Displacement sensors that work by taking advantage of the nonlinear displacement-current relationship of an electron vacuum-tunneling probe (VTP) are theoretically analyzed in this paper. We show, using the language of electromechanical two-port transducers, that the VTP is nonreciprocal and that its noise is intrinsically quantum limited. We present a semiquantitative analysis of a VTP used to monitor the displacement of a simple mechanical harmonic oscillator and show that the Heisenberg uncertainty relation for the position and momentum of the mechanical oscillator is enforced by the noise in the VTP. The results of an optimal filter calculation of the sensitivity of the VTP-mechanical oscillator system for impulsive force detection are presented. These results are contrasted with results for a conventional capacitive transducer, and we show that the VTP may offer vastly increased sensitivity as a consequence of its nonreciprocity. The maximum sensitivity of the VTP system is calculated as a function of the temperature, the dc tunneling current, and the mass, frequency, and quality factor of the mechanical oscillator. For typical operating conditions the maximum sensitivity is obtained for small-mass systems, which makes the VTP ideal for miniature accelerometers and related devices.

• Received 5 July 1989

DOI:https://doi.org/10.1103/PhysRevA.40.6615