Analyzing Rydberg excitation dynamics using different numerical methods

Abstract

The exponential scaling of the Hilbert space dimension makes a quantum many-body system impossible to solve using even the best supercomputers available. However, recent experimental breakthroughs in realizing quantum many-body systems using quantum simulators have resulted in tremendous development in the field especially using ultracold Rydberg atoms. As a result, one can study non-equilibrium dynamics in closed quantum many-body systems in an unprecedented control. Yet, the theoretical side of the field lacks the requisite computational tools to study the non-equilibrium dynamics in a quantum many-body system. Thus there is solid demand for developing approximate computational techniques to benchmark these experiments.

In this regard, many numerical methods, such as phase-space methods, tensor networks, etc., are in place for studying the non-equilibrium dynamics. However, all of them are restricted to either weakly correlated systems or lower dimensional systems. Recently, new numerical approaches such as discrete truncated Wigner approximation (DTWA) and artificial neural networks (ANN) have been introduced to study the dynamics in strongly interacting and higher dimensional quantum many-body systems. Nonetheless, there is also a need for testing these numerical methods to understand their range and limitations against direct experimental observations. The recent development of the highly scalable Rydberg-based quantum simulators would be an excellent platform to test the capabilities of these two numerical methods.

This thesis will focus on understanding the power and limitations of DTWA and ANN in studying non-equilibrium dynamics in a chain of atoms with Rydberg excitations. We consider both the systems with van der Waals and dipole-dipole interactions. We mainly look at the Rydberg excitation dynamics for different interaction strengths, with the initial state being all the atoms in the ground state. For small systems, we compare the above results with the exact dynamics obtained from numerically solving the Schrodinger equation.

We observe that the DTWA results perfectly match with the exact results for a wide range of interaction strengths and up to intermediate time. For large interactions and later time, although we observe deviations from the exact results because of higher-order correlations, long-time averages calculated using DTWA match well with that of the exact dynamics. Using DTWA, we also see that we can study large systems of size up to 200. We further notice that the ANN method works very well for small systems, even for large interaction strengths, unlike DTWA. However, further study is required to check the capability of ANNs in large systems.