Optical spectroscopy in the gas phase is a key tool for elucidating the structure of atoms and molecules and their interaction with external fields. The line resolution is usually limited by a combination of first-order Doppler broadening due to particle thermal motion and a short transit time through the excitation beam. For trapped particles, suitable laser cooling techniques can lead to strong confinement (the Lamb–Dicke regime) and thus to optical spectroscopy free of these effects. For non-laser-coolable spectroscopy ions, this has so far only been achieved when trapping one or two atomic ions, together with a single laser-coolable atomic ion^1,2. Here we show that one-photon optical spectroscopy free of Doppler and transit broadening can also be obtained with more easily prepared ensembles of ions, if performed with mid-infrared radiation. We demonstrate the method on molecular ions. We trap ~100 molecular hydrogen ions (HD⁺) within a Coulomb cluster of a few thousand laser-cooled atomic ions and perform laser spectroscopy of the fundamental vibrational transition. Transition frequencies were determined with a lowest uncertainty of 3.3 × 10⁻¹² fractionally. As an application, we determine the proton–electron mass ratio by matching a precise ab initio calculation with the measured vibrational frequency.

气相光谱是阐明原子和分子结构及其与外场相互作用的关键工具。线分辨率通常受到粒子热运动引起的一阶多普勒展宽和通过激发光束的短传输时间的限制。对于捕获的粒子，合适的激光冷却技术可以导致强限制（Lamb-Dicke 方案），从而使光谱学不受这些影响。对于非激光可冷却的光谱离子，到目前为止，这仅在捕获一个或两个原子离子以及一个可激光冷却的原子离子^1,2时实现. 在这里，我们表明，如果使用中红外辐射进行，也可以使用更容易制备的离子集合获得没有多普勒和传输展宽的单光子光谱。我们演示了分子离子的方法。我们将约 100 个分子氢离子 (HD ⁺ ) 捕获在由数千个激光冷却原子离子组成的库仑簇中，并对基本振动跃迁进行激光光谱分析。^{跃迁频率以 3.3 × 10 -12}的最低不确定度分数确定。作为一种应用，我们通过将精确的从头计算与测量的振动频率相匹配来确定质子 - 电子质量比。