Theoretical basis for quantum simulation with a planar ionic crystal in a Penning trap using a triangular rotating wall

TL;DR

This paper provides a theoretical framework for improving quantum simulation in Penning trap ion crystals by using anharmonic potentials and a triangular rotating wall to achieve more uniform ion spacing and more predictable spin-spin interactions.

Contribution

It introduces a method to enhance uniformity in ion spacing in Penning traps, leading to more consistent spin-spin interactions for quantum simulation.

Findings

More uniform ion spacing achieved with anharmonic and triangular rotating wall potentials.

Spin-spin interactions behave more like a power law with improved uniformity.

Enhanced control over quantum simulation properties in Penning trap systems.

Abstract

One of the challenges with quantum simulation in ion traps is that the effective spin-spin exchange couplings are not uniform across the lattice. This can be particularly important in Penning trap realizations where the presence of an ellipsoidal boundary at the edge of the trap leads to dislocations in the crystal. By adding an additional anharmonic potential to better control interion spacing, and a triangular shaped rotating wall potential to reduce the appearance of dislocations, one can achieve better uniformity of the ionic positions. In this work, we calculate the axial phonon frequencies and the spin-spin interactions driven by a spin-dependent optical dipole force, and discuss what effects the more uniform ion spacing has on the spin simulation properties of Penning trap quantum simulators. Indeed, we find the spin-spin interactions behave more like a power law for a wide range of parameters.