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

Abstract

We propose and experimentally demonstrate an analog scheme for generating XY-type (J_{ij}^{x}σ_{x}^{i}σ_{x}^{j}+J_{ij}^{y}σ_{y}^{i}σ_{y}^{j}) Hamiltonians on trapped ion spins with independent control over the J_{ij}^{x} and J_{ij}^{y} terms. The Ising-type interactions σ_{x}^{i}σ_{x}^{j} and σ_{y}^{i}σ_{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}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.