Intraexciton transitions in semiconductor quantum wells are modulated by strong and tunable few-cycle terahertz pulses. Time-resolved terahertz-pump and optical-probe measurements demonstrate that the 1s heavy-hole and light-hole exciton resonances undergo large-amplitude spectral modulations when the terahertz radiation is tuned near the 1s-2p intraexciton transition. The strong nonlinear optical transients exhibit the characteristics of Rabi sidebands. The spectral features also reveal the dephasing properties of the optically dark 2p states. A microscopic theory shows that the 2p-dephasing rate is three times that of the 1s-state. The ultrafast nonlinear optical effects and their quantum nature suggest promising applications to ultrahigh-speed optical signal processing and quantum information processing in the THz region. (C) 2010 Elsevier Ltd. All rights reserved.