Synthesizing a $\hat{\sigma}_z$ spin-dependent force for optical, metastable, and ground state trapped-ion qubits

TL;DR

This paper presents a comprehensive theoretical and experimental study of a scheme to generate a $_z$ spin-dependent force in trapped-ion qubits using a bichromatic field, demonstrating its robustness and versatility across different qubit states.

Contribution

It expands previous work by thoroughly investigating the scheme with a near-resonant laser in $^{88}$Sr$^+$ and demonstrating entanglement across various qubit states.

Findings

Successfully synthesized a $_z$ spin-dependent force.

Demonstrated robustness to optical phase and qubit frequency offsets.

Entangled optical, metastable, and ground state qubits.

Abstract

A single bichromatic field near-resonant to a qubit transition is typically used for $\hat{\sigma}_x$ or $\hat{\sigma}_y$ M{\o}lmer-S{\o}rensen type interactions in trapped ion systems. Using this field configuration, it is also possible to synthesize a $\hat{\sigma}_z$ spin-dependent force by merely adjusting the beat-note frequency. Here, we expand on previous work and present a comprehensive theoretical and experimental investigation of this scheme with a laser near-resonant to a quadrupole transition in $^{88}$Sr$^+$. Further, we characterise its robustness to optical phase and qubit frequency offsets, and demonstrate its versatility by entangling optical, metastable, and ground state qubits.