Stimulated Emission of Terahertz Radiation from Internal ExcitonTransitions in Cu$_{2}$O*

Excitons are among the most fundamental optical excitation modes in semiconductors. Resonant infrared pulses have been used to sensitively probe absorptive transitions between hydrogen-like bound pair states [1,2]. We report the first observation of the reverse quantum process: stimulated emission of electromagnetic radiation from intra-excitonic transitions [3]. Broadband terahertz pulses monitor the far-infrared electromagnetic response of Cu$_{2}$O after ultrafast resonant photogeneration of 3$p$ excitons. Stimulated emission from the 3$p$ to the energetically lower 2$s$ bound level occurs at a photon energy of 6.6 meV, with a cross section of $\sim $10$^{-14}$ cm$^{2}$. Simultaneous excitation of both exciton levels, in turn, drives quantum beats which lead to efficient terahertz emission sharply peaked at the difference frequency. Our results demonstrate a new fundamental process of THz quantum optics and highlight analogies and differences between excitonic and atomic systems. [1] R. A. Kaindl et al., Nature \textbf{423}, 734 (2003). [2] M. Kubouchi et al., Phys. Rev. Lett. \textbf{94}, 016403 (2005). [3] R. Huber et al., Phys. Rev. Lett., to appear.