Phase-modulated spin-motional decoupling with trapped ions

We present a technique to minimize residual spin-motional entanglement after a phonon-mediated entangling gate in trapped $^{171}\textrm{Yb}^{+}$ ion qubits. Phonon-mediated gates, such as the Mølmer-Sørensen gate, engineer spin-spin entanglement by coupling the qubits to their collective modes of motion. Consequently, a major experimental limitation is residual motional entanglement at the conclusion of the gate, resulting in a degradation of the final spin state purity. Our work utilizes phase-modulated pulse sequences to decouple the qubits from multiple motional modes simultaneously at a variable gate time. In addition, we extend this technique to the suppression of time-dependent noise using concatenated gate sequences, which allows for the recovery of a higher purity spin state. Using a single, experimentally controllable modulation parameter we are able to achieve more optimal quantum control in these gate sequences.