Optimal preparation of many-body Rydberg states

多体里德伯态的最佳制备

• 批准号: 316184660
• 负责人: Professor Dr. Tommaso Calarco
• 金额: --
• 依托单位: Forschungszentrum Jülich
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/316184660?language=en
• 关键词: Optimal; preparation; many; body; Rydberg

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.

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平台。 与普通的超冷原子相比，里德伯原子的相互作用被有效地限制在短程，里德伯原子克服了这个困难，具有非常大的和长程的货车德瓦尔斯或偶极相互作用。 为了最终发挥里德伯原子平台的潜力，实验必须在里德伯原子的有限寿命内进行;这对多体系统来说是非常重要的。在这个提议中，我们计划通过为里德伯原子提供与时间相关的控制参数来减少实验时间，以最佳方式制备多体量子态，使得（1）主要品质因数，即保真度或纠缠度，接近其最大值，（2）所需时间比绝热方案短得多;（3）所获得的控制参数对相关的实验缺陷具有鲁棒性。除了为实验组提供支持外，我们还致力于在物理学基本问题的研究中取得理论进展，例如相变动力学和Kibble Zurek机制（KZM），在Rydberg原子的平台上。此外，我们还将研究里德堡系统的可控性以及接近固有“量子速度极限”的可能性。为此，在本提案中，我们将应用最优控制策略结合先进的数值算法的里德堡原子。我们计划使用的优化策略将是“斩波随机基”（CRAB）的方法，其中控制参数将迭代优化，在每次迭代中提高品质因数，直到收敛到最佳值。关于每次迭代中的动力学数值模拟，由于多体系统的希尔伯特空间太大而无法精确处理，我们将使用张量网络算法，该算法根据提供的纠缠或基于Rydberg封锁机制的截断来截断希尔伯特空间。该项目包括三大研究方向。首先，我们将找到的时间形状的控制参数，允许引导里德堡原子在一维和二维光学晶格向结晶状态与给定的激发数与最短的持续时间。制备多体纠缠态，包括W态、GHZ态和其他高纠缠态是我们的第二个研究重点。最后，我们将利用最优控制研究里德堡原子线性-锯齿形跃迁的KZM。