  We use a small atomic Bose-Einstein condensate as an interferometric scanning
probe to map out a microwave field near a chip surface with a few micrometers
resolution. Using entanglement between the atoms we overcome the standard
quantum limit of interferometry by 4 dB and maintain enhanced performance for
interrogation times up to 20 ms. This demonstrates the usefulness of quantum
metrology with entangled states when the particle number is limited due to the
small probe size. Extending atom interferometry to micrometer spatial
resolution enables new applications in electromagnetic field sensing, surface
science, and the search for fundamental short-range interactions.
