Through a semiquantal procedure, we study the perturbed modulation of amplitude and phase of Gross-Piteavskii equation describing trapped Bose–Einstein condensates in an optical lattice potential. By introducing quantum correctional parameters, the problem is quantized and leads to the derivation of a novel dynamical instability criterion. Additional degrees of freedom carrying quantum properties play a central role on the refine of the instability bandwidth, and, combined to the strength of optical lattice potential, entail unstable modes into full stability. A set of computational tools exhibited various features that bear instability characteristics, to confirm analytically predicted results. The quantum fluctuations thus have a stabilizing effect on the dynamics of harmonically trapped Bose–Einstein condensates in an optical lattice potential.

中文翻译：

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量子校正对周期性光学晶格中俘获的玻色-爱因斯坦凝聚物调制不稳定性的影响

通过半量子过程，我们研究了描述在光学晶格势中捕获的玻色-爱因斯坦凝聚物的Gross-Piteavskii方程的振幅和相位的扰动调制。通过引入量子校正参数，该问题得以量化，并导致了新的动力学不稳定性判据的推导。携带量子性质的其他自由度在不稳定性带宽的细化中起着中心作用，并且结合光学晶格势的强度，需要将不稳定模式转变为完全稳定性。一组计算工具展示了具有不稳定性特征的各种功能，以确认分析预测结果。因此，量子涨落对光学晶格势中被谐波俘获的玻色-爱因斯坦凝聚物的动力学具有稳定作用。