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Europhysics Letters (EPL)

(2 + 1)-D spatial ring solitons in a semiconductor quantum well system

Ji-Bing Liu, Tang-Kun Liu, Hong Li, Xiao-Tao Xie, D. N. Wang, Ray‐Kuang Lee

Published Dec 1, 2015• 4 citations
Publisher

Abstract

In this paper, we investigate the interaction between the semiconductor quantum well (QW) structure, a weak probe field and a strong control field. Due to the quantum interference effect induced by the strong control field, the absorption of the weak probe field is small and the Kerr nonlinearity can be greatly enhanced. The results show that the spatial soliton can form in the semiconductor QW structure via electromagnetically induced transparency (EIT). We also discuss the optical response of the system and obtain the giant χ (3) and χ (5) susceptibilities with opposite signs. In the one-dimension case, we obtain the analytical solutions for bright and dark spatial solitons. For a general case, we present numerical solutions for ring solitons with experimental parameters and show that the ring solitons are stable against azimuthal perturbation.

DOI
10.1209/0295-5075/112/56002

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In this paper, we investigate the interaction between the semiconductor quantum well (QW) structure, a weak probe field and a strong control field. Due to the quantum interference effect induced by the strong control field, the absorption of the weak probe field is small and the Kerr nonlinearity can be greatly enhanced. The results show that the spatial soliton can form in the semiconductor QW structure via electromagnetically induced transparency (EIT). We also discuss the optical response of the system and obtain the giant χ (3) and χ (5) susceptibilities with opposite signs. In the one-dimension case, we obtain the analytical solutions for bright and dark spatial solitons. For a general case, we present numerical solutions for ring solitons with experimental parameters and show that the ring solitons are stable against azimuthal perturbation.
Considering the exciton-biexciton coherence, we analytically study the linear absorption and nonlinear propagation properties of the probe and signal field in a semiconductor quantum dot. It is found that in the linear case, in the system takes place an electromagnetically induced transparency phenomenon. Furthermore, we obtain that in the system there occurs one- or two-transparency window, or optical gain, which is controlled by adjusting the coupling control field. For the nonlinear case, the weak probe field, which is induced by a signal field, splits into two parts. When their excited self-Kerr and cross-Kerr nonlinear effects balance the refractive effect of the beam, the system exhibits bright-bright, bright-dark, dark-bright, dark-dark soliton pairs.
By using multiple-scale method，we analytically study the nonlinear dynamical properties of an electromagnetically induced transparency medium with three-level atoms and a strong coupling light field. It is shown that a weak probe light beam can form spatial weak-light dark solitons. When it propagates along axial direction，the dark soliton will transforms into a steady spatial weak-light ring dark soliton，which results from the balance of the interplay between beam diffraction and refractive nonlinearity.
We propose a scheme to realize a (2+1)-dimensional vectorial Thirring model in a coherent atomic system via electromagnetically induced transparency (EIT). We show that under EIT conditions the probe field envelopes obey coupled nonlinear Schr\"odinger equations, which are reduced to a Thirring model when system parameters are suitably chosen. We present spatial soliton-pair solutions exhibiting many interesting features, including controllability (i.e., the soliton property of one component can be adjusted by the propagation constant of another component in which the soliton remains unchanged), diversity (i.e., many different types of soliton-pair solutions can be found, including bright-bright, dark-bright, dark-dark, darklike-dark, dark-dipole, darklike-multidark, and high-dimensional bright-bright, dark-darklike soliton pairs), and stability. Furthermore, we demonstrate that the stability of soliton pairs in the system can be strengthened by adjusting the propagation constant. Comparing with previous studies, in addition to supporting much more stable (1+1)-dimensional and (2+1)-dimensional spatial soliton-pair solutions, the present scheme needs only a single atomic species and hence is easy to realize experimentally.
By using semiclassical theory combined with multiple-scale method, we analytically study the linear absorption and the nonlinear dynamical properties in a lifetime broadened Λ-type three-level self-assembled quantum dots. It is found that this system can exhibit the transparency, and the width of the transparency window becomes wider with the increase of control light field. Interestingly, a weak probe light beam can form spatial weak-light dark solitons. When it propagates along the axial direction, the soliton will transform into a steady spatial weak-light ring dark soltion. In addition, the stability of two-dimensional spatial optical solitons is testified numerically.
We show that a weak probe light beam can form spatial solitons in an electromagnetically induced transparency (EIT) medium composed of four-level atoms and a coupling light field. We find that the coupling light beam can induce a highly controllable nonlinear waveguide and exert very strong effects on the dynamical behavior of the solitons. Hence, in the EIT medium, it is not only possible to produce spatial solitons at very low light intensities but also simultaneously control these solitons by using the coupling-light-induced nonlinear waveguide.
We have investigated the nonlinear interaction between a weak-pulsed probe field and a four-level Y-type atomic system with dual ladder-type electromagnetically induced transparency. Two strong coupling fields induce a quantum destructive interference effect which depletes the population in the two nearly degenerate uppermost levels of the system and dramatically enhances the linear as well as nonlinear dispersion while simultaneously significantly suppressing the probe field absorption. We present the semiclassical quantum analysis of the system. The perturbation method of multiple scales is used to derive a differential envelope equation that describes the propagation of the probe field in the Y-type atomic system. It is then demonstrated that bright and dark optical solitons can be formed in this system.