Precise Determination of Excited State Rotational Constants and Black-Body Thermometry in Coulomb Crystals of Ca⁺ and CaH⁺

We present high-resolution rovibronic spectroscopy of calcium monohydride molecular ions (CaH⁺) cotrapped in a Coulomb crystal with calcium ions (⁴⁰Ca⁺), focusing on rotational transitions in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>|</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msup><mml:msup><mml:mi>Σ</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math>, <i>ν</i>″ = 0⟩ → |<i>A</i>¹Σ⁺, <i>ν</i>' = 2⟩ manifold. By resolving individual P and R branch transitions with record precision and using Fortrat analysis, we extract key spectroscopic constants for the excited state |<i>A</i>¹Σ⁺, <i>ν</i>' = 2⟩, specifically, the band origin, the rotational constant, and the centrifugal correction. Additionally, we demonstrate the application of high-resolution rotational spectroscopy of CaH⁺ presented here as an in situ probe of the local environmental temperature. We correlate the relative amplitudes of the observed transitions to the underlying thermalized ground-state rotational population distribution and extract the blackbody radiation (BBR) temperature.