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$^+$) co-trapped in a Coulomb crystal with calcium ions ($^{40}$Ca$^+$), focusing on rotational transitions in the $|X^1Σ^+, ν" = 0> \rightarrow |A^1Σ^+, ν’ = 2>$ 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 $|A^1Σ^+, ν’ = 2>$, 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 local environmental temperature. We correlate the relative amplitudes of the observed transitions to the underlying thermalized ground-state rotational population distribution and extract the black-body radiation (BBR) temperature.

💡 Research Summary

This work presents a high‑resolution rovibronic spectroscopic study of calcium monohydride ions (CaH⁺) sympathetically cooled within a Coulomb crystal of laser‑cooled 40Ca⁺ ions. The authors employ resonance‑enhanced multi‑photon dissociation (REMPD) using a narrow‑linewidth continuous‑wave Ti‑Sapphire laser frequency‑doubled to the ultraviolet (≈380 nm). By scanning the laser across the |X¹Σ⁺, ν″ = 0⟩ → |A¹Σ⁺, ν′ = 2⟩ band, they resolve individual P‑branch (ΔJ = −1) and R‑branch (ΔJ = +1) transitions up to J = 15 with a spectral resolution better than 0.1 cm⁻¹ for high‑J lines and 0.3 cm⁻¹ for low‑J lines.

The experimental sequence begins with the formation of CaH⁺ via reaction of trapped Ca⁺ with a controlled H₂ leak (≈4.5 × 10⁻⁸ torr). Approximately a quarter of the calcium ions are converted, and the molecular ions are sympathetically cooled by the co‑trapped atomic ions. After a brief waiting period that allows the rotational population to thermalize with the ambient black‑body radiation (BBR), the UV laser is applied. The first photon resonantly excites a specific rovibrational transition; a second photon of the same wavelength promotes the molecule to a dissociative state that yields Ca⁺(2P) + H(1S). The newly created Ca⁺ ion is recaptured and its fluorescence is monitored. The time‑dependent fluorescence recovery follows A(t) = A