Machine Learning for Quantum Rotor Dynamics: A Surrogate Model Approach to Rotational Excitation in External Electric Fields

The quantum rotor in external fields such as static electric, magnetic, and time-dependent fields is one of the most studied research problems due to its applicability in chemical physics, molecular dynamics, and many other related areas. The problem finds applications in quantum chaos and nonlinear dynamics as well. In this work, we present a Machine learning (ML) approach to model a one-dimensional quantum rotor in an external electric field. Our approach is to develop a surrogate model, keeping in mind the inherent smoothness of the eigenenergies of the dressed rotor and the directional parameters such as orientation, i.e., expectation value of $\cos ？$ , and the alignment parameter ($？{\cos }^2？？$ ) with the applied static field. The model we developed is very efficient, achieving microsecond-scale predictions with high accuracy. The model we developed is as follows: first, we train it on the basis of data generated from numerical calculations taking rotor-static field interaction into account and expanding the wavefunction as a finite basis. The model gives an excellent performance with R² values exceeding 0.9999 for all predicted quantities. We further explore the physics of the system and the data generation, the details of the ML model, and its uses in designing an inverse model. The work shows that ML can be used to speed up computational time in related areas such as molecular physics and may be used to optimize the experimental parameters. This approach is directly extensible to three-dimensional rotors, time-dependent fields, and multi-parameter optimization, with potential applications in quantum control, molecular alignment, and spectroscopic fitting.