NanoSQUID sensitivity for isolated dipoles and small spin populations

The sensitivity of nanoscale SQUIDs (nanoSQUIDs; SQUID: superconducting quantum interference device) to single and small populations of magnetic dipoles is considered. The simple estimate given previously for the atomic spin sensitivity of a nanoSQUID coupled to an isolated magnetic dipole at its centre is confirmed. It is demonstrated that the sensitivity is constrained in most practical situations by the finite size of the SQUID loop and nanobridges. An exact analytic result is obtained for a nanoSQUID composed of an idealized filamentary circular loop. The issue of optimum placement and orientation of the dipole with respect to the nanoSQUID hole is also considered, and it is shown that the optimum position for the dipole depends upon the height of the dipole above the plane of the nanoSQUID. It is pointed out that the conclusion quoted by previous authors, that the optimum position is above one of the Josephson junctions or Dayem bridges, although true in the limit of very narrow bridges with tight magnetic coupling, is not true in general, and estimates of the potential sensitivity when the dipole is placed in this region based on simple filamentary models are likely to overestimate the sensitivity achievable in practice.