The vacuum tunneling probe used in the scanning tunneling microscope represents a new class of nonreciprocal electromechanical transducers. Nonreciprocity implies reduced back action and consequently increased sensitivity over conventional, reciprocal transducers. A vacuum tunneling probe may reach the quantum limit for a measurement of the position of a macroscopic mechanical oscillator even with use of a non-quantum-limited amplifier. The quantum limit is enforced by the momentum shot noise associated with the tunneling current.
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.
Displacement transducers based upon quantum mechanical tunneling of electrons can potentially achieve a sensitivity far superior to conventional transducers. The reason for this is that the dynamical influence of the tunneling transducer on a test mass is insignificant compared to that of traditional capacitive, inductive or piezoelectric transducers. Thus the fluctuating ‘‘back action’’ force from electrical noise in the tunneling transducer is nearly eliminated. The ‘‘back action’’ force becomes dominant as the test mass is miniaturized, thus the tunneling transducer may be especially useful in micro-fabricated sensors. In this paper we present an equivalent circuit model for a tunneling transducer including noise and outline a method for calculating the minimum detectable signal in any given application. We also discuss some practical limits for tunneling-based sensors.
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