发表机构
Nantong University; University College Cork; Okinawa Institute of Science and Technology Graduate University; Rinn Quantum（南通大学; 科克大学; 冲绳科学技术大学院大学; 林量子）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出变分捷径绝热方案，通过调节Feshbach共振附近的非线性实现一维量子液滴的快速控制，数值模拟显示保真度超过0.99，为自束缚量子流体操控提供新途径。
AI 中文摘要
我们提出了一种变分捷径绝热方案，用于超冷玻色-玻色混合物中一维量子液滴的快速动力学控制。该控制通过时间依赖的平均场（MF）和超越平均场（BMF）非线性实现，这些非线性可通过调节Feshbach共振附近的种内和种间散射长度来调整。利用亮液滴变分拟设，结合逆向工程，我们推导出时间依赖的相互作用协议，该协议连接预定的初始和目标自束缚态，同时抑制残余激发。我们分析了三种代表性情形：MF和BMF项的同步控制、BMF非线性固定而MF相互作用时间依赖的控制，以及MF非线性固定而BMF相互作用时间依赖的控制。对于受约束的情形，引入额外的变分自由度以在尊重所施加限制的同时优化协议。扩展Gross-Pitaevskii方程的直接数值模拟证实，在短时间尺度上最终保真度超过0.99，并表明优化后的协议对非线性控制强度的有限校准误差具有鲁棒性。我们的结果为自束缚量子流体的快速态间操控提供了一条途径，并可能有助于超冷混合物中的受控物质波工程。
英文摘要
We propose a variational shortcut-to-adiabaticity scheme for the fast dynamical control of one-dimensional quantum droplets in ultracold Bose-Bose mixtures. The control is implemented through time-dependent mean-field (MF) and beyond-mean-field (BMF) nonlinearities, which can be adjusted by tuning intra- and interspecies scattering lengths near Feshbach resonances. Using a bright-droplet variational ansatz, together with inverse engineering, we derive time-dependent interaction protocols that connect prescribed initial and target self-bound states while suppressing residual excitations. We analyze three representative settings: simultaneous control of the MF and BMF terms, control with fixed BMF nonlinearity and time-dependent MF interaction, and control with fixed MF nonlinearity and time-dependent BMF interaction. For the constrained cases, additional variational degrees of freedom are introduced to optimize the protocols while respecting the imposed restrictions. Direct numerical simulations of the extended Gross-Pitaevskii equation confirm final fidelities exceeding $0.99$ on short time scales, and show that the optimised protocols are robust against finite calibration errors of the nonlinear control strength. Our results provide a route toward fast state-to-state manipulation of self-bound quantum fluids and may be useful for controlled matter-wave engineering in ultracold mixtures.
Comments9 pages, 5 figures
