The scanning tunneling microscope as a high-gain, low-noise displacement sensor

Abstract

We consider the capabilities of the tunneling probe of the scanning tunneling microscope as a displacement sensor as distinguished from its better established application to surface imaging. Electromechanical transducers that operate on this principle can achieve very large gain and a noise temperature equal to the minimum required by quantum mechanics for any linear amplifier. We present a two-port network representation of the tunneling transducer, including noise, that allows us to discuss the differences between the tunneling transducer and more conventional electromechanical transducers and to draw analogies between a tunneling transducer and a transistor. We present a simple equivalent circuit for the tunneling transducer including two uncorrelated noise generators, the tunneling current shot noise and the fluctuating force that the tunneling probe exerts on a test mass. In practice the fluctuating ‘‘back action’’ force spectral density is exceedingly small. We give an example of a system in which a tunneling transducer is used to monitor the motion of a very small mechanical harmonic oscillator. A transducer gain of approximately 108 should be achieved in this system that makes negligible the noise contribution of conventional following electronics. The contribution to the noise of the tunneling transducer itself should be near the quantum limit and the most significant remaining source of noise is the mechanical oscillator’s Brownian motion. The tunneling transducer represents a new approach for measuring mechanical displacements and may profoundly influence transducer technology in applications from gravity wave detectors down to measurements on single molecules.