Single-particle dynamics and interactions of stationary-light polaritons

本项目旨在探索暗态极化子(DSP)在研究物质波现象和多体物理方面的潜力。我们将研究数字信号处理器在一、二、三个空间维度上的不同性质。我们将分析产生旋量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。我们将用标量势和规范势研究标量和旋量数字信号处理器的空间限制极限。我们将分析有趣的和未观察到的现象的可观测条件，这些现象存在于狄拉克粒子，但不存在于自由薛定谔粒子，如Zitterbewegung和Klein隧穿。在项目的第二部分，我们将在平均场水平或线性化近似下研究数字信号处理器之间的相互作用。特别令人感兴趣的是由于受限数字信号处理器与原子系统相互作用而产生的非线性。我们将研究在有效磁场存在的情况下，DSP玻色气体中涡旋的形成。我们将对相互作用的旋量数字信号处理器进行详细的研究，并讨论经典大质量Thirring模型的实现。

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.