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arXiv:1410.4283 · Physical Review A

Goos-Hänchen shifts in spin-orbit-coupled cold atoms

Lu Zhou, Jieli Qin, Zhihao Lan, Guangjiong Dong, Weiping Zhang

Published Mar 17, 2015• 14 citations
arXivHTMLPDF

Abstract

We consider a matter wave packet of cold atom gas impinging upon a step potential created by an optical light field. In the presence of spin-orbit coupling, the atomic eigenstates contain two types of evanescent states, one of which is an ordinary evanescent state with a pure imaginary wave vector while the other possesses a complex wave vector and is recognized as an oscillating evanescent state. We show that the presence and interplay of these two types of evanescent states can give rise to two different mechanisms for total internal reflection, and thus lead to an unusual Goos-H\"anchen (GH) effect. As a result, not only large positive but also large negative GH shifts can be observed in the reflected atomic beam. The dependence of the GH shift on the incident angle, energy, and height of the step potential is studied numerically.

DOI
10.1103/physreva.91.031603

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We consider a matter wave packet of cold atom gas impinging upon a step potential created by an optical light field. In the presence of spin-orbit coupling, the atomic eigenstates contain two types of evanescent states, one of which is an ordinary evanescent state with a pure imaginary wave vector while the other possesses a complex wave vector and is recognized as an oscillating evanescent state. We show that the presence and interplay of these two types of evanescent states can give rise to two different mechanisms for total internal reflection, and thus lead to an unusual Goos-H"anchen (GH) effect. As a result, not only large positive but also large negative GH shifts can be observed in the reflected atomic beam. The dependence of the GH shift on the incident angle, energy, and height of the step potential is studied numerically.
Artificial spin-orbit coupling in neutral cold atom have been experimentally implemented in alkali-metal atoms. Nowadays people begin to explore its possible applications. One of the most interesting applications is the atomic mirror, which is a key element in atom optics. And spin-orbit coupling provides the atomic beam with the possibility that the atomic spin can flip during its propagation, thus can be used to prepare the quantum-state-selective atomic mirror. In 2008, Juzeliūnas, et al. [Juzeliūnas G, et al. 2008 Phys. Rev. Lett. 100 200405] studied a spin-orbit-coupled matter wave packet of cold atom gas impinging on an infinite step potential created by the optical light field. Results showed that there is not only ordinary specular reflection, but also non-specular one. The reflected atoms split into two beams and double reflection takes place. Based on the previous study, here we consider a matter wave packet of spin-orbit-coupled cold atom gas impinging on a finite step potential created by the optical light field. Due to the effect of the spin-orbit coupling, in addition to the propagating state, the eigenstates of cold atoms include evanescent state and oscillating evanescent state. Under suitable conditions double reflection will take place. If there are just evanescent waves in the step potential, total internal reflection will take place. In other words, when there is propagating wave in the step potential, partial reflection will take place. By taking into account both the total internal reflection and partial reflection, we study not only the polarization rate but also the reflectivity each as a function of incident energy, incident angle and spin-orbit coupling strength. The properties different from those of previous studies are found. In the case of total internal reflection, we find that the polarization rate of the reflected atoms is sensitive to incident angle instead of the spin-orbit coupling strength and incident energy. While in the case of partial reflection, all these factors strongly affect the polarization rate and reflectivity. We carefully study these properties and find that, on one hand, high efficiency atomic mirror can be acquired in the case of total internal reflection, and on the other hand, we can acquire the different polarization rates by adjusting the incident angle, the spin-orbit coupling strength and incident energy in the case of partial reflection.
We consider the propagation of a matter wave packet of two-level atoms through a square potential created by a super-Gaussian laser beam. We explore the matter wave analog of Goos-H\"anchen shift within the framework of atom optics where the roles of atom and light are exchanged with respect to conventional optics. Using a vector theory, where atoms are treated as particles possessing two internal spin components, we show that not only large negative but also large positive Goos-H\"anchen shifts can occur in the reflected atomic beam.
The negative and positive Goos-H\"anchen (GH) shifts in reflected light are revisited for a partial coherent light incident on a cavity. A three-level dilute gaseous atomic medium, which follows two-photon Raman transitions, is considered in a cavity. The anomalous (negative group index) and normal (positive group index) dispersions of the intracavity medium lead to negative and positive GH shifts, respectively. The effects of beam width, spatial coherence, and mode index of partial coherent light fields are studied on the negative and positive GH shifts. It is observed that the amplitude of negative and positive GH shifts are relatively large for a small range of beam width and for a small value of spatial coherence of partial coherent light beams. The amplitude of GH shifts becomes small for large beam width and spatial coherence of incident light. Further, the distortion in the reflected light field increases when the amplitude of the GH shifts increases and vice versa.
Abstract This study explores the Goos–Hänchen (GH) shift phenomenon within a cavity hosting a V-type three-level atomic system, engaged with two independent broadband squeezed baths. Our exploration encompasses a thorough analysis of the lateral shifts in both reflected and transmitted light beams, with a focus on the impact of critical factors, i.e, coupling field strength, incoherent pumping field strength, and squeezed vacuum intensity. Our results reveal an interplay of these parameters, resulting in distinctive negative and positive GH shifts in both reflected and transmitted light. In addition, a remarkable enhancement of GH shifts at specific angles of incidence is observed, presenting a wide-ranging modulation across diverse system parameters. This study not only enriches the understanding of the GH shift in complex atomic systems but also highlights the potential for the manipulation of these lateral shifts by fine-tuning key variables of the system, and contributes valuable insights to the broader field of optical phenomena in quantum systems.
The Goos-Hänchen (GH) shift refers to a lateral displacement (from the path expected from geometrical optics) along an interface in totally internal reflection. This phenomenon results from a coherence effect. In order to bring to light the role of coherence, the reflection of partially coherent light fields was investigated within the framework of the theory of coherence. A formal expression for the GH shifts of partially coherent light fields is obtained in terms of Mercer's expansion. It is shown that both the spatial coherence and the beam width have an important effect on the GH shift, especially near the critical angles (such as totally reflection angle). These results are important to observe the GH shifts of the beams with imperfect coherence, like x-ray and matter-wave beams.
The Goos-H\"anchen (GH) shift is a specifical optical phenomenon that describes a shift parallel to the reflected light inside the plane of incidence, when a finite-width light undergoes total internal reflection at the interface of medium. Although the GH shift in optics has been widely observed experimentally, its generalization remains uncovered completely in relativistic quantum mechanics for the spinor structure and the possible existence of Klein's paradox. Through approximation and angular spectrum analysis, we calculate the GH shift for Dirac fermions under relativistic conditions when they are incident obliquely on a three-dimensional infinite potential barrier. Furthermore, we find that the relativistic quantum GH shift will degenerate into the result based on Schr\"odinger equation under nonrelativistic limit, while the GH shift can be negative in Dirac's framework, which is different from the nonrelativistic case.