The influence of high-order effects on the stability of the optical soliton in a semiconductor three-quantum-dot molecular system under the excitation of narrow pulse probe light is analyzed analytically by using the multi-scale method. The results show that optical soliton described by the standard nonlinear Schrödinger equation will have a large attenuation in the propagation process, while the optical soliton described by the high-order nonlinear Schrödinger equation has relatively good stability. In addition, numerical simulations of the interaction between optical solitons show that the amplitudes of the two optical solitons described by the standard nonlinear Schrödinger equation attenuate rapidly after the collisions and radiation of more serious dispersion waves, while the shapes of the two optical solitons described by the high-order nonlinear Schrödinger equation hardly changes after the collision. This is mainly because when the incident probe light pulse is narrow enough, the system must be described by a higher-order equation. The physical reason is that the higher-order effects in the equation, including non-instantaneous effects and third-order dispersion effects, cannot be ignored or treated as perturbations. This kind of stable optical soliton has potential application value for future optical information processing and transmission technology.
The influence of high-order effects on the stability of the optical soliton in a semiconductor three-quantum-dot molecular system under the excitation of narrow pulse probe light is analyzed analytically by using the multi-scale method. The results show that optical soliton described by the standard nonlinear Schrödinger equation will have a large attenuation in the propagation process, while the optical soliton described by the high-order nonlinear Schrödinger equation has relatively good stability. In addition, numerical simulations of the interaction between optical solitons show that the amplitudes of the two optical solitons described by the standard nonlinear Schrödinger equation attenuate rapidly after the collisions and radiation of more serious dispersion waves, while the shapes of the two optical solitons described by the high-order nonlinear Schrödinger equation hardly changes after the collision. This is mainly because when the incident probe light pulse is narrow enough, the system must be described by a higher-order equation. The physical reason is that the higher-order effects in the equation, including non-instantaneous effects and third-order dispersion effects, cannot be ignored or treated as perturbations. This kind of stable optical soliton has potential application value for future optical information processing and transmission technology.
We investigate the influence of high-order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a lifetime broadened four-state atomic system under a Raman excitation. Using a standard method of multiple-scales we derive a generalized nonlinear Schrödinger equation and show that for realistic physical parameters and at the pulse duration of 10(-6)s, the effects of third-order linear dispersion, nonlinear dispersion, and delay in nonlinear refractive index can be significant and may not be considered as perturbations. We provide exact soliton solutions for the generalized nonlinear Schrödinger equation and demonstrate that optical solitons obtained may still have ultraslow propagating velocity. Numerical simulations on the stability and interaction of these ultraslow optical solitons in the presence of linear and differential absorptions are also presented.
Soliton, which can travel over long distance without attenuation or shape change due to the balance of the interplay between dispersion (or diffraction) and nonlinearity in nonlinear medium, becomes a good information carrier in quantum information processing and transmission. Up to now, the study on the optical solitons mainly focuses on ultra-cold atomic electromagnetic induction transparency (EIT) medium. This is mainly because ultra-cold atomic system can generate strong nonlinear effect under low light excitation. However, for the practical application, it is a big challenge to control accurately the optical soliton dynamics in the atomic EIT medium due to its low temperature (which approaches to absolute zero) and rarefaction. Fortunately, with the maturity of semiconductor quantum production technology, quantum dots have extensive application prospect in quantum information processing and transmission. So, in the paper, we study the optical soliton dynamics in a four-level asymmetric array-type three-quantum-dot EIT medium. Based on the current experimental results, we first propose a four-level asymmetric array-type three-quantum-dot EIT model. Subsequently, by using amplitude variable approach combined with multi-scale method, we study analytically the propagation of a probe pulse in this system. It is shown that when one (the another) inter-dot tunneling coupling is turned on (off), only a single transparency window appears in the center range of the probe field detuning. Only if two inter-dot tunneling couplings are turned on will two transparent windows be distributed on both sides of the central region of the probe field detuning. And the width of the single transparent window or the widths of two transparent windows become wider with the strength of the inter-dot tunneling coupling increasing. For the nonlinear case, by choosing appropriate parameters in the area of the transparency window, the stable propagation of soliton can be realized. Interestingly, we find that the strength of the inter-dot tunneling coupling has an important effect on the soliton dynamic behaviors. In the case that one (the another) inter-dot tunneling coupling is turned on (off), with the increase of strength of the inter-dot tunneling coupling, the velocity of the soliton exhibits a trend of first increasing and then decreasing, and the amplitude of the soliton presents a increasing trend for ever. For the case that two inter-dot tunneling couplings are turned on, with the strength of the two inter-dot tunneling coupling increasing, the velocity of the soliton presents a decreasing trend for ever, while the amplitude of the soliton exhibits a trend of first decreasing and then increasing. Thus, the amplitude modulation effect of optical soliton can be realized in semiconductor quantum dot devices.
We present a systematic study on the dynamics of a ultraslow optical soliton in a cold, highly resonant three-state atomic system under Raman excitation. Using a method of multiple scales we derive a modified nonlinear Schrödinger equation with high-order corrections that describe effects of linear and differential absorption, nonlinear dispersion, delay response of nonlinear refractive index, diffraction, and third-order dispersion. Taking these effects as perturbations we investigate in detail the evolution of the ultraslow optical soliton using a standard soliton perturbation theory. We show that due to these high-order corrections the ultraslow optical soliton undergoes deformation, change of propagating velocity, and shift of oscillating frequency. In addition, a small radiation superposed by dispersive waves is also generated from the soliton. The results of the present work may provide a guidance that is useful for experimental demonstration of ultraslow optical soliton in cold atomic systems.
This paper investigates the stability of higher-order nonlinear optical systems using cold atomic gases. We explore the behavior of optical solitons in such systems by analyzing the Schrödinger equation (NLSE) and its third-(cubic) and fifth-order(quintic) nonlinear effects. Firstly, we solve the travelling wave solutions of bright solitons in the third-order nonlinear regime by the F-expansion method. We then consider the fifth-order nonlinear case to compare and analyze the important influence of higher-order effects on the soliton morphology and stability. Finally, we analyze the stability of bright solitons in the resulting fiber system. We find that higher-order effects play a critical role in maintaining the long-distance transport of solitons. This study definitively guides experimental studies of steady-state optical soliton teleportation in fiber-optic systems containing higher-order nonlinear interactions.
The best carrier for quantum information transmission is light signal, which has a fast propagation speed and can carry a large amount of information. However, during the propagation of light, dispersion effect and diffraction effect can cause quantum information to be distorted to a certain extent. On the contrary, optical solitons are formed due to the balance between the system’s dispersion (diffraction) effect and nonlinear effect, and they exhibit very high stability and fidelity. Therefore, they have received widespread attention in electromagnetically induced transparency (EIT) media with ultracold atoms. However, cold atomic gas media require extremely low operating temperatures, and the performances of the materials are difficult to control precisely. These factors are unfavorable for the miniaturization and integration of future information devices, thus significantly limiting their practical applications. Semiconductor quantum dot media, on the other hand, possess advantages such as discrete energy level structures and spectral properties similar to those of cold atomic gases, longer decoherence times, larger electric dipole moments, more significant nonlinear optical effects, and easy integration, making them an ideal alternative to cold atomic media. In this work, semiconductor quantum dots are coupled with optical fibers, the most common carrier in optical communication, to explore the formation, storage, and retrieval of temporal optical solitons in the coupled system. The results show that due to the tunneling-induced transparency effect between dots in semiconductor quantum dot molecules, light absorption in the system is greatly suppressed. At the same time, the transverse confinement of the nanofiber can enhance the interaction between light and the system, and the enhanced nonlinear response of the system can balance the dispersion effect, resulting in stable temporal optical solitons. Further research indicates that by turning on and off the inter-dot tunneling coupling, the high-efficiency and high-fidelity storage and retrieval of optical solitons can be realized in the system. These findings have certain guiding significance and potential application value for the processing all-optical information in solid quantum materials.
We investigate the formation and propagation of optical solitons in an asymmetric double quantum-well structure. Using a standard method of multiple scales we derive a nonlinear Schr\"odinger (NLS) equation with some high-order correction terms that describe effects of linear and differential absorption, nonlinear dispersion, delay response of nonlinear refractive index, and third-order dispersion of a probe field. We show that in order to make slowly varying envelope approximation be valid an excitation scheme of interband transition should be adopted. We also show that for realistic quantum-well parameters the probe field with time length of picosecond or shorter must be used to make dispersion and nonlinear lengths of the system be smaller than absorption length, only by which a shape-preserving propagation of optical solitons is available. In addition, we clarify validity domains for the perturbed NLS equation as well as the high-order NLS equation and provide various optical soliton solutions in different regimes both analytically and numerically. We demonstrate that the solitons obtained have ultraslow propagating velocity and can be generated under very low input light intensity.