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

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.

11 pages, 9 figures, typeset in RevTex

References in corpus (8)

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Cited by in corpus (7)

• Simulating generic spin-boson models with matrix product states
• Boson-mediated quantum spin simulators in transverse fields: XY model and spin-boson entanglement
• Sideband cooling of small ion Coulomb crystals in a Penning trap
• Site-resolved imaging of beryllium ion crystals in a high-optical-access Penning trap with inbore optomechanics
• Individual-Ion Addressing and Readout in a Penning Trap
• The Effect of Micromotion and Local Stress in Quantum simulation with Trapped Ions in Optical Tweezers
• Adiabatic Cooling of Planar Motion in a Penning Trap Ion Crystal to Sub-Millikelvin Temperatures