Pathak Maitri R, Nath Ajay
Indian Institute of Information Technology Vadodara, Gandhinagar, Gujarat, 382 028, India.
Sci Rep. 2022 Apr 28;12(1):6904. doi: 10.1038/s41598-022-10468-6.
Recent theoretical and experimental results show that one-dimensional (1D) weakly interacting atomic Bose-Bose mixtures with repulsive interspecies mean field (MF) interaction are stabilized by attractive quadratic beyond-mean-field (BMF) effects into self-bound quantum droplet (QD) in free space. Here, we construct an exact analytical model to investigate the structure and dynamics of QDs in presence of external harmonic confinement by solving the 1D extended Gross-Pitäevskii equation (eGPE) with temporal variation of MF and BMF interactions. The model provides the analytical form of wavefunction, phase, MF and BMF nonlinearities. The generation of QDs and interesting droplet to soliton transition in presence of regular/expulsive parabolic traps by taking the comparable MF and BMF interactions are illustrated. We derive the phase diagram of the droplet-soliton phase transition between amplitude of MF, BMF interactions and harmonic oscillator frequency. The strength and form of oscillator frequency are identified as key parameter for tuning the compression, fragmentation and transport of droplets. Finally, the stability of the obtained solutions are confirmed from Vakhitov-Kolokolov (VK) criterion and are found stable.
最近的理论和实验结果表明，具有排斥性种间平均场（MF）相互作用的一维（1D）弱相互作用原子玻色 - 玻色混合物，通过吸引性二次超越平均场（BMF）效应在自由空间中稳定形成自束缚量子液滴（QD）。在此，我们构建了一个精确的解析模型，通过求解具有MF和BMF相互作用随时间变化的一维扩展格罗斯 - 皮塔耶夫斯基方程（eGPE），来研究存在外部谐波限制时量子液滴的结构和动力学。该模型给出了波函数、相位、MF和BMF非线性的解析形式。通过考虑可比的MF和BMF相互作用，展示了在存在规则/排斥性抛物线陷阱的情况下量子液滴的产生以及有趣的液滴到孤子的转变。我们推导了在MF、BMF相互作用幅度和谐波振荡器频率之间液滴 - 孤子相变的相图。振荡器频率的强度和形式被确定为调节液滴压缩、破碎和输运的关键参数。最后，根据瓦赫托夫 - 科洛科洛夫（VK）判据证实了所得解的稳定性，发现它们是稳定的。
