Anomalous Autler-Townes splitting in terahertz-driven quantum wells: interplay of Coulomb interactions, non-rotating wave effects and Stark shifts...


Anomalous Autler-Townes splitting in terahertz-driven quantum wells: interplay of Coulomb interactions, non-rotating wave effects and Stark shifts...

Zaks, B.; Stehr, D.; Truong, T. A.; Petroff, P. M.; Hughes, S.; Sherwin, M. S.

Semiconductor heterostructures are attractive for investigating intense light-matter interactions since the quantum energy levels and effective masses can be engineered at the growth stage, while the dimensionality of the system can be uniquely controlled by quantum confinement. With intense electromagnetic fields tuned resonantly to a two-level quantum transition, Autler and Townes found that absorption of a weak probe from a third state split into two symmetric peaks. Autler-Townes splitting has been studied in atomic and molecular systems for decades but has only recently been observed in the solid state in low dimensional semiconductors and in superconducting quantum systems. In semiconductors, effects such as Coulomb interactions between electrons and holes offer an interesting deviation from effects in atomic systems.
The Autler-Townes effect in a three-level system can be exactly calculated within the rotating wave approximation (RWA). In this model, the splitting in the absorption spectrum is symmetric when the driving frequency ωTHz is resonant with the transition frequency ω2-1. With a non-resonant driving frequency, the symmetry of the absorption spectrum is broken and the relative peak amplitudes are determined by the detuning, ωTHz - ω2-1. A positive (negative) detuning results in a larger (smaller) peak at higher energy. In the RWA model, ω2-1 is independent of the strength of the driving field.
The effect of abandoning the RWA was first studied by Bloch and Siegert in a two-level system. They found a blue shift to the energy of the two-level system ħω2-1 with increasing EM field amplitude. As the E-M field amplitude is increased in the three-level system, the amplitude of the higher energy Autler-Townes peak will decrease as a result of the Bloch-Siegert blue shift. A systematic investigation of Autler-Townes splitting for several quantum well systems demonstrated that the amplitude of the peak at higher energy increases with increasing terahertz intensity, indicating a red shift of the two-level transition energy ω2-1. At first sight this reverse Bloch-Siegert shift is a complete surprise. Only by solving a full four-subband semiconductor Bloch model outside the RWA are we able to achieve theoretical results that are in good agreement with experiment (Figure 1).We have observed large red shifts - exceeding 12% of the transition energy - in THz driven quantum wells. A non-RWA four subband model based on the full semiconductor Bloch equations including Coulomb effects was developed and calculations are shown to have excellent agreement with experimental data. We demonstrate that terahertz-driven quantum wells are an ideal system to investigate strong light-matter interactions on a quantitative level and to controllably explore the regime outside the three-level model and beyond the RWA.

Keywords: Terahertz; Semiconductor; Nonlinear Optics; Light-Matter Coupling; Free Electron Laser

  • Lecture (Conference)
    OTST 2011: International Workshop on Optical Terahertz Science and Technology 2011, 13.-17.03.2011, Santa Barbara, USA

Permalink: https://www.hzdr.de/publications/Publ-15079
Publ.-Id: 15079