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中国物理学会期刊

双势阱中玻色-爱因斯坦凝聚体的绝热捷径动力学

Dynamics of Shortcut to Adiabaticity for Bose-Einstein Condensates in a Double-Well Potential

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  • 针对一维对称双势阱中玻色-爱因斯坦凝聚体(BEC)的高效量子调控问题,本文提出一种新型绝热捷径动力学方案。该方案基于含时Gross-Pitaevskii方程的标度不变性和广义Ermakov方程,结合逆向工程构建调控路径,通过实时调控系统参数动态补偿非绝热能量损耗,适配双势阱特有的势场结构。相较于传统绝热过程,该方案可在更短时间尺度内实现量子体系的高保真度调控,有效解决双势阱体系因几何复杂性与阱间相互作用导致的调控难题。研究为一维对称双势阱中BEC的精确量子操纵提供了可行路径,可进一步推广至多维双势阱量子体系的高效调控。

    To address the challenge of effcient quantum control of a Bose-Einstein condensate (BEC) in a one-dimensional symmetric double-well potential, we propose a novel shortcuts-to-adiabaticity (STA) dynamical protocol built upon the scaling invariance of the time-dependent Gross-Pitaevskii (GP) equation and the generalized Ermakov equation, with inverse engineering adopted to design the control trajectory. This approach enables high-fidelity quantum state manipulation on significantly shorter timescales, effectively overcoming control diffculties caused by the double-well structure’s geometric complexity and inter-well coupling. We constructed two coeffcient-dependent STA protocols: one based on the harmonic trap frequency, where fidelity increases with lower and narrower Gaussian barriers and an optimal parameter set maximizes fidelity at fixed control effciency; the other driven by interaction strength, where fidelity improves with longer evolution times but shows pronounced oscillations and sharp drops in short durations, with higher and narrower central barriers reducing fidelity and the single-well configuration yielding the highest fidelity. This work establishes a theoretical framework for STA-based effcient quantum control of BECs in symmetric double-well systems, which achieves high-fidelity manipulation with drastically reduced evolution times compared to conventional adiabatic methods. The framework lays a theoretical foundation for precise BEC control and is extendable to multi-dimensional and complex trapping potentials, providing practical guidance for parameter optimization in broader quantum engineering applications.

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