J. C. J. Koelemeij

Recently we reported a high precision optical frequency measurement of the (v,L):(0,2)->(8,3) vibrational overtone transition in trapped deuterated molecular hydrogen (HD+) ions at 10 mK temperature. Achieving a resolution of 0.85 parts-per-billion (p.p.b.) we found the experimental value ($ν_0= 383,407,177.38(41)$ MHz) to be in agreement with the value from molecular theory ($ν_\text{th}=383,407,177.150(15)$ MHz) within 0.6(1.1) p.p.b. [Biesheuvel et al., Nat. Commun. 7, 10385 (2016)]. This enabled an improved test of molecular theory (including QED), new constraints on the size of possible effects due to 'new physics', and the first determination of the proton-electron mass ratio from a molecule. Here, we provide the details of the experimental procedure, spectral analysis, and the assessment of systematic frequency shifts. Our analysis focuses in particular on deviations of the HD+ velocity distribution from thermal (Gaussian) distributions under the influence of collisions with fast ions produced during (laser-induced) chemical reactions, as such deviations turn out to significantly shift the hyperfine-less vibrational frequency as inferred from the saturated and Doppler-broadened spectrum, which contains partly unresolved hyperfine structure.

Doppler broadening plays an important role in laser rovibrational spectroscopy of trapped deuterated molecular hydrogen ions (HD$^+$), even at the millikelvin temperatures achieved through sympathetic cooling by laser-cooled beryllium ions. Recently, Biesheuvel \textit{et al.} \cite{Biesheuvel2016} presented a theoretical lineshape model for such transitions which not only considers linestrengths and Doppler broadening, but also the finite sample size and population redistribution by blackbody radiation, which are important in view of the long storage and probe times achievable in ion traps. Here, we employ the rate equation model developed by Biesheuvel \textit{et al.} to theoretically study the Doppler-broadened hyperfine structure of the $(v,L):(0,3)\rightarrow(4,2)$ rovibrational transition in HD$^+$ at 1442~nm. We observe prominent yet hitherto unrecognized ghost features in the simulated spectrum, whose positions depend on the Doppler width, transition rates, and saturation levels of the hyperfine components addressed by the laser. We explain the origin and behavior of such features, and we provide a simple quantitative guideline to assess whether ghost features may appear. As such ghost features may be common to saturated Doppler-broadened spectra of rotational and vibrational transitions in trapped ions composed of partly overlapping lines, our work illustrates the necessity to use lineshape models that take into account all the relevant physics.

A calculation of dynamic polarizabilities of rovibrational states with vibrational quantum number $v=0-7$ and rotational quantum number $J=0,1$ in the 1s$σ_g$ ground-state potential of HD$^+$ is presented. Polarizability contributions by transitions involving other 1s$σ_g$ rovibrational states are explicitly calculated, whereas contributions by electronic transitions are treated quasi-statically and partially derived from existing data [R.E. Moss and L. Valenzano, \textit{Molec. Phys.}, 2002, \textbf{100}, 1527]. Our model is valid for wavelengths $>4~μ$m and is used to to assess level shifts due to the blackbody radiation (BBR) electric field encountered in experimental high-resolution laser spectroscopy of trapped HD$^+$ ions. Polarizabilities of 1s$σ_g$ rovibrational states obtained here agree with available existing accurate \textit{ab initio} results. It is shown that the Stark effect due to BBR is dynamic and cannot be treated quasi-statically, as is often done in the case of atomic ions. Furthermore it is pointed out that the dynamic Stark shifts have tensorial character and depend strongly on the polarization state of the electric field. Numerical results of BBR-induced Stark shifts are presented, showing that Lamb-Dicke spectroscopy of narrow vibrational optical lines ($\sim 10$ Hz natural linewidth) in HD$^+$ will become affected by BBR shifts only at the $10^{-16}$ level.

We have constructed an optical clock with a fractional frequency inaccuracy of 8.6e-18, based on quantum logic spectroscopy of an Al+ ion. A simultaneously trapped Mg+ ion serves to sympathetically laser-cool the Al+ ion and detect its quantum state. The frequency of the 1S0->3P0 clock transition is compared to that of a previously constructed Al+ optical clock with a statistical measurement uncertainty of 7.0e-18. The two clocks exhibit a relative stability of 2.8e-15/ sqrt(tau), and a fractional frequency difference of -1.8e-17, consistent with the accuracy limit of the older clock.

We report for the first time, laser spectroscopy of the 1S0 - 3P0 clock transition in 27Al+. A single aluminum ion and a single beryllium ion are simultaneously confined in a linear Paul trap, coupled by their mutual Coulomb repulsion. This coupling allows the beryllium ion to sympathetically cool the aluminum ion, and also enables transfer of the aluminum's electronic state to the beryllium's hyperfine state, which can be measured with high fidelity. These techniques are applied to a measurement of the clock transition frequency, ν= 1 121 015 393 207 851(8) Hz. They are also used to measure the lifetime of the metastable clock state, τ= 20.6 +/- 1.4 s, the ground state 1S0 g-factor, g_S = -0.00079248(14), and the excited state 3P0 g-factor, g_P = -0.00197686(21), in units of the Bohr magneton.