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The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics

Kerr non-linearity and four-wave mixing in a double-cascade type four-level system of multiple quantum wells

Wei Yan, Tao Wang, Xiaoming Li, Chunchao Yu

Published Mar 18, 2013• 13 citations
Publisher

Abstract

We study the non-linear optical response in multiple quantum wells structure with a double-cascade type four-level configuration based on excitons and biexcitons transitions. By analysing the Kerr non-linear effects, we obtain the slow, mutually matched group velocities and giant Kerr non-linearity of probe and signal fields. While when the signal (or probe) field is removed, the non-linear optical phenomenon four-wave mixing (FWM) originating from quantum interference is demonstrated. The FWM efficiency of the system study is about 50%. Such a semiconductor system is much more practical than its atomic counterpart because of its flexible design and the controllable interference strength.

DOI
10.1080/14786435.2013.781281

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Chinese Physics B•Oct 1, 2014•1 citation
We study the non-linear optical response in multiple quantum wells structure with a double-cascade type four-level configuration based on excitons and biexcitons transitions. By analysing the Kerr non-linear effects, we obtain the slow, mutually matched group velocities and giant Kerr non-linearity of probe and signal fields. While when the signal (or probe) field is removed, the non-linear optical phenomenon four-wave mixing (FWM) originating from quantum interference is demonstrated. The FWM efficiency of the system study is about 50%. Such a semiconductor system is much more practical than its atomic counterpart because of its flexible design and the controllable interference strength.
Abstract A double‐cascade‐type four‐level system of semiconductor multiple quantum wells (MQWs) was constructed with biexcitons and excitons. The nonlinear optical properties for amplification, absorption, and dispersion of 2‐weak fields in this scheme are investigated. It shows that the amplification, absorption, and dispersion responses of 2‐weak fields can be achieved by appropriately adjusting the relative phase, the probe detuning, and the two control Rabi frequencies. The investigation is much more practical than its atomic counterpart because of its flexible design and the widely adjustable parameters. It may provide a new possibility in technological applications for the light amplifier and optical switch working on quantum coherence effects in MQW solid‐state systems.
Coherently controlled four-wave-mixing (FWM) measurements have turned out to be a very sensitive tool to investigate the microscopic origin of the nonlinear optical response of semiconductor quantum-well structures, in particular if excitons are excited [1-3]. The measured signal oscillates as a function of the phase difference of the two interferometric pulses and is modulated additionally by contributions that oscillate with integer multiples of the excitonic resonance frequency. The influence of these harmonics can be measured in background free directions, i.e., the first (FWM) or second (six-wave mixing, SWM) diffracted order in direction 2k2-k1 or 3k2-2k1, respectively. Their intensity is easily quantified by inspecting the corresponding Fourier transforms (FT). Here, we report on transient interferometric SWM measurements and the influence of biexcitons on the signal.
The paper presents a description of two-pair correlations in an electron-hole system in laser-excited direct-gap semiconductors in terms of the exciton-boson formalism. The dependence of the states of quasi-particles on their angular momentum orientation is properly taken into account following group theory rules. It is shown for the example of heavy hole excitons in GaAs quantum wells that Coulomb two-exciton correlations include effective repulsion between excitons with nonzero total momenta and effective attraction between excitons with zero total momenta. They generate exciton and biexciton nonlinearities, respectively, in the exciton-biexciton system. The Heisenberg equations of motion derived are applied to four-wave mixing in the coherent mode. Two components of Coulomb two-exciton correlations were found to generate coherent four-wave mixing either separately, one at the cocircular and the other at the perpendicular-linear polarization of applied pulses, or jointly at parallel-linear polarization. General equations are obtained for the amplitude of four-wave mixing signals with time resolution in these polarization configurations, which, in the limit of ultranarrow pulses, reduce to analytic functions of time and excitation and sample parameters. These equations are used to analyze signal characteristics in every polarization configuration. The results give a correct picture of biexciton effects and the polarization dependence of coherent four-wave mixing in GaAs quantum wells.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.
We study linear and nonlinear propagations of probe and signal pulses in a multiple quantum-well structure with a four-level, double Λ-type configuration. We show that slow, mutually matched group velocities and giant Kerr nonlinearity of the probe and the signal pulses may be achieved with nearly vanishing optical absorption. Based on these properties we demonstrate that two-qubit quantum polarization phase gates can be constructed and highly entangled photon pairs may be produced. In addition, we show that coupled slow-light soliton pairs with very low generation power can be realized in the system.
A double cascade-type four-level multiple-quantum-well-based exciton—biexciton transitions are proposed. The study is carried out on a 4.8-nm ZnSe single-quantum well which is embedded into ZnMgSSe cladding layers and pseudomorphically grown by molecular beam epitaxy on a (0 0 1) GaAs substrate. It is displayed that the exciton spin relaxation and relative phases between applied fields can influence the transient and steady-state behaviors of absorption, dispersion, and group velocity of two weak probe and signal fields. Also, transient behaviors of electron population of different levels are discussed. It is found that the probe or signal amplification occurs in the absence of population inversion.