Diffraction-Unlimited Position Measurement of Ultracold Atoms in an Optical Lattice

We consider a method of high-fidelity, spatially resolved position measurement of ultracold atoms in an optical lattice. We show that the atom-number distribution can be nondestructively determined at a spatial resolution beyond the diffraction limit by tracking the progressive evolution of the many-body wavefunction collapse into a Fock state. We predict that the Pauli exclusion principle accelerates the rate of wavefunction collapse of fermions in comparison with bosons. A possible application of our principle of surpassing the diffraction limit to other imaging systems is discussed.