Data for "Quantum state tracking and control of a single molecular ion in a thermal environment''

Supplementary data for the article "Quantum state tracking and control of a single molecular ion in a thermal environment" by Yu Liu, Julian Schmidt, Zhimin Liu, David R. Leibrandt, Dietrich Leibfried, Chin-wen Chou, submitted to Science in 2024. The manuscript describes a quantum state-specific investigation of the molecular state evolution of a single CaH+ ion in a thermal environment. The molecular state can be tracked in real time with single quantum-state resolution and the thermal radiation-induced transitions can be reversed with coherent molecular state manipulation according to the outcomes of state measurements. Results on the transition rates are used to infer the properties of the thermal environment. The data may be used to reproduce the plots shown in the figures.