Pinning an Ion with an Intracavity Optical Lattice

We report one-dimensional pinning of a single ion by an optical lattice. A standing-wave cavity produces the lattice potential along the rf-field-free axis of a linear Paul trap. The ion’s localization is detected by measuring its fluorescence when excited by standing-wave fields with the same period, but different spatial phases. The experiments agree with an analytical model of the localization process, which we test against numerical simulations. For the best localization achieved, the ion’s average coupling to the cavity field is enhanced from 50% to 81(3)% of its maximum possible value, and we infer that the ion is bound in a lattice well with over 97% probability.

Figure 1

Left: Relevant levels in ${}^{40}\mathrm{Ca}^{+}$. An ion in the metastable $D_{3/2}$ state is pinned by a far-detuned lattice field (thick arrows). A near-detuned probe field (thin arrows) tests the ion’s position distribution. The dominant scattering process is inelastic scattering to the $S_{1/2}$ dark state, producing observable 397 nm fluorescence (wavy arrow). Right: Position-dependent $D_{3/2}$ and $P_{1/2}$ energy levels of the ion on the cavity axis. Intracavity standing waves can be either in-phase or out-of-phase (shading) with the periodic potential for $D_{3/2}$, suppressing or enhancing fluorescence for a pinned ion. Lattice Stark shifts also affect the probe detuning (vertical arrows).

Figure 2

Comparisons of model predictions (lines) to molecular dynamics simulations (symbols). Upper graph: Initial thermal position distribution (gray Gaussian) and final position distribution in the lattice (black line and symbols). Lower graph: Distributions of total energy (teal line, circles) and lattice potential (black solid line, squares), measured relative to the local trap potential. Note logarithmic vertical scale. The simulations use typical experimental parameters, with a 5 mK initial temperature and a 24 mK final lattice depth.

Figure 3

Solid symbols: probability to scatter a lattice photon as a function of lattice depth for red- and blue-detuned lattices (squares and circles respectively). Solid curves: one-free-parameter model fit. Open symbols: probability to scatter a photon during lattice ramp-up. Dashed lines: model prediction.

Figure 4

Solid symbols: combined scattering probability for blue-detuned probe and lattice fields separated by 15 (blue circles) and 16 (green squares) cavity free spectral ranges. Open symbols: scattering probability from the lattice alone. Curves: two-free-parameter fit.