John Bollinger

Ion Coulomb crystals are ordered structures formed by laser-cooled ions in traps that are characterized by interparticle distances of several micrometers and energy scales on the order of $μ$eV. Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter in the strongly correlated regime and at low temperatures where their dynamics is manifestly quantum mechanical. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. We discuss their dynamical and thermodynamic properties in one, two, and three dimensions, and review recent investigations into their out-of-equilibrium behavior. We provide outlooks on future directions for exploring novel condensed matter phenomena with trapped ion crystals, as well as for exploiting these features for scientific and technical applications.

We propose the use of phonon$\unicode{x2013}$mediated interactions as an entanglement resource to engineer Einstein$\unicode{x2013}$Podolsky$\unicode{x2013}$Rosen (EPR) correlations and to perform teleportation of collective spin states in two$\unicode{x2013}$dimensional ion crystals. We emulate continuous variable quantum teleportation protocols between subsystems corresponding to different nuclear spin degrees of freedom. In each of them, a quantum state is encoded in an electronic spin degree of freedom that couples to the vibrational modes of the crystal. We show that high fidelity teleportation of spin-coherent states and their phase-displaced variant, entangled spin-squeezed states, and Dicke states, is possible for realistic experimental conditions in arrays from a few tens to a few hundred ions.

We propose a highly feasible technique with no experimental overhead to rapidly cool the in-plane degrees of freedom of large two-dimensional ion crystals in Penning traps. Through simulations, we demonstrate that our approach enables the in-plane modes to cool down to a temperature of around 1 mK in less than 10 ms. Our technique relies on near-resonant coupling of the poorly cooled in-plane motions and the efficiently cooled out-of-plane motions, and is achieved without introducing additional potentials. The rapid cooling enabled by our approach is in contrast to typical operating conditions, where our simulations of the laser cooling dynamics suggest that the ion crystal's in-plane motion cools very slowly on a timescale of several hundreds of milliseconds, a rate likely slower than experimental heating rates. Our work sets the stage for sub-Doppler laser cooling of the planar motion, and more robust and versatile quantum simulation and quantum sensing experiments with two-dimensional crystals in Penning traps.

Trapped ions offer a pristine platform for quantum computation and simulation, but improving their coherence remains a crucial challenge. Here, we propose and analyze a new strategy to enhance the coherent interactions in trapped ion systems via parametric amplification of the ions' motion--by squeezing the collective motional modes (phonons), the spin-spin interactions they mediate can be significantly enhanced. We illustrate the power of this approach by showing how it can enhance collective spin states useful for quantum metrology, and how it can improve the speed and fidelity of two-qubit gates in multi-ion systems, important ingredients for scalable trapped ion quantum computation. Our results are also directly relevant to numerous other physical platforms in which spin interactions are mediated by bosons.