Intrinsic anharmonic effects on the phonon frequencies and effective spin-spin interactions in a quantum simulator made from trapped ions in a linear Paul trap

TL;DR

This paper investigates how anharmonic effects influence phonon frequencies and spin-spin interactions in a trapped ion quantum simulator, finding that these effects are generally small but can be significant near certain detunings.

Contribution

It provides a detailed analysis of anharmonic effects in a linear chain of trapped ions, highlighting conditions under which these effects impact quantum simulation accuracy.

Findings

Frequency shifts due to anharmonicity are typically below 0.01%.

Small anharmonic effects on spin-spin interactions for blue-detuned frequencies.

Anomalous behavior where distant spins interact more strongly than closer ones.

Abstract

The Coulomb repulsion between ions in a linear Paul trap give rise to anharmonic terms in the potential energy when expanded about the equilibrium positions. We examine the effect of these anharmonic terms on the accuracy of a quantum simulator made from trapped ions. To be concrete, we consider a linear chain of $\text{Yb}^{171+}$ ions stabilized close to the zigzag transition. We find that for typical experimental temperatures, frequencies change by no more than a factor of $0.01\%$ due to the anharmonic couplings. Furthermore, shifts in the effective spin-spin interactions (driven by a spin-dependent optical dipole force) also tend to be small for detunings to the blue of the transverse center-of-mass frequency. However, detuning the spin interactions near other frequencies can lead to nonnegligible anharmonic contributions to the effective spin-spin interactions. We also examine an odd behavior exhibited by the harmonic spin-spin interactions for a range of intermediate detunings, where nearest neighbor spins with a larger spatial separation on the ion chain interact more strongly than nearest neighbors with a smaller spatial separation.