We have investigated the dynamic of cooled and trapped polariton state using Landau–Zener–Stückelberg interferometry theory (LZSIT). The effects of exciton–cavity coupling and the laser cooling over the qubit dynamics are analyzed in multi-crossing scenarios, supporting some of our basic results (Kenfack et al. in Comput Condens Matter 11:47–54, 2017; Ekengoue et al. in Comput Condens Matter 14:106–113, 2018). We have performed detailed calculations of the energy eigenvalues, non-adiabatic and adiabatic transition probabilities in the framework of weak- and strong-coupling regime under the laser light. As a main result, we pointed out the braking down of the Pauli exclusion principle providing the applicability of LZSIT for the analysis of polariton’s dynamic through a model which satisfies Fermi–Dirac statistics. Moreover, we found the generation of arbitrary waveforms of interferometric signals including sinusoidal, for weak coupling and strong laser amplitude. Thus, the dynamics of the polariton induces the destruction and the construction of interferences patterns in strong coupling between cavity laser and qubit. Extremely accurate interferometric signals generation by means of geometric phase effect has been demonstrated in this work with the goal of realizing robust control of the quantum coherent states of the polaritonic system. This geometric phase enhancement, which is essentially originated from the dynamic behavior of cooled and trapped polariton, is a significant consequence of the fastest population transfer and quantized energy of the system. Therefore, the geometric phase plays a crucial role in the study of the alter crossings behavior through cooled and trapped polariton, especially in the population transfer and energy of the system.

我们已经使用Landau–Zener–Stückelberg干涉测量理论（LZSIT）研究了冷却和捕获的极化子态的动力学。在多交叉场景中分析了激子-空穴耦合和激光冷却对量子位动力学的影响，支持了我们的一些基本结果（Kenfack等人，Comput Condens Matter 11：47-54，2017; Ekengoue等人。在Comput Condens Matter 14：106–113，2018）中。我们已经在激光的弱耦合和强耦合状态下对能量本征值，非绝热和绝热跃迁概率进行了详细的计算。作为主要结果，我们指出，通过满足费米-狄拉克统计量的模型，可以降低保利排斥原理，从而为LZSIT分析极化子动力学提供了适用性。此外，我们发现干涉信号的任意波形（包括正弦波）的生成都是弱耦合和强激光振幅。因此，极化子的动力学在腔激光器和量子比特之间的强耦合中引起破坏和干涉图案的构建。为了实现对极化子系统的量子相干态的鲁棒控制，在这项工作中已经证明了通过几何相位效应产生极其精确的干涉信号。这种几何相位增强基本上源于冷却和捕获的极化子的动态行为，是系统中最快的种群转移和量子化能量的重要结果。因此，