We performed high-resolution Fourier-transform spectroscopy measurements and direct-potential-fit of the shelflike RbCs $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ state. Overall, 2317 rovibronic ${v}^{\ensuremath{'}},{J}^{\ensuremath{'}}$ term values with ${v}^{\ensuremath{'}}\ensuremath{\in}[3,88]$, ${J}^{\ensuremath{'}}\ensuremath{\in}[7,276]$ were obtained with accuracy 0.01 cm${}^{\ensuremath{-}1}$ from the $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+},a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ laser-induced fluorescence (LIF) spectra. The mass-invariant potential energy curve constructed by means of the Chebyshev polynomial expansion reproduced the experimental term values of both
85Rb
133Cs and
87Rb
133Cs isotopologues with a standard deviation of 0.005 cm${}^{\ensuremath{-}1}$. We simulated the optical cycle $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+},a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}\ensuremath{'}},{J}^{\ensuremath{'}\ensuremath{'}}=0)\ensuremath{\rightarrow}(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}},{J}^{\ensuremath{'}}=1)\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}\ensuremath{'}}=0,{J}^{\ensuremath{'}\ensuremath{'}}=0)$ appropriate to transfer translationally ultracold RbCs molecules into their absolute ground state from the weakly bound rovibronic levels of both singlet $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and triplet $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ ground states. The optimal transfer via the intermediate $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ state with ${v}^{\ensuremath{'}}=58,60$, and 61 for
85Rb
133Cs as well as ${v}^{\ensuremath{'}}=59$ and 61 for
87Rb
133Cs was predicted. The required spin-allowed $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{-}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and spin-forbidden $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{-}a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ dipole transition moments were obtained within the framework of ab initio quasirelativistic calculations. The predicted $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+},a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ transition probabilities were consistent with the experimental relative intensity distributions for several $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}})\ensuremath{\rightarrow}X,a({v}^{\ensuremath{'}\ensuremath{'}})$ LIF progressions.
This thesis presents the results of my graduate work which has concentrated on applying laser-cooling techniques to molecular ions, specifically CaH⁺ and BH⁺ ions for the study of their rovibronic spectroscopy. The goal of my research has been to control external and internal degrees of freedom of these two ions. Each of these molecules is spectroscopically appealing in its own right. For starters, CaH⁺ has been identified as a potential system for the test for the time variation of fundamental constants, and it's also been speculated to be in space. BH⁺ has a nearly diagonal Franck-Condon structure, and could be directly laser-cooled using only a few lasers. This structure makes it a good candidate for the cooling of internal molecular degrees of freedom. Each of the experiments described in this review involves the trapping and laser-cooling of ions. We cool the molecular ions sympathetically with laser-cooled Ca⁺. The probing techniques used to collect data are mainly: laser induced fluorescence, mass spectrometry, and resonance-enhanced multi-photon dissociation (REMPD). We have demonstrated the ground state sympathetic cooling of CaH⁺ ion to less than 16
muK, and we have used to REMPD to measure for the first time four vibronic transitions in CaH⁺ ions. Together, these results are important for future quantum logic experiments on this molecule. Furthermore, we have also made some progress towards trapping and cooling BH⁺ ions by first trapping B⁺ ions with Ca⁺ ions. We use the motional resonance method to detect the B⁺ ions, which can be reacted with H atoms to produce the molecular ions. Following the measurement of the vibronic spectrum of CaH⁺, we have narrowed the linewidth of the laser source to resolve rotational lines.
In this Perspective, we examine the use of laser-cooled atomic ions and sympathetically cooled molecular ions in Coulomb crystals for molecular spectroscopy. Coulomb crystals are well-isolated environments that provide localization and long storage times for sensitive measurements of weak signals and cold temperatures for precise spectroscopy. Coulomb crystals of molecular and atomic ions enable the detection of single-photon molecular ion transitions at a range of wavelengths by a change in atomic ion fluorescence at visible wavelengths. We give an overview of the state of the art from action spectroscopy to quantum logic spectroscopy for a wide range of molecular transitions from rotational sublevels separated by 10 –7 cm –1 to rovibronic transitions at 25 000 cm –1 . We emphasize how this system allows for unparalleled control of the molecular ion state for precision spectroscopy with applications in astrochemistry and fundamental physics. We conclude with an outlook of the use of this control in cold molecular ion reactions.
We report on the use of depletion spectroscopy to detect ultracold ground-state KRb molecules with rotational resolution. The population of a specific ground-state vibrational level ${v}^{\ensuremath{''}}$, produced by photoassociation of ultracold atoms, is monitored by one-color two-photon pulsed-laser ionization. When a cw laser is resonant with a rovibrational transition to an excited state, the ground-state population, and hence the ion signal, is depleted. This narrow-band spectroscopic technique allows the individual rotational levels in both ground and excited states to be resolved, and thus the population of a single ground-state rovibrational level to be monitored. These resolved transitions are a necessary first step in transferring population from high vibrational levels of the ground state, such as produced by photoassociation, to the absolute molecular ground state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ (${v}^{\ensuremath{''}}=0$, ${J}^{\ensuremath{''}}=0$). This technique can also be used to determine binding energies of high-${v}^{\ensuremath{''}}$ molecules. Combining our binding energy measurement with the results of previous spectroscopy yields an improved dissociation energy of the
X state: ${D}_{e}=4217.822\ifmmode\pm\else\textpm\fi{}0.003\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. We also report on the two-color pulsed-laser ionization used to locate the depletion transitions.
We report a high-resolution spectroscopic study of molecular ions at millikelvin temperatures. We measured several rovibrational infrared transitions in
HD+ molecular ions, stored in a radio-frequency trap and sympathetically cooled to $\ensuremath{\approx}20\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ by laser-cooled
Be+ ions. We observed hyperfine splitting of the lines, in good agreement with theoretical predictions. The transitions were detected by monitoring the decrease in ion number after selective photodissociation of
HD+ ions in the upper vibrational state. The method described here is expected to be generally applicable.
High resolution Fourier transform spectra (FTS) of laser induced fluorescence (LIF) of $C\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+};D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}\ensuremath{\rightarrow}A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ and $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ transitions in
Na85Rb and
Na87Rb were obtained. An analysis of the direct LIF spectra together with the rotational relaxation satellites provided highly accurate rovibronic term values for $(4\ensuremath{\leqslant}J\ensuremath{\leqslant}163)$ of the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ complex, covering about 1950 mostly singlet levels $0\ensuremath{\leqslant}{v}_{A}\ensuremath{\leqslant}49$ and a considerable number
(>360) of the predominantly triplet $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0,1}$ sublevels. The direct deperturbation analysis of the singlet-triplet
A−−b complex was performed by means of the inverted channel-coupling approach with Hund's coupling case
a basis functions. The electronic matrix elements of the model $4\ifmmode\times\else\texttimes\fi{}4$ Hamiltonian were defined as piecewise analytical functions of the internuclear distance. Besides the Born-Oppenheimer potential energy curves of the mutually perturbed states and the off-diagonal spin-orbit (SO)
A−−b coupling function, the SO splitting of the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ state was determined due to the pronounced electronic-rotation interaction between the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0}$ and $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{1}$ components observed for high
J levels. Overall, 24 mass-invariant fitting parameters have been required to reproduce about 2300 experimental term values of both isotopomers with a standard deviation of $0.012\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is consistent with the uncertainty of the FTS experiment. An analytical mapping procedure based on a reduced variable representation of the radial coordinate was used to diminish the computational effort for the uniform finite-difference grid solution of the coupled-channel equations. The derived nonadiabatic
A−−b wave functions were used to evaluate the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}--D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$, $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$, $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ rovibronic transition probabilities. The relative intensity distributions predicted for the $D\ensuremath{\rightarrow}A--b$ and $A--b\ensuremath{\rightarrow}X$ LIF progressions agree with their experimental counterparts within the accuracy of the measurements. The calculated
A−−b−−a,
X transition probabilities were applied for simulation of the stimulated Raman $a\ensuremath{\rightarrow}A--b\ensuremath{\rightarrow}X$ processes, which can lead to efficient formation of ultracold NaRb molecules in the ground level
vX=0;
JX=0.