The absorption of multiple photons when there is no resonant intermediate state is a well-known nonlinear process in atomic vapours, dyes and semiconductors. The N-photon absorption (NPA) rate for donors in semiconductors scales proportionally from hydrogenic atoms in vacuum with the dielectric constant and inversely with the effective mass, factors that carry exponents 6N and 4N, respectively, suggesting that extremely large enhancements are possible. We observed 1PA, 2PA and 3PA in Si:P with a terahertz free-electron laser. The 2PA coefficient for 1s–2s at 4.25 THz was 400,000,000 GM (=4 × 10⁻⁴² cm⁴ s), many orders of magnitude larger than is available in other systems. Such high cross-sections allow us to enter a regime where the NPA cross-section exceeds that of 1PA—that is, when the intensity approaches the binding energy per Bohr radius squared divided by the uncertainty time (only 3.84 MW cm⁻² in silicon)—and will enable new kinds of terahertz quantum control.

在没有共振中间态时吸收多个光子是原子蒸气，染料和半导体中众所周知的非线性过程。半导体中给体的N光子吸收（NPA）速率与真空中的氢原子成比例，介电常数成比例，与有效质量成反比，分别具有6 N和4 N指数，这表明可能有极大的增强。我们用太赫兹自由电子激光在Si：P中观察到1PA，2PA和3PA。在4.25 THz时1 s –2 s的2PA系数为400,000,000 GM（= 4×10 ^-42  cm ⁴ s），比其他系统可用的数量级大许多数量级。如此高的横截面使我们能够进入NPA横截面超过1PA的状态，也就是说，当强度接近每玻尔半径的结合能的平方除以不确定时间（硅中只有3.84 MW cm ^{- 2}时） ），并将启用新型的太赫兹量子控制。