Frequency-robust M{\o}lmer-S{\o}rensen gates via balanced contributions of multiple motional modes

TL;DR

This paper presents a method for designing frequency-robust Molmer-Sorensen gates in trapped ion systems by balancing motional mode contributions, enhancing robustness against frequency errors in long ion chains.

Contribution

The authors introduce a novel gate design using Gaussian amplitude modulation and constant laser frequency to achieve frequency robustness in multi-ion chains.

Findings

Achieved less than 1% fidelity reduction over 20 kHz frequency offset in a three-ion chain.

Demonstrated robustness through numerical simulations on chains of 2 to 33 ions.

Validated the technique's effectiveness for long ion chains.

Abstract

In this work, we design and implement frequency-robust Molmer-Sorensen gates on a linear chain of trapped ions, using Gaussian amplitude modulation and a constant laser frequency. We select this frequency to balance the entanglement accumulation of all motional modes during the gate to produce a strong robustness to frequency error, even for long ion chains. We demonstrate this technique on a three-ion chain, achieving $<\,1\%$ reduction from peak fidelity over a $20\,$kHz range of frequency offset, and we analyze the performance of this gate design through numerical simulations on chains of two to 33 ions.