由於激子（exciton)在半導體共振腔内與光子強烈耦合作用形成半光及半子的極化激子 (polariton)，當入射激發雷射強度高於起始強度，極化激子可凝聚成極化激子凝聚態（polariton condensate)，簡稱極子態，極子態同時具有非平衡及非線性物理態，若考慮極化激子的自旋性對於 極子態的影響，則極子態變成二分量的極子態（spinor polariton condensate) ，二分量的極子態可有比 單分量的極子態更豐富的物理現象。吾人計晝研究二分量的極子態，此凝聚態在一維空間可形成自旋 光固子（spinor soliton)，而在二維空間此凝聚態可形成半自旋旋渦（half-quantum vortex)，自旋光 固子與半自旋旋渦的研究對於光自旋元件的研發提供關鍵知識。因此，吾人計晝第一年研究自旋光固 子在自旋極子態中的平穩態及其輻射強度分佈，藉由激發自旋光固子在自旋極子態中的激發態，吾人 可分析自旋光固子在自旋極子態中的穩定條件；第二年研究半自旋旋渦在自旋極子態中的平穩態及其 輻射強度分佈，探討半自旋旋渦在自旋極子態中的激發態，進而分析半自旋旋渦在自旋極子態中的穩 定條件及其自旋拓樸結構；第三年研究自旋光固子及半自旋旋渦受到缺陷作用後在自旋極子態中的平 穩態及其輻射強度分佈，自旋光固子及半自旋旋渦受到缺陷作用後的穩定度可由其激發態決定，我們 希望找到強化非線性與非平衡行為的最佳條件。 Spinor polariton condensates are two-component polariton condensates, which have richer physical phenomena than single-component polariton condensates. In this research project we would like to explore the formation and stability of spinor dark solitons (SDSs) and half-quantum vortices (HQVs) occurring in spinor polariton condensates (SPCs). SPCs, which mix both the phase and spin topologies, allow more complex and rich topological excitations than scalar ones. SDSs and half solitons can be created in a one-dimensional SPC. In the first year, we propose to study the stability of SDSs. Then we can see if the SDS can become stable in the regime that is supposed to be unstable in a homogeneous SPC. The realization and stabilization of the SDS will help us to extend our study on analyzing the physics and stability of half-solitons. After studying one-dimensional SPCs, we will change our attention on two-dimensional SPCs. In the second year, we propose to investigate the spin structure and stabilities of HQVs. The topological excitations of HQVs in a homogeneous SDS depend on the pump beam with tunable polarization and power. When the pump polarization is in favor of the vortex component of the HQV, the polarization texture is a polaritonic skyrmion with twisted pseudospin. Except the tunable polarization and power of a pump beam, the excitations of SDSs or HQVs in SDSs are also affected by the presence of defects. After finding the unstable region of SDSs and HQVs in a homogeneous SDS, in the third year, we propose to study the stabilization of SDSs and HQVs in SDSs by introducing a defect potential at the center of the density dip. We will investigate the topological excitations of HQVs pinned by a defect in SDSs. When the pump polarization is in favor of the vortex component of the HV pinned by a defect, the polarization texture is a skyrmion with twisted pseudospin. Except the stationary solution of the HQV pinned by a defect, a vortex-ring can exist in a SDS with an attractive and deep defect potential. The vortex ring is a ring with density being zero at the center of the ring. We propose to study the formation and stabilization of this vortex ring which is never studied in polariton condensates before. The polarization texture of the vortex ring is also another interesting physical phenomena, which is different the skyrmion of the HQV.
