Controlling collision properties of solitons in five-level M-type triple quantum dot electromagnetically induced transparency medium by inter-dot tunneling coupling

Experimentally, the triple-quantum-dots system can be produced on a GaAs \begin{document}$ \left[ {001} \right]$\end{document}substrate by molecular beam epitaxy or in-situ atomic layer precise etching, thus enabling a triangle triple quantum dot (QD) aligned along the \begin{document}$ \left[ {1\bar 10} \right]$\end{document}direction. According to this, we first propose a five-level M-type triple QD electromagnetically induced transparency (EIT) model which consists of a triple QD molecule interacting with a weakly linearly polarized probe field with two orthogonal polarization components under the action of a magnetic field parallel to the light propagation direction. Subsequently, by using the multiple-scale method combined with the Fourier integration method, the propagation characteristics of the optical solitons and the collision characteristics of two solitons in the system are studied. It is shown that the optical solitons can form and propagate stably in this system under the action of quantum inter-dot tunneling coupling whose formation mechanism is different from the soliton-forming mechanism in ultra-cold atomic, single QD, and double QD EIT system. This is because the necessary condition for forming a soliton is to use a strong light beam to modulate a weak light beam, whether it is in an ultra-cold atom system, or a single quantum dot EIT medium or a double quantum dot EIT medium. In a word, the formation of soliton in previous EIT systems needs an additional strong controlling field, while the five-level M-type triple QD EIT system is dependent on the inter-dot tunneling. Since the solitons can propagate stably, the collision properties of the solitons may be studied in this system. Finally, by applying Fourier integration method, it is found that the collision behaviors of two solitons are determined by their initial phase difference. When their initial phase difference is 0, the collision behavior between the solitons is periodic elastic collision. While their initial phase difference is separately \begin{document}$ {\rm{\pi }}/4$\end{document}, \begin{document}$ \text{π}/2$\end{document}, and \begin{document}$ \text{π}$\end{document}, the collision behaviors exhibit separation phenomenon due to repulsive effect. Interestingly, the collision characteristics of two solitons are controlled by the inter-dot tunneling strength. With the increase of inter-dot tunneling strength, the collision period of two solitons with the initial phase difference of 0 decreases, and the repulsive force of two solitons with the initial phase difference being separately π/4, π/2 and π increases. This provides some theoretical basis for experimentally controlling the soliton dynamical properties in semiconductor quantum dot devices.