see discussion below). The magnetomotive scheme has been employed for displacement detection in ref. [22] in order to study the temperature dependence of linear and nonlinear damping rates of a mechanical resonator made of aluminum near the normal to superconducting phase transition. The results indicate a significant reduction in the damping rate in the superconducting phase [22]. In our setup the optomechanical cavity is formed between two mirrors, a stationary fiber Bragg grating (FBG)