L. P. H. Gallagher

We study the occurrence of long-lived metastable states in the 4f$^{13}$5d6s electron configuration of Yb$^+$. By optical pumping of a single trapped ion on the $^2F^\text{o}_{7/2}\rightarrow (7/2,0)_{7/2}$ transition at 377.5 nm, we prepare a wide range of metastable electronic states. We use a co-trapped control ion to sympathetically cool the spectroscopy ion, allowing us to accurately time its subsequent decay. We record a strong decay signal corresponding to a lifetime of 0.92(8) s, a weaker decay signal with lifetime 9.8(+2.9, -2.0) s, and find evidence for a much longer lifetime, $>$ 30 s. We identify the metastable states with these lifetimes qualitatively, and corroborate our results with atomic structure calculations that support the observed lifetimes and decay paths. These long-lived states provide new opportunities in qubit and qudit state detection and optical clocks.

Tightly-focused laser beams, or optical tweezers, are essential for analogue and digital quantum simulation with neutral atoms and trapped ions. Despite this, most of the current intuition and theoretical treatment utilizes the paraxial approximation, which breaks down at the focus of optical tweezers. We develop an analytic model, which we use in tandem with numerical simulations, to quantify how non-paraxial effects will manifest in the next-generation of scalable quantum hardware, where tightly focused beams are used for individual qubit control. In particular, we calculate the light potentials of Gaussian and Laguerre-Gaussian beams driving the quadrupole $^2$S$_{1/2}\rightarrow$ $^2$D$_{5/2}$ transition in $^{40}$Ca$^+$. Longitudinal field components in the beam center cause spatially-dependent Rabi frequencies and AC Stark shifts, leading to unexpected qubit-motion coupling. We characterize single- and two-qubit gate infidelities due to this effect with an analytic model and numerical simulation. We identify regimes where non-paraxial effects should be taken into account for high-precision quantum control. Finally, we highlight that non-paraxial effects are potentially more severe in the case of neutral atom and molecule addressing.

We consider the quantum simulation of quadratic spin-phonon coupling in a crystal of trapped ions. The coupling is implemented using tightly focused optical tweezers on each ion that change the local trapping potential in a state-dependent way. By encoding spins in the internal states of the ions and adding a tunneling term via Mølmer-Sørensen-type interactions, we calculate the emergence of mobile bipolarons driven by the zero-point energy of the ion crystal phonons. We show that thermal occupation may pin the bipolarons for ion crystals at finite temperature. Our scheme can be used to study and illustrate the emergence of mobile bipolarons as a function of temperature.

This paper presents a routine to align an optical tweezer on a single trapped ion and use the ion as a probe to characterize the tweezer. We find a smallest tweezer waist of $2.3(2)\,μ$m, which is in agreement with the theoretical minimal attainable waist of $2.5(2)\,μ$m in our setup. We characterize the spatial dependence of the tweezer Rabi frequency which is suppressed by a factor of 19(3) in the immediate surrounding of the ion. We investigate the effects of optical forces and coherent population trapping on the ion. Finally, we show that the challenges posed by these forces can be overcome, and that the number of tweezers can be easily scaled up to reach several ions by using a spatial light modulator.