Vincent Jarlaud

We present a study of the coherence properties of a variety of motional states of a single ion confined in a Penning ion trap. We demonstrate that the motion of the ion has a coherence time of the order of one second, using Ramsey interferometry. We introduce a technique for preparing the ion in an incoherent superposition of highly-excited motional states using a simple modification of optical sideband cooling. Coherent manipulation of these states allow measurements of optical and motional coherence to be carried out. We show that these highly-excited motional state superpositions have long coherence times despite the incoherent preparation of the states. Such states can be useful for sensitive motional dephasing measurements.

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.