Rotating wave approximation (RWA) is an approximation in quantum optics and quantum control that simplifies the Hamiltonian of a driven quantum system by discarding rapidly oscillating terms. It reduces the full time-dependent driven Hamiltonian to a simpler time-independent one in the rotating frame, making Rabi oscillations analytically tractable.
When a qubit with transition frequency $\omega_0$ is driven by an oscillating field of frequency $\omega$ near resonance, the interaction Hamiltonian in the lab frame contains terms oscillating at the slow difference frequency $\delta = \omega - \omega_0$ and the fast sum frequency $\omega + \omega_0$. Since the fast (counter-rotating) terms oscillate much faster than the dynamics of interest, they average to zero over any relevant timescale and the RWA drops them.
Moving to a frame co-rotating with the drive at frequency $\omega$ (via the transformation $\rho \to e^{i\omega t Z/2}\rho e^{-i\omega t Z/2}$), the effective Hamiltonian becomes time-independent.
$$H_{\text{RWA}} = \frac{\hbar}{2}\begin{pmatrix}-\delta & \Omega \\ \Omega & \delta\end{pmatrix}$$
Here $\delta = \omega_0 - \omega$ is the detuning and $\Omega$ is the Rabi frequency, proportional to the drive amplitude. On resonance ($\delta = 0$), this Hamiltonian generates pure Rabi oscillations between $\lvert 0\rangle$ and $\lvert 1\rangle$.
The RWA is valid when the drive is near resonance ($|\delta| \ll \omega_0$) and the Rabi frequency is much smaller than the transition frequency ($\Omega \ll \omega_0$). Both conditions ensure the counter-rotating terms oscillate fast compared to the dynamics of interest. For strongly driven systems or systems with large detuning, the counter-rotating terms contribute a small frequency shift called the Bloch-Siegert shift, which must be included for high-precision spectroscopy.