AI 中文总结
研究多体系统中涌现二能级子空间的与时间无关反绝热驱动，利用量子态黎曼流形中测地线运动及相关关系，通过实例说明该方法能在短时间尺度实现单位保真度态制备，还讨论了其在实际多体系统中的局限性。
AI 中文摘要
我们表明，量子态的黎曼流形中的测地线运动为与时间无关的反绝热驱动提供了一条直接途径。利用反绝热哈密顿量与量子度量张量之间的关系，我们证明匀速测地线使反绝热哈密顿量的希尔伯特 - 施密特范数恒定。对于反绝热修正具有固定算符方向的有效二能级系统，这进一步意味着完整的反绝热哈密顿量本身与时间无关。我们用朗道 - 齐纳模型、三能级受激拉曼绝热通道和处于阻塞 regime 的集体驱动里德堡系综来说明这一结果。讨论了这种方法在实际多体系统中的局限性，其中二能级约化只是涌现的，并且从有效子空间的泄漏限制了可实现的加速。在所有情况下，与时间无关的反绝热驱动在比传统绝热协议短得多的时间尺度上实现了单位保真度的态制备，同时用固定幅度场取代了时间形状的辅助控制。
英文摘要
We show that geodesic motion in the Riemannian manifold of quantum states provides a direct route to time-independent counterdiabatic driving. Using the relation between the counterdiabatic Hamiltonian and the quantum metric tensor, we prove that a constant-speed geodesic makes the Hilbert-Schmidt norm of the counterdiabatic Hamiltonian constant. For effective two-level systems whose counterdiabatic correction has a fixed operator direction, this further implies that the full counterdiabatic Hamiltonian itself is time independent. We illustrate this result with the Landau-Zener model, three-level Stimulated Raman adiabatic passage and a collectively driven Rydberg ensemble in the blockade regime. Limitations of this approach in realistic many-body systems are discussed, where the two-level reduction is only emergent and leakage out of the effective subspace bounds the achievable speedup. In all cases, time-independent counterdiabatic driving achieves unit-fidelity state preparation on timescales substantially shorter than conventional adiabatic protocols while replacing temporally shaped auxiliary controls by fixed-amplitude fields.
Comments7+1 pages, 4 figures
