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Chinese Physics B

Optical absorption and electromagnetically induced transparency in semiconductor quantum well driven by intense terahertz field

Hongwei Wu, Xianwu Mi

Published Oct 1, 2012• 4 citations
Publisher

Abstract

An approach for solving the excitonic absorption in a semiconductor quantum well driven by an intense terahertz field is presented. The formalism relies on the stationary single-photon Schrodinger equation in the full quantum mechanical framework. The optical absorption dynamics in both weak and strong couplings are discussed and compared. The excitonic absorption spectra show the Autler—Townes doublets for the resonance terahertz field, a replica peak for the non-resonance terahertz field, and the electromagnetically induced transparency phenomenon for modulating the decay rate of the second electron state in the weak coupling. In particular, the electromagnetically induced transparency phenomenon window range is discussed. In the strong coupling region, the multi-order energy level resonance splitting due to the strong optical field is found. There are three (non-resonance terahertz field) or four (resonance terahertz field) peaks in the optical absorption spectra. This work provides a simple and convenient approach to deal with the optical absorption in the exciton system.

DOI
10.1088/1674-1056/21/10/107102

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An approach for solving the excitonic absorption in a semiconductor quantum well driven by an intense terahertz field is presented. The formalism relies on the stationary single-photon Schrodinger equation in the full quantum mechanical framework. The optical absorption dynamics in both weak and strong couplings are discussed and compared. The excitonic absorption spectra show the Autler—Townes doublets for the resonance terahertz field, a replica peak for the non-resonance terahertz field, and the electromagnetically induced transparency phenomenon for modulating the decay rate of the second electron state in the weak coupling. In particular, the electromagnetically induced transparency phenomenon window range is discussed. In the strong coupling region, the multi-order energy level resonance splitting due to the strong optical field is found. There are three (non-resonance terahertz field) or four (resonance terahertz field) peaks in the optical absorption spectra. This work provides a simple and convenient approach to deal with the optical absorption in the exciton system.
Optical interband excitonic absorption of semiconductor quantum wells (QW’s) driven by a coherent pump field is investigated on the basis of semiconductor Bloch equations. The pump field has a photon energy close to the intersubband spacing between the first two conduction subbands in the QW’s. An external weak optical field probes the interband transition. The excitonic effects and pump-induced population redistribution within the conduction subbands in the QW system are included. When the density of the electron–hole pairs in the QW structure is low, the pump field induces an Autler–Townes splitting of the exciton absorption spectrum. The split size and the peak positions of the absorption doublet depend not only on the pump frequency and intensity but also on the carrier density. As the density of the electron–hole pairs is increased, the split contrast (the ratio between the maximum and the minimum values) is decreased, because the exciton effect is suppressed at higher densities owing to the many-body screening.
Nonlinear optical properties of intersubband electrons in a 3-level quantum well under intense terahertz field are investigated by using a density matrix approach. The results show that the terahertz fields with different frequencies cause the distinct modulations of the intersubband absorptions. The terahertz-induced sideband and Autler–Towns splitting in the absorption spectrum are obtained, respectively for the terahertz-photon energy below and close to the transition energy between the ground and first excited state.
An analytical solution of the optical susceptibility of quantum wells driven by a terahertz (THz) field is achieved based on the density-matrix formalism. A simplified three-level model is adopted for the quantum well structures, with the levels coupled by a near-infrared (NIR) and a THz field. The equation of motion for the polarization is derived from Liouville's equation for the density matrix. Using Floquet's theorem, and under the rotating-wave approximation with respect to the NIR probe field, analytical expression for the optical susceptibility of the driven quantum wells is obtained. Different features rising induced by the driving THz field in the absorption spectrum of the NIR probe are discussed for the THz field near resonance and out of resonance of the intraexcitonic transition. This analytical investigation of the susceptibility of the THz-field-driven quantum wells is much useful for clearly identifying the physical principles obscured in the full numerical calculations.
The phenomenon of electromagnetically induced quantum coherence is demonstrated between three confined electron subband levels in a quantum well which are almost equally spaced in energy. Applying a strong coupling field, two-photon resonant with the 1-3 intersubband transition, produces a pronounced narrow transparency feature in the 1-2 absorption line. This result can be understood in terms of all three states being simultaneously driven into "phase-locked" quantum coherence by a single coupling field. We describe the effect theoretically with a density matrix method and an adapted linear response theory.
Electromagnetically induced transparency (EIT) in terahertz (THz) metamaterials relies on the coherent coupling between a radiative (bright) mode and a subradiant (dark) mode. Understanding the dynamic interplay between the bright and dark modes holds the key to manipulate the mutual interference and hence the transparency. Here, we use nonlinear 2D-THz spectroscopy to scrutinize the dynamics through nonlinearities of the EIT-like phenomenon in a metamaterial platform that comprises of two coupled resonators. From the temporal profiles of the nonlinear pump-probe and photon-echo signals, we found that the bright mode relaxation time is almost twice the time for the coherent exchange of energy between the two coupled resonators. The multi-peak nature of photon-echo signal and the corresponding temporal signatures further provides a direct visualization of the interference between the dressed states that drives the transparency window in our THz metamaterial. A time-resolved density matrix model accurately describes the observed features, including the cross-peak behavior and the temporal dynamics, establishing the coherent mode coupling as the origin of the transparency window.
Electromagnetically induced transparency (EIT) and Autler–Townes splitting (ATS) are two similar yet distinct phenomena that modify the transmission of a weak probe field through an absorption medium in the presence of a coupling field, featured in a variety of three-level atomic systems. In many applications it is important to distinguish EIT from ATS splitting. We present EIT and ATS spectra in a three-level cascade system, involving cold cesium atoms in the Rydberg state. The EIT linewidth, γ EIT , defined as the full width at half maximum of the transparency window, and the ATS splitting, γ ATS , defined as the peak-to-peak distance between AT absorption peaks, are used to delineate the EIT and ATS regimes and to characterize the transition between the regimes. In the cold-atom medium, in the weak-coupler (EIT) regime γ EIT ≈ A + B ( + , where Ω c and Ω p are the coupler and probe Rabi frequencies, Γ eg is the spontaneous decay rate of the intermediate 6P 3/2 level, and parameters A and B that depend on the laser linewidth. We explore the transition into the strong-coupler (ATS) regime, which is characterized by the relation γ ATS ≈ Ω c . The experiments are in agreement with numerical solutions of the Master equation. Our analysis accounts for non-ideal conditions that exist in typical realizations of Rydberg-EIT, including laser-frequency jitter, Doppler mismatch of the utilized two-color Rydberg EIT system, and strong probe fields. The obtained criteria to distinguish cold-atom EIT from ATS are readily accessible and applicable in practical implementations.