B. Yoshimura

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.

Due to the experimental time constraints of state of the art quantum simulations with trapped ions, the direct preparation of the ground state by adiabatically ramping the field of a transverse field Ising model becomes more and more difficult as the number of particles increase. We propose a spectroscopy protocol that intentionally creates excitations through diabatic ramping of the transverse field and measures a low-noise observable as a function of time for a constant field to reveal the structure of the coherent dynamics of the resulting many-body states. To simulate the experimental data, noise from counting statistics and decoherence error are added. Compressive sensing is then applied to Fourier transform the simulated data into the frequency domain and extract the the low-lying energy excitation spectrum. By using compressive sensing, the amount of data in time needed to extract this energy spectrum is sharply reduced making such experiments feasible with current technology.