Theory of a Quantum Scanning Microscope for Cold Atoms

TL;DR

This paper introduces a quantum scanning microscope for cold atoms that enables real-time, subwavelength imaging of atomic density and quantum states using cavity QED and continuous measurement techniques.

Contribution

It proposes a novel quantum microscope design that achieves non-demolition measurements of atomic spatial distributions and wave packet dynamics.

Findings

The microscope can monitor atomic wave packet dynamics with high temporal resolution.

It can map stationary quantum states with back-action free measurements in the good cavity limit.

The device functions as an effective quantum non-demolition measurement tool.

Abstract

We propose and analyze a scanning microscope to monitor `live' the quantum dynamics of cold atoms in a Cavity QED setup. The microscope measures the atomic density with subwavelength resolution via dispersive couplings to a cavity and homodyne detection within the framework of continuous measurement theory. We analyze two modes of operation. First, for a fixed focal point the microscope records the wave packet dynamics of atoms with time resolution set by the cavity lifetime. Second, a spatial scan of the microscope acts to map out the spatial density of stationary quantum states. Remarkably, in the latter case, for a good cavity limit, the microscope becomes an effective quantum non-demolition (QND) device, such that the spatial distribution of motional eigenstates can be measured back-action free in single scans, as an emergent QND measurement.