Terahertz nonlinear optics using intraexcitonic quantum well transitions: sideband generation and AC Stark splitting

Intense THz electric fields coupling to intraband excitations can modify the interband absorption of semiconductors. A classical nonlinear mixing process is the sideband generation, where a ps NIR laser beam is mixed with the THz beam to generate sidebands at ωNIR ± n × ωTHz (integer n). In an undoped GaAs/AlGaAs multi quantum well film (substrate etched away) we observe several even-order sidebands using an all-normal-incidence geometry for the NIR and THz laser pulses [1]. Varying THz and NIR frequencies, we identify several resonances, where the intraexciton 1s-2p transition (at ~9 meV) makes the strongest contribution. Fig. 1(a) shows a typical NIR transmission spectrum with the NIR fundamental at the hh(1s) state and the resulting even-order sidebands.
In a second experiment we monitor the sample’s broadband transmission under THz pumping. THz light can couple and “dress” two resonant states, giving rise to the Autler-Townes or AC Stark effect [2, 3]. Fig. 1(b) shows the measured transmission spectra without (dashed line) and with (solid line) THz light at a THz peak intensity of 220 kW/cm² for THz pumping above (14 meV), near (10.5 meV) and below (6.1 meV) resonance. Near resonance (10.5 meV) we observe a distinct line splitting (see arrows), which represents the first clear evidence of the Autler-Townes effect in an intraexcitonic transition. Above and below resonance, low- and high-energy shoulders, respectively, are observed (see arrows). We discuss our findings on the basis of a simple two-level model that describes the situation surprisingly well near resonance up to a THz field strength of 10 kV/cm, corresponding to a Rabi energy of 0.6 times the 1s-2p transition energy. This is already well beyond the rotating-wave approximation of our model. Observed deviations would have to be addressed within a full many-body theory dealing with the complete set of excitonic states as well as with the possibility of exciton field ionization. Note that for the above parameters the ponderomotive energy is 3 meV, comparable to the exciton transition/ionization energy and the Rabi energy, an extremely non-perturbative regime with a Keldysh parameter near unity.

References:

[1] M. Wagner et al., Appl. Phys. Lett. 94, 241105 (2009).
[2] S. H. Autler and C. H. Townes, Phys. Rev. 100, 703 (1955).
[3] S. G. Carter et al., Science 310, 651 (2005).