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Science

Quantum Coherence in an Optical Modulator

Sam Carter, Victoria Birkedal, C.S. Wang, L.A. Coldren, Alexey V. Maslov, David S. Citrin, Mark S. Sherwin

Published Oct 27, 2005• 120 citations
Publisher

Abstract

Semiconductor quantum well electroabsorption modulators are widely used to modulate near-infrared (NIR) radiation at frequencies below 0.1 terahertz (THz). Here, the NIR absorption of undoped quantum wells was modulated by strong electric fields with frequencies between 1.5 and 3.9 THz. The THz field coupled two excited states (excitons) of the quantum wells, as manifested by a new THz frequency- and power-dependent NIR absorption line. Nonperturbative theory and experiment indicate that the THz field generated a coherent quantum superposition of an absorbing and a nonabsorbing exciton. This quantum coherence may yield new applications for quantum well modulators in optical communications.

DOI
10.1126/science.1116195

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Semiconductor quantum well electroabsorption modulators are widely used to modulate near-infrared (NIR) radiation at frequencies below 0.1 terahertz (THz). Here, the NIR absorption of undoped quantum wells was modulated by strong electric fields with frequencies between 1.5 and 3.9 THz. The THz field coupled two excited states (excitons) of the quantum wells, as manifested by a new THz frequency- and power-dependent NIR absorption line. Nonperturbative theory and experiment indicate that the THz field generated a coherent quantum superposition of an absorbing and a nonabsorbing exciton. This quantum coherence may yield new applications for quantum well modulators in optical communications.
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.
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.
The manipulation of visible and near-infrared light at the single-photon level plays a key role in quantum communication systems where information is encoded into photonic degrees of freedom. In practical implementations, it is important to achieve this manipulation with high speeds, low loss, and low noise. In this Letter, we propose the use of terahertz electric fields as a pump source for electro-optic modulation of single photons in bulk media. We demonstrate spectral modulations of single photons in the form of frequency translation and bandwidth manipulations as the terahertz field imparts linear and quadratic phases on the photons at various time delays within 1 ps. Our results show frequency translations exceeding 500 GHz at multi-THz modulation speeds and loss levels of ≈1 dB, complementing the current state-of-the-art electro-optic modulation techniques limited to speeds up to 100 GHz. The proposed approach leverages recent developments in terahertz generation techniques, introducing new avenues to manipulate nonclassical light in an unexplored regime for quantum photonics.
Quantum-well excitons dressed by a terahertz field have multiple optical resonances. An optical beam tuned to any of the resonant frequencies excites the dressed-exciton state; therefore the optical beam experiences attenuation upon its transmission. For two coherent optical beams tuned to two different resonant frequencies, however, one can judiciously choose the amplitudes and phases in such a way that the beams do not produce any excitation, and thus they experience no attenuation, even though each of beams would be strongly attenuated in the absence of the other. This two-color scheme also suggests coherent control of dressed excitons by a pair of phase-locked pulses with different carrier frequencies and nonoverlapping spectra.
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.