This work derives an analytical expression for the decoherence measure of a single-qubit ion gate based on a three-level atomic model driven by two laser fields. Under the rotating-wave approximation and large detuning conditions, an effective Raman Hamiltonian is constructed to describe the ion-laser interaction. The resulting decoherence measure captures the influence of effective detuning differences and phase shifts between the driving fields.
Fedichkin et al. (Mon,) studied this question.