Optimal preparation of many-body Rydberg states

在过去的几十年里，具有高度可控性的超冷原子已经成为研究多体系统物理的最强大的平台。与有效地将相互作用限制在短范围内的普通超冷原子不同，里德堡原子通过极大和远程的范德华或偶极相互作用克服了这一困难。为了最终发挥里德堡原子平台的潜力，实验必须在里德堡原子的有限寿命内进行；事实证明，这对多体系统来说是非常重要的。在这个方案中，我们计划通过为里德堡原子提供依赖于时间的控制参数来以最佳方式制备多体量子态，从而有助于缩短实验时间，使得(1)主要品质因数，即保真度或纠缠，接近其最大值，(2)时间成本比绝热方案所需的(远)短，(3)所获得的控制参数对相关的实验缺陷是健壮的。除了为实验小组提供支持外，我们还致力于在物理基本问题的研究方面取得理论进展，例如在里德堡原子平台上的相变动力学和Kibble Zurek机制(KZM)。此外，我们还将研究Rydberg系统的可控性和逼近固有的“量子速度极限”的可能性。为此，在本方案中，我们将把最优控制策略与先进的数值算法相结合应用于里德堡原子。我们计划使用的优化策略将是‘斩波随机基’(CRAB)方法，在该方法中，控制参数将在每次迭代中以增强的品质因数进行迭代优化，直到收敛到最优值。对于每一次迭代的动力学数值模拟，由于多体系统的Hilbert空间太大而不能精确处理，我们将使用张量网络算法，它根据提供的纠缠截断Hilbert空间或截断到基于Rydberg阻塞机制的截断。这项建议涵盖三个主要研究方向。首先，我们将找到控制参数的时间形状，这些参数允许将一维和二维光学晶格中的里德堡原子引导到具有给定激发数和最短持续时间的晶态。制备多体纠缠态，包括W态、GHZ态和其他高纠缠态将是我们的第二个重点。最后，我们将借助最优控制，研究里德堡原子在非线性猝灭下的线性-锯齿跃迁形式的KZM。

In the past decades ultra-cold atoms with high controllability have emerged as the most powerful platform to study the physics of many-body systems. In contrast to ordinary ultra-cold atoms where interactions are effectively restricted to short range, Rydberg atoms overcome this difficulty with extremely large and long-range van der Waals or dipolar interactions. To ultimately the potential of the Rydberg atomic platform, experiments have to be performed within the limited lifetime of Rydberg atoms; this turns out to be highly nontrivial for many-body systems. In this proposal we plan to contribute to reducing the experimental time by providing time dependent control parameters for Rydberg atoms to prepare many-body quantum states in an optimal fashion such that (1) the main figure of merit, i.e. fidelity or entanglement, is close to its maximum, (2) the time cost is (much) shorter than that required for adiabatic schemes and (3) the obtained control parameters are robust against relevant experimental imperfections. Besides offering support for experimental groups, we also aim at achieving theoretical progress in the investigation of fundamental question in physics, for instance the dynamics of phase transitions and Kibble Zurek mechanism (KZM), on the platform of Rydberg atoms. Moreover we will also study the controllability and the possibility to approach the intrinsic 'Quantum Speed Limit' for Rydberg systems. To this end, in the present proposal we will apply optimal control strategies combined with advanced numerical algorithms to Rydberg atoms. The optimization strategy we plan to use will be the 'Chopped Random-Basis' (CRAB) method, in which control parameters will be iteratively optimized with enhanced figure of merit at each iteration until convergence to an optimal value is reached. Regarding the numerical simulations of dynamics in each iteration since the Hilbert space for a many-body system is too large for exact treatment, we will use tensor network algorithms, which truncate the Hilbert space according to the afforded entanglement or to a truncation based on the Rydberg blockade mechanism. This proposal covers 3 major research lines. Firstly, we shall find the temporal shape of the control parameters that permit to steer the Rydberg atoms in both one dimensional and two dimensional optical lattices towards crystalline states with given excitation numbers with shortest time duration. Preparing multipartite entangled states including the W state, GHZ state and other states with high entanglement will be our second focus. Finally, we will study the KZM in terms of linear-zigzag transitions on Rydberg atoms for nonlinear quenches with the help of optimal control.