AI 中文总结
本研究将量子最优控制扩展为可同时优化任意中间时间的可观测量，应用于Heisenberg XXX自旋链实现Dicke态激发的传播与复兴操控，为量子态动态跟踪及主动操控提供了新框架。
AI 中文摘要
标准量子最优控制（QOC）协议通常仅在最终目标时间最大化物理目标，但在时间演化过程中跟踪或测量量子态需要对演化中间阶段的控制。本研究将QOC扩展为可同时优化任意中间时间的可观测量。利用变分方法，我们证明中间观测会导致伴随态轨迹出现不连续性，该问题可通过Krotov算法处理，在零时间测量窗口极限下实现单调优化与收敛结果。我们将该多时间公式应用于Heisenberg XXX自旋链，以控制Dicke态激发的传播（包括无场复兴）。结果表明，同时优化同一可观测量会重塑驱动场，以平衡中间目标与最终布居。最后，我们展示该框架如何实现自旋激发的动态跟踪及脉冲后量子态复兴的主动操控。
英文摘要
Standard Quantum Optimal Control (QOC) protocols typically maximize a physical objective just at a final target time. However, tracking or measuring the quantum state during the time evolution requires the control at intermediate stages of their evolution. In this work, we extend QOC to accommodate the simultaneous optimization of observables at arbitrary intermediate times. Using a variational approach, we show that intermediate observations induce discontinuities in the costate trajectory, which can be handled with a Krotov algorithm leading to monotonic optimization and convergent results in the limit of zero temporal measurement windows. We apply this multi-time formulation to a Heisenberg XXX spin chain to control the propagation, including field-free revivals, of a Dicke state excitation. Our results demonstrate that simultaneous optimization of the same observable reshapes the driving field to balance intermediate targets with final populations. Finally, we show how this framework enables dynamic tracking of spin excitations and the active manipulation of post-pulse quantum state revivals.
Comments9 pages, 7 figures
