Creation of two-dimensional Coulomb crystals of ions in oblate Paul traps for quantum simulations

Bryce Yoshimura,Danilo Dadic,Marybeth Stork,James K Freericks,Wesley C Campbell

doi:10.1140/epjqt14

Abstract

We develop the theory to describe the equilibrium ion positions and phonon modes for a trapped ion quantum simulator in an oblate Paul trap that creates two-dimensional Coulomb crystals in a triangular lattice. By coupling the internal states of the ions to laser beams propagating along the symmetry axis, we study the effective Ising spin-spin interactions that are mediated via the axial phonons and are less sensitive to ion micromotion. We find that the axial mode frequencies permit the programming of Ising interactions with inverse power law spin-spin couplings that can be tuned from uniform to with DC voltages. Such a trap could allow for interesting new geometrical configurations for quantum simulations on moderately sized systems including frustrated magnetism on triangular lattices or Aharonov-Bohm effects on ion tunneling. The trap also incorporates periodic boundary conditions around loops which could be employed to examine time crystals.

Highlights

Using a digital computer to predict the ground state of complex many-body quantum systems, such as frustrated magnets, becomes an intractable problem when the number of spins becomes too large
One successful platform for simulating lattice spin systems is the trapped ion quantum simulator, which has already been used to simulate a variety of scenarios [ – ]
4 Results that we have constructed the formal structure to determine the equilibrium positions, phonon eigenvectors, and phonon frequencies, and we have determined the total pseudopotential of the trap, we are ready to solve these systems of equations to determine the expected behavior of the trapped ions

Summary

Introduction

Using a digital computer to predict the ground state of complex many-body quantum systems, such as frustrated magnets, becomes an intractable problem when the number of spins becomes too large. In one realization [ ], ions are cooled in a trap to form a regular array known as a Coulomb crystal and the quantum state of each simulated spin can be encoded in the internal states of each trapped ion. Laser illumination of the entire crystal can be used to program the simulation (spin-spin interactions, magnetic fields, etc.) via coupling to phonon modes, and readout of the internal ion states at the end of the simulation corresponds to a projective measurement of each simulated spin on the measurement basis

Methods

Results

Conclusion