Programmable XY-type couplings through parallel spin-dependent forces on the same trapped ion motional modes

TL;DR

This paper introduces a method to generate programmable XY-type spin interactions in trapped ions using parallel spin-dependent forces, enabling exploration of complex quantum phases.

Contribution

The paper presents an experimental scheme for independently controlling XY-type couplings in trapped ions, extending quantum simulation capabilities beyond Ising interactions.

Findings

Successfully demonstrated XY-type interactions with trapped ions.

Validated the scheme through numerical and experimental results.

Extended the range of accessible quantum Hamiltonians for simulation.

Abstract

We propose and experimentally demonstrate an analog scheme for generating XY-type ($J_{ij}^x \sigma_x^i \sigma_x^j \;$ + $J_{ij}^y \sigma_y^i \sigma_y^j \;$) Hamiltonians on trapped ion spins with independent control over the $J_{ij}^x$ and $J_{ij}^y$ terms. The Ising-type interactions $\sigma_x^i \sigma_x^j \;$ and $\sigma_y^i \sigma_y^j \;$ are simultaneously generated by employing two spin-dependent forces operating in parallel on the same set of normal modes. We analytically calculate the region of validity of this scheme, and provide numerical and experimental validation with $^{171}\rm{Yb}^+\;$ ions. This scheme inherits the programmability and scalability of the Ising-type interactions with trapped ions that have been explored in numerous quantum simulation experiments. Our approach extends the capabilities of existing trapped ion quantum simulators to access a large class of spin Hamiltonians relevant for exploring exotic quantum phases such as superfluidity and spin liquids.