Laser control of polariton using Landau–Zener–Stückelberg interferometry theory

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.