Paul Hamilton

We present a spectroscopic investigation of $^{169}\mathrm{Tm}^+$ that provides two key foundations for its use as a platform for advanced quantum applications. First, we establish the complete spectroscopic road map for optical cycling (including laser cooling) by performing high-resolution spectroscopy on $^{169}\mathrm{Tm}^+$ ions in an ion trap. We characterize the primary $313\,\mathrm{nm}$ and complementary $448/453\,\mathrm{nm}$ cycling transitions, identify the essential near-infrared repumping frequencies, and determine the magnetic-dipole hyperfine $A$ constants for all relevant levels. Second, we report a detailed characterization of a metastable state as a candidate for hosting a robust qubit, performing lifetime measurements and Zeeman-resolved microwave hyperfine spectroscopy with $\mathrm{kHz}$ precision.

We perform entanglement of spin and motional degrees of freedom of a single, ground-state trapped ion through the application of a $16$ ps laser pulse. The duration of the interaction is significantly shorter than both the motional timescale ($30$ $μ$s) and spin precession timescale ($1$ ns) , demonstrating that neither sets a fundamental speed limit on this operation for quantum information processing. Entanglement is demonstrated through the collapse and revival of spin coherence as the spin components of the wavefunction separate and recombine in phase space. We infer the fidelity of these single qubit operations to be $(97^{+3}_{-4})\%$.

Laser-controlled entanglement between atomic qubits (`spins') and collective motion in trapped ion Coulomb crystals requires conditional momentum transfer from the laser. Since the spin-dependent force is derived from a spatial gradient in the spin-light interaction, this force is typically longitudinal -- parallel and proportional to the average laser $k$-vector (or two beams' $k$-vector difference), which constrains both the direction and relative magnitude of the accessible spin-motion coupling. Here, we show how momentum can also be transferred perpendicular to a single laser beam due to the gradient in its transverse profile. By controlling the transverse gradient at the position of the ion through beam shaping, the relative strength of the sidebands and carrier can be tuned to optimize the desired interaction and suppress undesired, off-resonant effects that can degrade gate fidelity. We also discuss how this effect may already be playing an unappreciated role in recent experiments.