The role of a chiral quantum-dot molecule (QDM) system in controlling and enhancing the Goos-Hänchen (GH) shift is revealed here. The proposed setup is a four-level atomic system excited by incoherent pump and probe fields where the electron tunneling is prominent in affecting the GH shift upon the reflection and transmission of probe beams. The GH shifts in the chiral QDM system are calculated analytically by using stationary phase theory, whereas the dynamics of the quantum-dot system are derived by the density-matrix method. It is demonstrated that the GH shifts through transmission and reflection light beams are strongly influenced due to right-circularly polarized (RCP) and left-circularly polarized light. The GH shifts through RCP light are enhanced in the presence of chiral QDM systems, and these shifts could become either highly negative or highly positive, sensitively depending on the electron tunneling and chiral coefficients. This proposal can be viewed as a theoretical approach to the potential application of GH shifts in nano-optoelectronic sensors.

We present an efficient two-dimensional atomic localization in a tripod-type four-level atomic medium using standing-wave fields. The localization behavior is significantly improved, and the maximum localization probability can be achieved under suitable conditions within the one-wavelength domain. Multiple sharp localized peaks are observed in the one-wavelength domain through examination of the absorption of the weak probe field, and theoretically, high-resolution and high-precision atomic localization can be achieved within a region smaller than λ /12 × λ /12, via the exploitation of quantum-coherence effects in laser–matter interactions. The spatial resolution of the atomic localization is extensively improved, compared to the cases with or without microwave fields studied previously. We believe that the results revealed here might have potential applications for atomic nanolithography, neutral-atom laser cooling and trapping, Bose–Einstein condensation and the center-of-mass wave-function measurements.

By using the contemporary theory of inequalities, this study is devoted to proposing a number of refinements inequalities for the Hermite-Hadamard’s type inequality and conclude explicit bounds for two new definitions of $(p_1{p}_2,q_1{q}_2)$ -differentiable function and $(p_1{p}_2,q_1{q}_2)$ -integral for two variables mappings over finite rectangles by using pre-invex set. We have derived a new auxiliary result for $(p_1{p}_2,q_1{q}_2)$ -integral. Meanwhile, by using the symmetry of an auxiliary result, it is shown that novel variants of the the Hermite-Hadamard type for $(p_1{p}_2,q_1{q}_2)$ -differentiable utilizing new definitions of generalized higher-order strongly pre-invex and quasi-pre-invex mappings. It is to be acknowledged that this research study would develop new possibilities in pre-invex theory, quantum mechanics and special relativity frameworks of varying nature for thorough investigation.

We present a novel methodology for enhancing superluminal surface plasmon polaritons (SPPs) propagations within a hybrid nanostructure configuration consisting of gold (Au) metal and chiral quantum dots (CQDs) medium. The arrangement of CQDs and metal hybrid nanostructures enables the production of SPPs when exposed to incident light. The resonances of SPPs within a hybrid nanostructure are determined through analytical calculations using Maxwell’s equations under specified boundary conditions, while the dynamics of the CQDs system are calculated using the density matrix approach. It is demonstrated that the propagation of SPPs is significantly influenced by both right-circularly polarized (RCP) and left-circularly polarized (LCP) SPPs. Additionally, we investigate the enhancement of superluminal SPPs propagation by varying the electron tunneling strength and the intensity of the control field within the hybrid system. The characteristics of RCP and LCP SPPs have been investigated, indicating a large negative group index and advancement in time. The observation of a large negative group index and advancement in time provides strong evidence for enhanced superluminal SPPs propagation within the proposed hybrid nanostructure. The results have potential applications in the fields of optical information processing, temporal cloaking, quantum communication, and the advancement of computer chip speed.