 Rabi vector

For a rotating-frame two-state Hamiltonian operator $H=\hslash \mathbf{W}\cdot \mathbf{\sigma }/2$, the Bloch vector obeys $\dot{\mathbf{R}}=\mathbf{W}\times \mathbf{R}$. Thus $\mathbf{W}$ specifies a rotation axis and angular speed. With detuning defined as drive frequency minus transition frequency and the lower state at positive $R_z$, a phase-zero transverse drive can give $\mathbf{W}=(\Omega ,0,\delta )$. Changing basis or detuning convention requires changing the corresponding signs consistently.