Effects of the Bloch-Siegert Oscillation on the Precision of Qubit Rotations: Direct Two-Level vs. Off-Resonant Raman Excitation

In a direct two-level qubit system, when the Rabi frequency is comparable to the resonance frequency, the rotating wave approximation is not appropriate. In this case, the Rabi oscillation is accompanied by another oscillation at twice the frequency of the driving field, the so called Bloch-Siegert oscillation (BSO), which depends on the initial phase of the driving field. This oscillation may restrict the precise rotation of a qubit made of direct two-level system. Here, we show that in case of an effectively two-level lambda system, the BSO is inherently negligible, implying a greater precision for rotation of a qubit made of such a lambda system when compared to a direct two-level qubit in a strong driving field.