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 and the uncertainty in the momentum transfer during the measurement. For realistic barrier parameters we find that the uncertainty product differs by less than 1% from /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.