Optimal preparation of many-body Rydberg states

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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.