Temperature mediated back-action in micro- and nanomechanical resonators

Abstract: We theoretically investigate the thermally induced back-action effects in absorption-sensitive micro- and nanomechanical resonators. We propose a unified approach, enabling to simultaneously address both the effective dynamics and non-equilibrium phononic state, depending on the position of a punctual sensing (and heating) probe at the surface of the mechanical device. We present an analytical solution in terms of green functions for a unidimensional resonator whose thermomechanical deformation profile generally follows that of the mechanical losses. In particular, we find that both the dynamics and the mechanical fluctuations strongly depend on the loss distribution. The effect of the quantum fluctuations of the heat source is also discussed. Our approach provides the first steps towards a thorough, general platform for analyzing thermal back-action effects and their consequences, which may be of significance for future development in ultrasensitive nanomechanical research.