Quantum Scanning Microscope for Cold Atoms

TL;DR

This paper provides a detailed theoretical framework for a cavity QED-based atomic scanning microscope capable of nondestructively imaging atomic densities with subwavelength resolution by exploiting internal atomic dark states and quantum measurement techniques.

Contribution

It introduces a novel theoretical model connecting homodyne detection signals with atomic densities, enabling continuous quantum nondemolition measurements of atomic states.

Findings

Achieves subwavelength resolution in atomic density imaging.

Establishes a quantum nondemolition measurement regime.

Relates homodyne current to local atomic density.

Abstract

We present a detailed theoretical description of an atomic scanning microscope in a cavity QED setup proposed in Phys. Rev. Lett. 120, 133601 (2018). The microscope continuously observes atomic densities with optical subwavelength resolution in a nondestructive way. The super-resolution is achieved by engineering an internal atomic dark state with a sharp spatial variation of population of a ground level dispersively coupled to the cavity field. Thus, the atomic position encoded in the internal state is revealed as a phase shift of the light reflected from the cavity in a homodyne experiment. Our theoretical description of the microscope operation is based on the stochastic master equation describing the conditional time evolution of the atomic system under continuous observation as a competition between dynamics induced by the Hamiltonian of the system, decoherence effects due to atomic spontaneous decay, and the measurement backaction. Within our approach we relate the observed homodyne current with a local atomic density, and discuss the emergence of a quantum nondemolition measurement regime allowing continuous observation of spatial densities of quantum motional eigenstates without measurement backaction in a single experimental run.