QUANTUM-THEORY OF CORRELATED-ATOMIC-POSITION MEASUREMENTS BY RESONANCE IMAGING

Recently demonstrated methods for resonance imaging of moving atoms in the potential due to a spatially varying light shift have yielded spatial resolution of 200 nm, with linearity of a few percent over several micrometers. With single-atom detection and a potential uncertainty-principle Limited resolution of a few nanometers, this method can be used to perform spatial correlation experiments in beams and traps, with ultrahigh spatial resolution. In this paper we present a theoretical treatment for methods to extend the resonance imaging technique to include position measurements of moving atoms at multiple points, and thereby to measure appropriately defined multiatom correlation functions which depend generally on both position and momentum. Results are given for both fermions and bosons and simple examples show how correlated position measurement by resonance imaging reveals the atomic statistical properties at the long length scales which arise at low temperature.