Quadrupole transitions and quantum gates protected by continuous dynamic decoupling

TL;DR

This paper presents a method for protecting quantum states in trapped ions using nested continuous dynamical decoupling, enabling prolonged coherence and potential integration with quantum gates for advanced quantum information processing.

Contribution

It provides a compact theoretical framework for nested continuous dynamical decoupling in trapped ions, including effective transition parameters and rules, facilitating the combination with quantum gate operations.

Findings

Effective transition frequencies and Rabi rates derived

Selection rules for dressed states established

Feasibility of combining decoupling with quantum gates discussed

Abstract

Dynamical decoupling techniques are a versatile tool for engineering quantum states with tailored properties. In trapped ions, nested layers of continuous dynamical decoupling by means of radio-frequency field dressing can cancel dominant magnetic and electric shifts and therefore provide highly prolonged coherence times of electronic states. Exploiting this enhancement for frequency metrology, quantum simulation or quantum computation, poses the challenge to combine the decoupling with laser-ion interactions for the quantum control of electronic and motional states of trapped ions. Ultimately, this will require running quantum gates on qubits from dressed decoupled states. We provide here a compact representation of nested continuous dynamical decoupling in trapped ions, and apply it to electronic $S$ and $D$ states and optical quadrupole transitions. Our treatment provides all effective transition frequencies and Rabi rates, as well as the effective selection rules of these transitions. On this basis, we discuss the possibility of combining continuous dynamical decoupling and M{\o}lmer-S{\o}rensen gates.