Single-particle dynamics and interactions of stationary-light polaritons

本计画旨在探讨暗态极化激元（DSP）在研究物质波现象与多体物理上的潜力。我们将调查的DSP在一个，两个和三个空间维度的不同属性。我们将讨论制作旋量DSP的可能性以及光诱导阿贝尔和非阿贝尔规范势对单粒子和多粒子动力学的影响。我们将探讨标量和旋量DSP的标量和规范位的空间限制的限制。我们将分析有趣的和未观察到的现象的可观察性条件，这些现象存在于狄拉克粒子中，但不存在于自由薛定谔粒子中，如Zitterbewegung和Klein隧穿。在项目的第二部分，我们将研究DSP之间的相互作用的平均场水平或线性化近似。特别令人感兴趣的是非线性，由于有限的DSP与原子系统的相互作用。将研究在有效磁场存在下DSP玻色气体中涡旋的形成。一个相互作用的旋量DSP的详细调查将和一个经典的大规模Thirring模型的讨论。

The present project aims to explore the potentials of dark-state polaritons (DSP) to study matter-wave phenomena and many-body physics. We will investigate the different properties of the DSPs in one, two and three spatial dimensions. Possibilities to create spinor DSPs and the influence of light-induced Abelian and non-Abelian gauge potentials on the single and multi-particle dynamics will be analyzed. We will investigate limits of spatial confinement for scalar and spinor DSPs by scalar and gauge potentials. We will analyze conditions for the observability of interesting and unobserved phenomena, present for Dirac particles but absent for free Schrödinger particles such as Zitterbewegung and Klein tunneling. In the second part of the project we will study interactions between DSPs on the mean-field level or in linearization approximation. Of particular interest are nonlinearities due to the interaction of confined DSPs with the atomic system. The formation of vortices in the DSP bose gas in the presence of effective magnetic fields will be investigated. A detailed investigation of interacting spinor DSPs will be made and an implementation of a classical massive Thirring model discussed.