  The effectiveness of self-mixing interferometry has been demonstrated across
the electromagnetic spectrum, from visible to microwave frequencies, in a
plethora of sensing applications, ranging from distance measurement to material
analysis, microscopy and coherent imaging. Owing to their intrinsic stability
to optical feedback, quantum cascade lasers (QCLs) represent a source that
offers unique and versatile characteristics to further improve the self-mixing
functionality at mid infrared and terahertz (THz) frequencies. Here, we show
the feasibility of detecting with nanometer precision deeply subwalength (<
{\lambda}/6000) mechanical vibrations of a suspended Si3N4-membrane used as the
external element of a THz QCL feedback interferometric apparatus. Besides
representing a platform for the characterization of small displacements, our
self-mixing configuration can be exploited for the realization of
optomechanical systems, where several laser sources can be linked together
through a common mechanical microresonator actuated by radiation pressure.
