Quantum-limited measurement of magnetic-field gradient with entangled atoms

We propose a method to detect the amplitude gradient of a microwave field by using a pair of entangled two-component Bose-Einstein condensates. We consider the two spatially separated condensates to be coupled to the two different magnetic fields. The magnetic-field gradient can be determined by measuring the variances of population differences and relative phases between the two-component condensates in two wells. The precision of measurement can reach the Heisenberg limit. We study the effects of one-body and two-body atom losses on the detection. We find that the entangled atoms can outperform the uncorrelated atoms in probing the magnetic fields in the presence of atom losses. The effect of atom-atom interactions is also discussed. DOI: 10.1103/PhysRevA.87.043602