Steffen Meyer

We reflect on the prospect of exploiting the recoil associated with absorption and emission of photons to perform spectroscopy of a single molecular ion. For this recoil to be detectable, the molecular ion is sympathetically cooled by a laser-cooled atomic ion to near their common quantum mechanical ground state within a trapping potential. More specifically, we present a general framework for simulating the expected photon recoil spectra in regimes where either the natural transition linewidth $Γ_t$ of the molecular ion or the spectral width $Γ_L$ of the exciting light source exceeds the motional frequencies of the two-ion system. To exemplify the framework, we present two complementary cases: spectroscopy of the broad 3s $^2$S$_{1/2}$ - 3p $^2$P$_{3/2}$ electronic transition ($Γ_t/2π= 41.8$ MHz) of a single $^{24}$Mg$^+$ ion at $λ=279.6$ nm by a narrow laser source ($Γ_L/2π\lesssim 1$ MHz) and mid-infrared vibrational spectroscopy of the very narrow $|v=0,J=1\rangle$ - $|v'=1,J'=0\rangle$ transition ($Γ_t/2π= 2.50 $ Hz) at $λ=6.17$ $μ$m in the $^1Σ^+$ electronic ground state of $^{24}$MgH$^+$ by a broadband laser source ($Γ_L/2π\gtrsim$ 50 MHz). The atomic ion $^{24}$Mg$^+$ has been picked to introduce a simple system to make comparisons with experimental results while still capturing most of the physics involved in electronic excitations of molecular ions.

We demonstrate the use of a femtosecond frequency comb to coherently drive stimulated Raman transitions between terahertz-spaced atomic energy levels. More specifically, we address the $3d~^2D_{3/2}$ and $3d~^2D_{5/2}$ fine structure levels of a single trapped $^{40}$Ca$^+$ ion and spectroscopically resolve the transition frequency to be $ν_D = 1{,}819{,}599{,}021{,}534 \pm 8$ Hz. The achieved accuracy is nearly a factor of five better than the previous best Raman spectroscopy, and is currently limited by the stability of our atomic clock reference. Furthermore, the population dynamics of frequency-comb-driven Raman transitions can be fully predicted from the spectral properties of the frequency comb, and Rabi oscillations with a contrast of 99.3(6)\% and millisecond coherence time has been achieved. Importantly, the technique can be easily generalized to transitions in the sub-kHz to tens of THz range and should be applicable for driving, e.g., spin-resolved rovibrational transitions in molecules and hyperfine transitions in highly charged ions.