Quantum state tracking and control of a single molecular ion in a thermal environment

Over the past decade, cold molecular ions have emerged as a powerful platform for precision spectroscopy, controlled chemistry, and quantum information, yet the efficient control of their quantum states remains challenging. Recently, the use of quantum-logic spectroscopy (QLS), which maps information between a molecular ion and a motionally-coupled atomic ion, has enabled the state preparation/detection and coherent manipulation of diatomic ions [C.-W. Chou et al., Nature 545, 203 (2017)]. While QLS can project a molecular ion into a pure state, it only does so probabilistically. At room temperature, one must contend with the statistical population of hundreds to thousands of molecular states driven by black-body radiation. Here, we demonstrate a protocol to trap the population of a single CaH⁺ ion in its ground state |X¹Σ, v = 0, J = 0〉against the effects of thermal depopulation. Through repeated detection of population in |J = 1〉, we can catch and reverse the population driven out of |J = 0〉, thus effectively extending the lifetime of the |J = 0〉 state. We also show that the improved state control can lead to substantially higher data rates for precision spectroscopy. The generalizability of this protocol makes it a valuable tool for controlling larger molecular species.