Optical super-resolution sensing of a trapped ion's wave packet size

TL;DR

This paper presents a super-resolution optical sensing method for measuring the wave packet size of a single trapped ion, extending the ground state depletion technique into the coherent regime for high-precision quantum measurements.

Contribution

The authors adapt the ground state depletion imaging technique for coherent regimes to measure quantum wave packet sizes of trapped ions with nanometer precision.

Findings

Achieved a spatial resolution of 4.2 μm in the depletion beam.

Measured a wave packet size of 39 nm for a near ground state cooled ion.

Results agree with independent sideband spectroscopy measurements.

Abstract

We demonstrate super-resolution optical sensing of the size of the wave packet of a single trapped ion. Our method extends the well known ground state depletion (GSD) technique to the coherent regime. Here, we use a hollow beam to strongly saturate a coherently driven dipole-forbidden transition around a sub-diffraction limited area at its center and observe state dependent fluorescence. By spatially scanning this laser beam over a single trapped $^{40}\mathrm{Ca}^+$ ion, we are able to measure the wave packet sizes of cooled ions. Using a depletion beam waist of $4.2(1)\,\mu$m we reach a spatial resolution which allows us to determine a wave packet size of $39(9)\,$nm for a near ground state cooled ion. This value matches an independently deduced value of $32(2)\,$nm, calculated from resolved sideband spectroscopy measurements. Finally, we discuss the ultimate resolution limits of our adapted GSD imaging technique in view of applications to direct quantum wave packet imaging.