Quantum electrodynamic uncertainty relations for magnetic flux measurements in circuits

Abstract

The magnetic flux sensitivity in electrical circuits is discussed in the time domain. It is shown that the quantum electrodynamic uncertainty principle implies that measurements of the magnetic flux at two different times interfere. Thus, an initial measurement of flux, at time t1, to within Delta phi (t1) will induce a random back EMF which will affect the uncertainty Delta phi (t2) of the flux measurement at a later time t2. The authors derive the 'interference' rule that Delta phi (t1) Delta phi (t2)>or=(h(cross)/2) mod G(t1,t2) mod , where G(t1,t2) describes the transient circuit response in flux to a weak current source impulse. As an example, this rule is applied to the case of a current-fed, singly connected Josephson weak link to give an expression for the minimum measurement uncertainty in the weak link critical current.