Detection of AC magnetic signals by parametric mode coupling in a mechanical oscillator

Abstract

Parametric coupling has been demonstrated between mechanical vibration modes in a magnet-tipped microcantilever. An external magnetic field, coupled to the magnetic tip, pumps the effective spring constant at a frequency which is either the sum or the difference of the mode resonance frequencies. The presence of the pump field can be detected by driving one mode and observing the parametrically pumped excitation of the other mode, even though the pump frequency is off-resonance with respect to both mechanical modes. In a room temperature experimental realization, the magnetic flux coupling the pump field to the tip was approximately one flux quantum and the dominant noise source was the thermal vibration of the cantilever. Parametric mode coupling is a useful new design option in magnetic resonance force microscopy, whereby modulation is advantageously performed off-resonance to avoid parasitic excitations caused by stray couplings. Parametric coupling also provides a low-noise technique for amplifying mechanical oscillations. The reported experiment completes the set of all possible force microscope interaction Hamiltonians up to third order in time-dependent fields.