Displacement linear detection down to thermal fluctuations of a silicon nitride membrane with self-mixing technique*

Active optomechanical systems exploit the interaction between photons and mechanical vibrations inside a laser cavity. A compound cavity made of a laser diode and an external vibrating reflector is a suitable platform, due to its ease of construction and coupling modulation. Here we use it as a linear displacement detector, by studying the motion of a silicon nitride suspended membrane as the external mirror of a near infrared laser diode. The membrane vibrations cause fluctuations in the laser optical power, which are collected by a photodiode and measured with a spectrum analyzer. The dynamics of the membrane driven by a piezo actuator was investigated in a homodyne configuration. The high Q-factor ($\sim$ $10^5$ at low pressure) of the fundamental mechanical mode at $74$ kHz enabled direct measurement of thermal motion at room temperature, which holds an average displacement of $20$ pm. Therefore, compound cavity systems can be employed as table-top, cost-effective displacement linear detectors. Furthermore, nonlinear optomechanical interactions could be observed, with new possibilities in the study of non-Markovian quantum properties at the mesoscale.