Theory of coherent two-photon resonance

A theory of coherent two-photon resonance is developed by applying a canonical transformation on the Heisenberg equation of atomic motion. The theory leads both to the optical Bloch equation and the second-order induced polarization which drives the classical Maxwell's equation. The expressions for the Rabi frequency and the induced polarization are given explicitly for two-photon absorption and Raman effect. The results are applied to coherent steady-state propagation, and two kinds of pulses are derived for different-frequency two-photon absorption, including the atomic frequency shift.