Giant multiphoton absorption for THz resonances in silicon hydrogenic donors

• Published in: Nature photonics Vol. 12; no. 3; pp. 179 - 184
• Main Authors: van Loon, M. A. W., Stavrias, N., Le, Nguyen H., Litvinenko, K. L., Greenland, P. T., Pidgeon, C. R., Saeedi, K., Redlich, B., Aeppli, G., Murdin, B. N.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 01-03-2018; Nature Publishing Group
• Subjects: 140/125; 639/624/399/1099; 639/624/400/385; 639/624/400/561; Absorption; Applied and Technical Physics; Cross-sections; Dielectric constant; Multiphoton absorption; Photon absorption; Photons; Physics; Physics and Astronomy; Quantum Physics; Semiconductors; Silicon; Vacuum
• ISSN: 1749-4885; 1749-4893
• DOI: 10.1038/s41566-018-0111-x

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 6
N
and 4
N
, 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 1
s
–2
s
at 4.25 THz was 400,000,000 GM (=4 × 10
−42
 cm
4
 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.
By using a terahertz free-electron laser, multiphoton transitions between impurity states in p-doped Si are investigated. The two- and three-photon integrated absorption cross-sections are found to be the highest ever reported for a discrete oscillator system.