The nonlinear interaction dynamics of two first-order rogue waves (RWs) with opposite incident momentum in two-component Bose-Einstein condensates (BECs) are studied by solving the two-component one-dimensional Gross-Pitaevskii (GP) equation. It is demonstrated that the introduction of appropriate incident momentum successfully promotes the generation of second-order RWs in the case of relatively weaker interspecies interactions compared to intraspecies interactions. The range of incident momentum that can facilitate the generation of second-order RWs under different interspecies interaction strengths is determined, and machine learning is employed to find and analyze relationships among the interspecies interaction, the incident momentum, and the offset that can lead to the generation of second-order RWs. It shows that any two parameters above exhibit a positive or negative correlation when the third parameter is fixed. These findings provide additional possibilities for generating and controlling high-order RWs.

Objective In recent years, significant attention has been devoted to the study of optical soliton storage and retrieval, which holds great promise for optical information processing and transmission. To date, research on optical soliton storage and retrieval has primarily focused on ultracold atomic systems and semiconductor quantum dot (QD) media. In ultracold atomic electromagnetically induced transparency (EIT) systems, optical solitons can be stored and retrieved by manipulating a control field. However, practical applications face substantial challenges because such systems require ultra-low temperatures and dilute gaseous conditions. In a single QD, optical soliton storage and retrieval can also be achieved through control field manipulation, analogous to the mechanism in ultracold atomic EIT media. Optical solitons may further be stored in triple QDs, but this requires the simultaneous presence of two inter-dot tunneling couplings (IDTCs). Experimentally, realizing triple QDs is highly challenging. In contrast, double QDs are easier to implement, as they require only a single IDTC, unlike triple QDs. Recent studies suggest that optical solitons can be stored in double QDs by controlling the single IDTC. Nevertheless, the influence of the single IDTC on the velocity and amplitude of the stored optical soliton remains unreported. Motivated by this gap, we investigate in this paper the effect of single IDTC on the velocity and amplitude of stored optical solitons. Methods In this study, we propose a three-level asymmetric double-QD model comprising a probe field and a tunneling coupling between the two QDs. The dynamics of the probe field are governed by the Maxwell equations of classical electromagnetism, while the double QDs are described by the Bloch equations of quantum mechanics. This yields the Maxwell-Bloch (M-B) equations, which characterize the interaction between the probe field and the double QDs. However, exact analytical solutions of the M-B equations are generally difficult to obtain. To address this, the multi-scale method is employed to approximate the solution. Furthermore, to investigate probe field storage and retrieval in the system, the soliton solution given by Eq. (28) is used as the initial condition. Numerical simulations of the M-B equations are then performed using the fourth-order Runge-Kutta method. Results and Discussions For the linear case, it is shown that when the gate voltage is turned off, the absorption spectrum of the system exhibits a Lorentzian absorption peak [Fig. 2(a), solid line]. Upon application of the gate voltage, a tunneling-induced transparency (TIT) window emerges in the absorption profile [Fig. 2(a), dashed line], which differs from the EIT observed in ultracold atomic systems and single QD configurations. As the IDTC strength increases further, the TIT window broadens significantly [Fig. 2(a), dotted line]. Concurrently, the propagation velocity of the probe field is reduced within a specific spectral range due to the dispersive effects induced by IDTC [Fig. 2(b)]. For the nonlinear case, numerical simulations confirm that the velocity, amplitude, and width of optical solitons remain invariant during propagation (Fig. 3). Subsequently, storage and retrieval of the probe field are achieved by switching the IDTC off and on, respectively (Fig. 4). Further analysis reveals that the fidelity of the regenerated optical soliton [Fig. 4(b)] after storage and retrieval exceeds that of both the weak probe field [Fig. 4(a)] and the strong probe field [Fig. 4(c)]. Moreover, robust storage and retrieval of optical solitons are maintained even when the IDTC strength is varied [Fig. 5(a)-(c)]. Notably, as the IDTC strength increases, the amplitude of the retrieved soliton increases-a behavior distinct from that observed in triple-QD systems. This enhancement becomes progressively more pronounced with increasing IDTC strength [Fig. 5(d)]. Conclusions In this study, a three-level model of asymmetric double QDs is proposed, incorporating a probe field and an IDTC. The propagation of the probe field is described by the Maxwell equations of classical electromagnetism, while the dynamics of the double QDs are modeled using the Bloch equations of quantum mechanics. When the gate voltage is applied, the system exhibits a TIT window in its absorption spectrum, distinct from the EIT observed in ultracold atomic systems or single QD configurations. Furthermore, the width of the transparency window increases with stronger IDTC. Within a specific range, the IDTC also reduces the group velocity of the probe field, enabling slow light propagation. In the nonlinear regime, optical solitons propagate stably over long distances. Additionally, the storage and retrieval of optical solitons can be controlled by switching the IDTC off and on. Notably, the amplitude of the retrieved soliton increases with higher IDTC strength-a behavior differing from that observed in triple-QD systems. These results suggest that IDTC, regulated via gate voltage, offers a convenient means to modulate stored and retrieved optical signals in semiconductor QD-based devices.

Modulation instability provides an important framework for understanding rogue wave (RW) formation on continuous backgrounds. However, the formation mechanism and nonlinear spectral structures of RWs in Bose-Einstein condensate (BEC) matter-wave systems with vanishing boundary conditions remain largely unexplored. Here, we employ the nonlinear Fourier transform (NFT), based on the integrable structure of the focusing nonlinear Schrödinger equation and the Zakharov-Shabat scattering problem, to investigate two representative classes of first-order RWs in BEC systems. Through nonlinear spectral analysis and Darboux reconstruction, we demonstrate that both Gaussian-wave-packet-induced extreme localization events and experimentally observed Peregrine solitons are governed by the coherent dynamics of discrete soliton modes encoded in the nonlinear spectrum. For Gaussian initial states, increasing the initial width leads to an increasing number of discrete eigenvalues, resulting in a transition from fundamental solitons and bound states to Christmas-tree-like RW structures. For experimentally observed Peregrine solitons, localized perturbations reshape the discrete spectral configuration and phase evolution, enabling coherent focusing of multiple bound soliton modes. Furthermore, we reveal the spectral mechanism of higher-order RWs and propose an inverse spectral-engineering approach based on discrete-spectrum phase matching. Our results provide a nonlinear spectral perspective for understanding and controlling RW formation in matter-wave systems with vanishing boundary conditions.

Resolution is one of the key indicators in the cavity optomechanical mass sensing. The bound states in the continuum (BIC) enable extremely narrow linewidths, which have great potential for enhancing the resolution of cavity optomechanical mass sensors. In order to enhance the resolution of cavity optomechanical mass sensing, we propose a simple double-cavity optomechanical system under the blue-detuning condition to realize the BIC singularity, and present an ultrahigh-resolution mass sensing scheme based on BIC in this paper. By solving the linearized Heisenberg-Langevin equations, the expressions for the susceptibility and transmission rate of the system are derived. Based on the system's susceptibility, we study the absorption characteristics of the probe field under the blue-detuning condition. The absorption spectrum of the system exhibits three peaks, among which the central narrow peak exhibits optical gain characteristics, collectively forming a phenomenon analogous to double optomechanically induced transparency. Then, analysis of the dressed-state energy-level structure reveals that the formation of the central narrow peak stems from quantum interference effects in a double-L-type dark-state resonance. The linewidth evolution of the quasi-BIC central narrow peak is investigated by analyzing the dependence of the real part and imaginary part of the corresponding eigenvalue on the optomechanical coupling strength. It can be found that the imaginary part of the eigenvalue for the central narrow peak becomes zero when the optomechanical cooperativity coefficient equals the double-cavity cooperativity coefficient plus one, enabling the realization of BIC. The linewidth of the central peak is ultrasmall under this BIC condition, and the shift of the transmission peak in the transmission spectrum is linearly related to the adsorbed mass. Based on these characteristics, the system under the BIC condition can achieve mass sensing with an ultrahigh resolution, with a resolution of approximately 1 ag. Meanwhile, the linewidth of the transmission peak can be suppressed below 1 Hz, which is superior to the traditional optomechanical mass sensing schemes based on four-wave mixing, photonic molecules, and plasmon polaritons. Systematic investigation of eigenvalue variations and the corresponding sensitivity enhancement factors under mechanical resonator frequency shift reveals that the real part and the imaginary part of the eigenvalue associated with the central peak exhibit negligible variations under such perturbations. This indicates that the mass sensing scheme based on BIC in the double-cavity optomechanical system can maintain ultrahigh resolution and precise mass measurement under mechanical resonator frequency shift. Our scheme provides an approach for realizing the BIC singularity in optomechanical systems, and presents a new route to improving the resolution of mass sensors based on cavity optomechanical systems.

The collision dynamics of two first-order rogue waves (RWs) with opposite incident momentum in two-component Bose-Einstein condensates (BECs) is studied by solving the two-component one-dimensional Gross-Pitaevskii (GP) equation. It is demonstrated that the introduction of appropriate incident momentum successfully promotes the generation of second-order RWs in the case of relatively weaker interspecies interactions compared to intraspecific interactions. The range of incident momentum that can facilitate the generation of second-order RWs under different interspecies interaction strengths is determined, and machine learning is employed to find and analyze relationships among the interspecies interaction, the incident momentum, and the offset that can lead to the generation of second-order RWs. It shows that any two parameters above exhibit a positive or negative correlation when the third parameter is fixed. These findings provide additional possibilities for generating and controlling high-order RWs.

We present a scheme for the electromagnetically-induced-absorption(EIA)-like ground state cooling in a hybrid optomechanical system which is combined by two-level quantum systems(qubits) and a high-Q optomechanical cavity. Under the weak qubit-cavity coupling, the system exhibits an EIA-like effect and this effect is caused by quantum destructive interference that is distinct from the conventional EIA effect driven by quantum constructive interference. More importantly,the EIA-like cooling mechanism can significantly enhance the cooling rate of the hybrid system, enabling the final phonon number beyond the classical cooling limit in the strong optomechanical coupling regime. Meanwhile, the cooling effects of the EIA case is better than that of the normalmode splitting case under the same optomechanical coupling strength and qubit dissipation rate.

Compared with light, the solitons, which are from the balance between dispersion and nonlinearity of the system, possess high stability and fidelity as the information carries in quantum information processing and transmission, and have gained considerable attention in ultra-cold atomic electromagnetically induced transparent (EIT) media. To date, the EIT models on the three-level ultra-cold atoms realized experimentally, are ladder-, \begin{document}$\Lambda $\end{document}-, and V-type mode. Current studies show that the solitons cannot be stored in V-type three-level ultra-cold atomic EIT media but they can be stored in ladder- and \begin{document}$\Lambda $\end{document}-type three-level ultra-cold atomic EIT media. It is mainly because the atoms of the V-type system initially are in a excited state, while the atoms of the ladder- and \begin{document}$\Lambda $\end{document}-type systems initially are in the ground state. For the practical applications, it is a large challenge to control accurately the solitons stored in the ultra-cold atomic EIT media due to their ultralow temperature and rarefaction. Fortunately, with the maturity of semiconductor quantum technology, quantum dots have extensively application prospect in quantum information processing and transmission. However, the solitons cannot be stored in V-type three level InAs/GaAs quantum dot EIT media either, while it can be stored in ladder-type system and \begin{document}$\Lambda $\end{document}-type system.Therefore, herein we propose a V-type three-level nitrogen-vacancy (NV) center EIT model in which a weakprobe field and a strong control field are coupled to different energy levels of NV center in diamond. Subsequently, the linear and nonlinear properties of system are studied by using semiclassical theory combined with multi-scale method. It is shown that when control field is turned on, the linear absorption curve of the system presents an EIT window. And the width of the EIT window increases with the strength of magnetic induction of the control field increasing. In the nonlinear case, the solitons formed can stably propagate over a long distance. Interestingly, the solitons can be stored and retrieved by switching off and on the magnetic field of control field. Moreover, the amplitude of the stored solitons can be modulated by the magnetic induction strength of control field. This result indicates that solitons as information carriers in quantum information processing and transmission of NV center can greatly improve the fidelity of information processing.

Objective As soliton can travel over long distance without attenuation and shape change due to the interplay balance between dispersion and nonlinearity in nonlinear media, it becomes a good information carrier in quantum information processing and transmission. Till now, the research on the storage and retrieval of optical soliton mainly focuses on ultra-cold atomic electromagnetic induction transparency (EIT) media. This is mainly because ultra-cold atomic systems can generate strong nonlinear effects under low light excitation. However, for practical applications, it is a great challenge to accurately control the optical soliton storage in the atomic EIT media due to the low temperature approaching to absolute zero and rarefaction. Fortunately, with the mature semiconductor quantum production technology, quantum wells have extensive application prospect in quantum information processing and transmission. Thus, we study the storage and retrieval of optical soliton in the GaAs/AlGaAs double quantum well EIT system. Methods Based on the current experiments, we first propose an N-type four-level asymmetrical semiconductor GaAs/AlGaAs double quantum well EIT model. Subsequently, the interaction properties between the optical field and semiconductor quantum wells in the system are studied by a semi-classical theory. The physical properties of the optical field are described by the Maxwell equation, while the semiconductor quantum well is described by the Bloch equation of quantum mechanics. Therefore, the Maxwell-Bloch (M-B) equations which govern the linear absorption and nonlinear propagating properties of the system are obtained. Generally, the analytic solution of the M-B equations cannot be obtained directly. Thereby, M-B equations are solved approximately by adopting a multiple-scale method. Correspondingly, the soliton solution [Eq. (63)] is chosen as the initial condition, and the M-B equations are numerically simulated by the Runge-Kutta method to explore the storage and retrieval of the probe pulse. Results and Discussions Through the above methods, when the second control field is turned off, the linear absorption curve of the system exhibits a Lorentz absorption peak whatever the first control field changes [Fig. 2 (a)]. Fig. 2 (b) shows that when the second control field is only turned on, which means that the first control field is turned off, there is a single transparent window, and the width of the single transparent window becomes wider with the increasing strength of the second control field. When both the control fields are turned on, the double transparent window will occur, and the width of the double transparent windows is wider with the rising strength of any control field [Fig. 2 (c)]. Interestingly, after both the control fields are turned on, the double EIT windows show symmetrical distribution regardless of whether the strengths of the two control fields are equal or not [Fig. 2 ( c)]. For the nonlinear case, Fig. 3 shows that with the low-order effect being considered, the optical soliton cannot propagate stably over a long distance with attenuation. The soliton instability is from the high-order dispersion of the system. After the high-order effects are only considered, the formed optical soliton can propagate stably over long distances (Fig. 4). Furthermore, Fig. 5 indicates that the optical soliton can be stored and retrieved by switching off and on the control fields, and the storage and retrieval fidelity of the optical soliton is higher than that of the ordinary optical pulse. Moreover, the amplitude of the stored optical soliton can be modulated by the strength of the control field. Specifically, when only the second control field is turned on, the amplitude of the stored optical soliton increases with the rising strength of the second control field [Fig. 6 (a)]. When both the control fields are turned on, the amplitude of the stored optical soliton rises with the increasing strength of the second control field under the unchanged first control field. However, if the second control field keeps unchanged, the amplitude of the stored optical soliton decreases with the increasing strength of the first control field [Fig. 6 (b)]. Conclusions In this paper, we propose an N-type four-level asymmetrical semiconductor double quantum well EIT model. Subsequently, we obtain the M-B equations governing the linear and nonlinear properties of the system through the semi-classical theory combined with the multiple-scale method. When both the control fields are turned on, the linear absorption curve of the system exhibits double EIT windows. Interestingly, the double EIT windows show symmetrical distribution regardless of whether the strengths of the two control fields are equal or not. For the nonlinear case, only after the high-order effects are considered, the formed optical soliton can propagate stably over long distances, and the optical soliton can be stored and retrieved by switching off and on the control fields. Meanwhile, the amplitude of the stored optical soliton can be modulated by the strength of the control field. When the first control field keeps unchanged, the amplitude of the stored optical soliton increases with the rising strength of the second control field. However, the amplitude of the stored optical soliton decreases with the increasing strength of the first control field under the unchanged second control field. The results can improve the fidelity for the storage and retrieval of quantum information in semiconductor quantum well devices.

We demonstrate the formations of optomechanically controllable double electromagnetically induced transparency (DEIT) and parametric amplification in a quantum well (QW) optomechanical system with the anti-Stokes and Stokes sideband effects. We analytically solve the Heisenberg-Langevin equations under the steady-state condition and give the expression of the susceptibility of the QW. For the optomechanical cavity driven into the anti-Stokes sideband, the coupling between the anti-Stokes sideband process and the process of the interaction between the QW and the cavity field leads to the double-dark resonances, resulting in DEIT. In the Stokes sideband case, a similar coupling can lead to the appearance of parametric amplification. These two effects are interconvertible by adjusting the relevant detuning and can be regulated by the optomechanical and QW-cavity coupling strengths. This work may be applied in the achievement of optical switches with a more obvious contrast ratio.

We study the storage and retrieval of the optical field in an aligned asymmetric triple quantum dot molecule with both sides inter-dot tunneling coupling effect. It is shown that the optical solitons can be stored and retrieved by manipulating two inter-dot tunneling coupling effect, different from light memory in the ultra-cold atom system. Furthermore, the amplitude of the optical soliton emerges a trend of first decreasing and then increasing with the increasing strength of the two inter-dot tunneling coupling. It is possibility to improve the fidelity of the storage and retrieval of the optical information in semiconductor quantum dots devices.

We examine the effect of cavity field fluctuations on Kerr nonlinearity in an atom-assisted optomechanical system. It is found that a new self-Kerr (SK) nonlinearity term, which can greatly surpass that of a classical Λ type atomic system when the hybrid system has numerous atoms, is generated based on cavity field fluctuations by atom-cavity interactions. A strong photon-phonon cross-Kerr (CK) nonlinearity is also produced based on cavity field fluctuations. These nonlinearity features can be modified by atom-cavity and optomechanical interactions. This work may provide a new method to enhance the SK nonlinearity and generate the photon-phonon CK nonlinearity.

We propose an asymmetric linear triple quantum dot molecule model for a recent experimental device with a double neighboring dot-dot tunneling coupling, of which the linear and nonlinear dynamical properties are analytically studied by using an amplitude variable approach combined with multi-scale method. It is shown that double transparency windows are formed by the double tunneling coupling. Both dark and bright optical solitons are then obtained, of which both the types and the propagating velocity can be controlled by the two tunneling coupling strengths. Interestingly, the propagating velocity of the solitons can approach to zero at certain tunneling coupling strengths, the motionless optical solitons appearing there. The results indicate potential applications of the semiconductor quantum devices for optical soliton storage.

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.

By developing quasi-discrete multiple-scale method combined with tight-binding approximation, a novel quadratic Riccati differential equation is first derived for the soliton dynamics of the condensed bosons trapped in the optical lattices. For a lack of exact solutions, the trial solutions of the Riccati equation have been analytically explored for the condensed bosons with various scattering length as. When the lattice depth is rather shallow, the results of sub-fundamental gap solitons are in qualitative agreement with the experimental observation. For the deeper lattice potentials, we predict that in the case of as>0, some novel intrinsically localized modes of symmetrical envelope, topological (kink) envelope, and anti-kink envelope solitons can be observed within the bandgap in the system, of which the amplitude increases with the increasing lattice spacing and (or) depth. In the case of as<0, the bandgap brings out intrinsically localized gray or black soliton. This well provides experimental protocols to realize transformation between the gray and black solitons by reducing light intensity of the laser beams forming optical lattice.

We propose a scheme which can generate group velocity matching bright and/or dark solitons in a four-level tripod configuration atomic system via double-dark resonances. It is shown that the linear absorption properties can be controlled by the controlling fields. For the nonlinear case, the optical soliton can form in the first and second electromagnetically induced transparency windows and their group velocities can be matched under the condition of equal half Rabi frequencies of the two controlling fields. We also show that adjusting the amplitude and group velocity of the soliton as well as the bright and dark solitons conversion can be realized. (C) 2018 Elsevier B.V. All rights reserved.

In the past few years, with developing the technology of electromagnetically induced transparency (EIT) and improving the semiconductor technology, it has become possible to realize the application of optical soliton to commu-nication device. Studies show the reduction of group velocity of the optical soliton in EIT medium under weak driving condition, which possibly realizes the storing of optical pulses in information storage. More importantly, semiconductor quantum wells have the inherent advantages such as large electric dipole moments of the transitions, high nonlinear optical coefficients, small size, easily operating and integrating. So it is considered to be the most potential EIT medium to realize the application of quantum devices. The optical soliton behavior in the semiconductor quantum well is studied, which can provide a certain reference value for the practical application of information transmission and processing to-gether quantum devices. Although there has been a series of researches on both linear and nonlinear optical properties in semiconductor quantum wells structures, few publications report the effects of the cross-coupling longitude-optical phonon (CCLOP) relaxation on its linear and nonlinear optical properties. However, to our knowledge, the electron-longitude-optical phonon scattering rate can be realized experimentally by varying the sub-picosecond range to the order of a picosecond. According to this, we in the paper study the effects of the CCLOP relaxation on its linear and nonlinear optical properties in a cascade-type three-level EIT semiconductor quantum well. According to the current experimental conditions, we first propose a cascade-type three-level EIT semiconductor quantum well model. And in this model we consider the longitudinal optical phonons coupling between the bond state and anti-bond state. Subsequently, by using the multiple-scale method, we analytically study the dynamical properties of solitons in the cascade-type three-level EIT semiconductor quantum well with the CCRLOP. It is shown that when the CCRLOP strength is smaller, there exhibits the dark soliton in the EIT semiconductor quantum well. Only if the strength of the CCRLOP is larger, will in the system there exists bright soliton. That is to say, with increasing the strength of the CCRLOP, the soliton type of the system is converted from dark to bright soliton little by little. So, the temporal soliton type can be effectively controlled by the strength of the CCRLOP. In addition, we also find that the group velocity of the soliton can also be controlled by the strength of CCRLOP and the control light. These results may provide a theoretical basis for manipulating experimentally the dynamics of soliton in semiconductor quantum wells.

Based on the current experimental conditions, a model of annular four-level semiconductor quantum dot electromagnetically induced transparency medium is constructed by considering the phonon-assisted transition effect in semiconductor quantum dot. Dynamical behaviors of the temporal optical soliton in this system is analytically studied by using multiple-scale method. The results show that dynamical properties such as amplitude, width and group velocity of the temporal optical soliton can be controlled by adjusting the strength of the phonon-assisted transition. The group velocity of the temporal optical soliton is much smaller than the velocity of light. And when the strength of the phonon-assisted transition increases, the group velocity of the soliton decreases continuously. So, the group velocity may slowly close to zero that it appears stagnation. The optical stagnation is helpful for light storing in quantum devices. It provides some reference values to realize optical storage in the semiconductor quantum devices.

The linear optical properties and Kerr nonlinear optical response in a four-level loop configuration Ga As/Al Ga As semiconductor quantum dot are analytically studied with the phonon-assisted transition（PAT）. It is shown that the changes among a single electromagnetically induced transparency（EIT） window, a double EIT window and the amplification of the probe field in the absorption curves can be controlled by varying the strength of PAT κ. Meanwhile, double switching from the anomalous dispersion regime to the normal dispersion regime can likely be achieved by increasing the Rabi energy of the external optical control field. Furthermore, we demonstrate that the group velocity of the probe field can be practically regulated by varying the PAT and the intensity of the optical control field. In the nonlinear case, it is shown that the large SPM and XPM can be achieved as linear absorption vanishes simultaneously, and the PAT can suppress both third-order self-Kerr and the cross-Kerr nonlinear effect of the QD. Our study is much more practical than its atomic counterpart due to its flexible design and the controllable interference strength, and may provide some new possibilities for technological applications.

A theory model of the four-level type semiconductor quantum dot system under the mechanism of electromagnetically induced transparency (EIT) is proposed.The model is composed of a semiconductor quantum dot (SQD) system interacting with a weak,linear-polarized probe field with two orthogonally polarized components under the applied longitudinal magnetic field and two strong coupling control fields.By using the multiple-scale method,the stability and collision dynamical characteristics of two coupled temporal vector optical solitons in the semiconductor quantum dot media are analytically investigated.It is shown that the collision properties of two coupled temporal vector optical solitons are correlated with their initial phase shift.Especially,when two solitons components are in phase or out of phase,the collisions between them are almost elastic without energy transfer.While the initial phase shift is π/2,they will be separated from each other after their collision and there is energy transfer between two solitons.

By using the multiple-scale method, we analytically study the dynamical properties of atemporal optical soliton under the consideration of the high order effects andcross-coupling relaxation of longitudinal optical phonons (CCRLOP) in an asymmetricalfour-level semiconductor double quantum wells. The results reveal that when increasingstrength of CCRLOP, the amplitude of the soliton shows a decrease-to-increase behavior. Atfixed CCRLOP intensity, the amplitude and width of the soliton both exhibit a minimumor/and a maximum as a function of three-photon detuning. Moreover, these extremums willshift to the smaller side of the three-photon detuning with the increasing strength ofCCRLOP. In addition, with the increasing strength of CCRLOP, the whole trend of groupvelocity of the soliton changes from an initial increase followed by a decrease to adirect decrease. These results may supply a reference value for experimentally adjustingand controlling the dynamical characteristics of the solitons.