Marcel Morillas-Rozas

We propose a fast laser pulse sequence for the generation of non-thermal Fock state mixtures of the motion of a trapped ion, targeted at displacement metrology beyond the standard quantum limit. Using a polaron-frame description of the ion-laser interaction, we identify a resonant operating point-zero detuning and a Rabi frequency matching the trap frequency-at which selective population trapping survives strong driving, enabling preparation speeds beyond the weak-driving limit of previous protocols without requiring ground-state cooling. We trace the residual infidelity at large Lamb-Dicke parameter $η$ to a single coherent process, the counter-rotating blue-sideband term neglected in the rotating-wave approximation, and show that it is suppressed by two routine calibrations: a percent-level refocusing of the pulse duration and a small compensating Bloch-Siegert detuning. Numerical simulations of the full sequence show that this refinement keeps the preparation error at or below the $10\%$ level up to $η\approx0.5$ and restores the displacement-sensing Fisher information that the uncorrected protocol loses at strong coupling, recovering up to 9 dB relative to the nominal sequence.

Conventional laser control schemes for cooling and gate operation of trapped ions are limited to the regime of weak laser intensities and small Lamb-Dicke parameters. To overcome this limitation, we present the concept of dark polarons: spatially extended states of pseudospin polarization that are fully decoupled from a lambda laser configuration. In this picture, all high-order Lamb-Dicke terms collapse into a single linear coupling independent of laser intensity. We apply it to definitively elucidate the reasons behind cooling rate limitations observed in recent experimental implementations of electromagnetically induced transparency with high-intensity lasers.