Abstract:
This master's thesis investigates the excitation and correlation dynamics of a one-dimensional chain of Rydberg atoms with van der Waals interactions, utilizing two numerical methods: discrete truncated Wigner approximation (dTWA) and artificial neural networks (ANN). Specifically, the total number of excitations, the long-time average number of excitations, the maximum number of excitations, and second-order half-chain R\'enyi entanglement entropy is analyzed over time.
The research findings show that, for intermediate timescales and smaller interaction strengths, the 1st-order dTWA is effective in capturing the excitation dynamics. However, due to the numerical instability of the 2nd-order dTWA equations, this thesis proposes an approach to handle the instabilities by identifying and eliminating the terms causing the divergence in the 2-point correlation equations of motion. This method has resulted in delayed divergence and improved results compared to the 1st-order dTWA. Additionally, this thesis demonstrates that the ANN approach provides a reliable method to capture the excitation dynamics and 2nd-order Renyi entanglement entropy, achieving better results with an increase in the number of parameters. This thesis suggests further exploration of other neural network architectures for studying this system and the inclusion of higher-order dTWA to address the instability issue in the 2-point correlation equation of motion. Overall, these numerical methods could facilitate the development of theoretical and numerical tools for benchmarking and improving the performance of Rydberg quantum simulators. Therefore, this master's thesis highlights the potential of dTWA and ANN as powerful numerical methods for studying Rydberg quantum simulators.
