Abstract
We demonstrate the use of a compound optical cavity as linear displacement detector, by measuring the thermal motion of a silicon nitride suspended membrane acting as the external mirror of a near-infrared Littrow laser diode. Fluctuations in the laser optical power induced by the membrane vibrations are collected by a photodiode integrated within the laser, and then measured with a spectrum analyzer. The dynamics of the membrane driven by a piezoelectric actuator is investigated as a function of air pressure and actuator displacement in a homodyne configuration. The high Q-factor (~3.4 · 104 at 8.3 · 10−3 mbar) of the fundamental mechanical mode at ~73 kHz guarantees a detection sensitivity high enough for direct measurement of thermal motion at room temperature (~87 pm RMS). The compound cavity system here introduced can be employed as a table-top, cost-effective linear displacement detector for cavity optomechanics. Furthermore, thanks to the strong optical nonlinearities of the laser compound cavity, these systems open new perspectives in the study of non-Markovian quantum properties at the mesoscale.
Highlights
To estimate the sensitivity of our setup we roughly evaluated the numerical solution of equations (1) for displacements from 0 to 1 μm around the initial position
We first characterized the effect of the air pressure on the motion of the suspended mirror
The membrane was placed inside a vacuum chamber, where the internal pressure was changed from 1bar to 8.3 · 10−3 mbar
Summary
We numerically solved for the lasing modes, roughly equathree orders of magnitude smaller than TM In this case the e.m. radiation envelope can be assumed to evolve through states which verify equations (1) instantaneously[25]. This allows us to solve equations (1) for different static displacements of the membrane around its equilibrium position. The two sets of data are linearly proportional to the piezo drive, we correlated the measured displacements with the voltage readout to get a calibrated setup sensitivity:. Given the experimental ΔV(t), it is possible to define the experimental RMS displacement Δx ±δx, where δx includes different contributions coming from the laser RIN, detector noise, calibration-induced error and the error on the theoretical linear fit. A detailed explanation of the different terms is reported in section 1.3 of SI
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