Momentum noise in vacuum tunneling transducers

The vacuum tunneling probe can serve as a sensitive transducer of position into current. The performance of such a transducer is characterized by both the uncertainty in the inferred position x and the uncertainty in the momentum transfer p during the measurement. For realistic barrier parameters we find that the uncertainty product x p differs by less than 1% from Latin small letter h with stroke/2. We also calculate the expectation values of the force associated with tunneling electrons. If sufficiently sensitive force measurements can be made, this force can provide information about a surface or an absorbed atom, differing from that provided by the tunneling current.