A complete one-dimensional scattering of a spinless particle on a time-independent potential barrier is considered. To describe separately transmitted and reflected particles in the corresponding subsets of identical experiments, we introduce the notions of scattering channels for transmission and reflection. We find for both channels the (unitary) scattering matrices and reconstruct, by known out asymptotes (i.e., by the transmitted and reflected wave packets), the corresponding in asymptotes. Unlike the out asymptotes for transmission and reflection, their in asymptotes represent nonorthogonal functions. As is shown, the position distributions of to-be-transmitted and to-be-reflected particles, except their average positions, are unpredictable. At the same time, the momentum distributions of these particles are physically meaningful and can be observed to the full. We show that both the subensembles of particles must start (on the average) from the same spatial point, and the momentum distributions of to-be-scattered and scattered particles must be the same for each scattering channel. Taking into account these properties, we define the (individual) delay times for transmission and reflection for wave packets of an arbitrary width. Besides, to estimate the duration of the scattering event, we derive the expression for a (total) scattering time.
On the base of a 1D Shrödinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a single rectangular barrier. Both the scattering and the bound states problem were reformulated in terms of a quantum wave impedance and its application for solving both these problems was considered. The expressions for a reflection and a transmission coefficient were found on the base of a quantum wave impedance approach.
Quantum simulation of Liouville equation in geometrical optics with partial transmission and reflection via Schrödingerization
School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）；Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学自然科学研究院）；Ministry of Education Key Laboratory in Scientific and Engineering Computing, Shanghai Jiao Tong University（上海交通大学教育部科学和工程计算重点实验室）
We consider the scattering problems of a quantum particle in a system with a single Y-junction and in ring systems with double Y-junctions. We provide new formalism for such quantum mechanical problems. Based on a path integral approach, we find compact formulas for probability amplitudes in the ring systems. We also discuss quantum reflection and transmission in the ring systems under scale-invariant junction conditions. It is remarkable that perfect reflection can occur in an anti-symmetric ring system, in contrast with the one-dimensional quantum systems having singular nodes of degree 2.
We report strongly non-reciprocal behaviour for quantum dot exciton spins coupled to nano-photonic waveguides under resonant laser excitation. A clear dependence of the transmission spectrum on the propagation direction is found for a chirally-coupled quantum dot, with spin up and spin down exciton spins coupling to the left and right propagation directions respectively. The reflection signal shows an opposite trend to the transmission, which a numerical model indicates is due to direction-selective saturation of the quantum dot. The chiral spin-photon interface we demonstrate breaks reciproci…
Structure orientation determined in transmission and reflection: q-plate
Swinburne University of Technology（斯威本科技大学）；Australian Research Council (ARC) Industrial Transformation Training Centre in Surface Engineering for Advanced Materials (SEAM)（澳大利亚研究理事会（ARC）先进材料表面工程工业转型培训中心（SEAM））；Melbourne Center for Nanofabrication (MCN)（墨尔本纳米制造中心（MCN））；School of Materials and Chemical Technology, Institute of Science Tokyo（东京科学大学物质理工学院）；Laser Research Center, Physics Faculty, Vilnius University（维尔纽斯大学物理学院激光研究中心）；Infrared Microspectroscopy (IRM) Beamline, ANSTO‒Australian Synchrotron（红外显微光谱（IRM）光束线，ANSTO-澳大利亚同步辐射加速器）；Paul Scherrer Institut（保罗谢尔研究所）；World Research Hub (WRH), School of Materials and Chemical Technology, Institute of Science Tokyo（世界研究枢纽（WRH），东京科学大学物质理工学院）；Research Center for Autonomous Systems Materialogy (ASMat), Institute of Innovative Research, Institute of Science Tokyo（东京科学大学创新研究院自主系统材料学研究中心（ASMat））
We study strong light-mediated resonant dipole-dipole interactions in two-dimensional planar lattices of cold atoms. We provide a detailed analysis for the description of the dipolar point emitter lattice plane as a "super-atom", whose response is similar to electromagnetically-induced transparency, but which exhibits an ultra-narrow collective size-dependent subradiant resonance linewidth. The super-atom model provides intuitively simple descriptions for the spectral response of the array, including the complete reflection, full transmission, narrow Fano resonances, and asymptotic expressions…
