Reassigning the Cah $^+ $1$^{1}\Sigma\Rightarrow $2$^{1

$Reassigning the Cah $^+ $1$^{1}\Sigma\Rightarrow $2$^{1$

Reassigning the CaH+ 11Σ → 21Σ vibronic transition with CaD+ John Condoluci,1 Smitha Janardan,1 Aaron T. Calvin,1 Ren´eRugango,1 Gang Shu,1 and Kenneth R. Brown1, 2, 3, a) 1)School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA 30332, USA 2)School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA 3)School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA (Dated: 5 July 2021) We observe vibronic transitions in CaD+ between the 11Σ and 21Σ electronic states by resonance enhanced multiphoton photodissociation spectroscopy in a Coulomb crystal. The vibronic transitions are compared with previous measurements on CaH+. The result is a revised assignment of the CaH+ vibronic levels and a disagreement with CASPT2 theoretical calculations by approximately 700 cm−1.

I. INTRODUCTION in the electronic energy from CASPT2 and leads to a revised labeling of the CaH+ and CaD+ vibronic transi- Co-trapping molecular ions with Doppler-cooled tions. atomic ions sympathetically cools the molecular motion to millikelvin temperatures, enabling studies in spectroscopy and reaction dynamics.1–5 Cold ionic ensembles II. METHODS in a variety of platforms have proved useful for astro- 6–8 chemical identification and studies of internal state A. Experimental Setup distributions,3,9 while co-trapping with Doppler-cooled ions offers advantages for probing the possible time varia- The experiment employed a manually-tuned, tion of fundamental constants,10–12 and performing quan- 13–16 frequency-doubled Ti:Sapphire laser to probe the tum logic spectroscopy. Ionic metal-hydrides like + + + vibronic transitions of CaD co-trapped with laser- CaH and MgH are promising candidates for these + 17 cooled Ca in a heterogeneous Coulomb crystal. By applications due to their large rotational constants and measuring the Ca+ fluorescence increase upon laser Doppler-cooled dissociation products. exposure, a spectrum of molecular dissociation rate was To date, spectroscopy on CaH+ is limited to two vi- 18 generated. The experiments take place in an ultrahigh brational overtones, four vibrational levels within the vacuum chamber with a background pressure of 10−10 21Σ state,19 a photodissociative electronic transition,20 and single-ion quantum logic probes of rotational state.16 The vibronic transitions of Ref. 19 were previously as- 5.4×104 signed according to theory. The observed transition frequencies agreed to within 50 cm−1 of theory, but the 5.2×104 v = 0 → v0 = 0 transition was not observed. A simi- Ca++H Ca++D lar issue was encountered for the isoelectronic KH neu- 5.0×104 tral, where the first few vibronic lines were experimentally absent and KD spectroscopy was required in order

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21–24 1 to correctly assign the KH transitions. Isotopic sub- - 2.8×10 v' = 3 v' = 4 4 m v' = 2 v' = 3

stitution changes the reduced mass but maintains the c 2.7×10 1 ( v' = 1 2 Σ v' = 2 4

adiabatic electronic potential energy. The resulting shift ν 2.6×10 v' = 1 v' = 0 v' = 0 in vibrational energy levels can be compared to theory to 2.5×104 conﬁrm peak assignments. 8.0×102 v = 0 Here we apply this method to the spectroscopy of 1 2 1 Σ arXiv:1705.01326v1 [physics.atom-ph] 3 May 2017 + + 6.0×10 v = 0 CaH and CaD . Vibronic transitions were calculated 2 25 4.0×10 using a CASPT2 internuclear potential and then com- 2 pared to measured transition frequencies obtained by 2.0×10 resonance enhanced multiphoton photodissociation spec- CaH+ CaD+ troscopy (REMPD). Instead of observing the predicted shifts for deuterium substitution based on our previous FIG. 1. Energy level diagram of the CaH+ and CaD+ tran- assignment, this study reveals a 687 cm−1 disagreement sitions probed by applying a doubled Ti:Sapphire laser and observing resonance enhanced photodissociation. The photodissociation of dark CaD+ ions in the crystal into trapped Ca+ and free H can be observed in the crystal image and by + a)Electronic mail: [email protected] an increase in 397 nm Ca ﬂuorescence signal. 2

1.02 a ﬁrst-order model by assuming the dissociation rate is much greater than the ﬁrst excitation rate. 1.00 The spectra labeled “Theory” in Fig. 3 rely heavily on CASPT2 ab initio calculations: the potential energy 0.98 surfaces, transition dipole moments µv→v0 , and vibronic ∞ transition frequencies G (v0) come from Ref. 25. Har-

A 0→1 /

A monic, ω1, and anharmonic, ωχ1, constants were gen- 0.96 erated using the internuclear potential curves and R.J. 396 nm 27 396 nm fit LeRoy’s open-source project, Level 8.2. Relative peak 0.94 392 nm heights were determined by assuming a thermal distribu- 392 nm fit tion of the rotational states in 11Σ. The first 15 J rota- 0.92 tional levels contribute >99.99% of the initial state pop- 0 100 200 300 400 ulation and dominate the shapes of the vibronic peaks. Time (ms) During spectral simulation, the spectral density of the laser was held at a constant linewidth of 80 cm−1 to FIG. 2. Observed Ca+ fluorescence of composite Coulomb crystals exposed to two laser frequencies. An increase in flu- match the laser linewidth based on spectrometer mea- orescence indicates resonance-enhanced dissociation of CaD+ surements. The model’s invariant peak intensity of 4.77 8 2 into Ca+ and D. Dissociation rates extracted from Eqn. 1 are × 10 W/m was calculated from the laser power and plotted against frequency in Fig. 3. beam waist diameter at the trap center. The ab initio calculated energy of the 11Σ ground vibrational state was used as a reference for all transitions due to lack of torr and the ions are held in a linear Paul trap. CaD+ experimental data on the ground state potential. + is generated by reaction of D2 with excited Ca at pres- sures of 10−8 torr. The Ca+ is observed and laser cooled by the laser-induced fluorescence at 397 nm. A repump III. RESULTS AND DISCUSSION laser at 866 nm is also required to close the transition. Details of the experimental setup may be found in our A. Comparison of Spectra previous work19 on the vibronic spectroscopy of CaH+. + The CASPT2 potential energy surface of CaH guided + + 25 Fig. 3 compares the REMPD spectra of CaH and our spectroscopic search for CaD vibronic transitions. + + To achieve the desired 24390 to 27100 cm−1 range, the CaD . As expected, the CaD transition frequencies mode-locked Ti:Sapphire laser was frequency-doubled by were more tightly-packed, owing to the decrease in ωe ac- a BBO crystal before being sent along the trap axis. Each companying the increase in reduced mass. Complication arose when matching the ab initio predictions to exper- fluorescence measurement was taken for 8 ms after ten −1 sets of alternating 200 µs delay and 200 µs exposure to imental values: the theory, shifted by -50 cm to agree with CaH+, systematically underestimated the CaD+ vi- the AOM-shuttered 20 mW Ti:Sapph beam. A fit of the −1 fluorescence intensity to the total exposure time t to the bronic transition frequencies by >100 cm . If the as- exponential equation signments proposed in Ref. 19 were correct, this study would imply a 150 cm−1 isotopic shift of the electronic energy potential and further evidence the experimentally −Γ(λ)t 0 At = A∞ − (A∞ − A0)e (1) unobserved transition to the v = 0 state. The isotopic shift of the electronic energy level is large compared yields the dissociation rate Γ as a function of wavelength to the 10 cm−1 shifts seen in KH.22,24 These spectral λ. A∞ and A0 are the steady-state and initial fluorescence counts, respectively. Scans exhibiting first-order CaD+ dissociation are presented in Fig. 2. Dissociation TABLE I. Observed transitions from 11Σ(v = 0) → 21Σ(v = rate plotted as a function of frequency yielded the spec- 0 trum in Fig. 3.26 v ). Frequencies are determined by fitting a convolution of laser linewidth and parameter-dependent level structure to laser-induced dissociation rates of CaH+ and CaD+. The resulting experimental fit is compared to an ab-initio spectrum B. Theoretical Model for Parameter Estimation in Figure 3. The frequency in parentheses was unobserved but predicted by the CASPT2 model. + To compare theory and experiment, CaD dissociation Previous CaH+ Revised CaH+ CaD+ spectra were modeled using theoretical and experimental v0 Assign: -50 cm−1 Assign: +687 cm−1 Experimental parameters. Calculation of the Einstein A for each tran- 0 (23887) 24635 ± 49 24683 ± 128 sition gave a dissociation rate, and the total rate at each 1 24635 ± 74 25401 ± 21 25321 ± 22 wavelength was obtained by summing all transitions cov- 2 25401 ± 31 26158 ± 18 25792 ± 49 ered by the laser linewidth.19 Although the experimental 3 26158 ± 27 26879 ± 29 26268 ± 60 CaD+ dissociation is a multi-photon process, we used 4 26879 ± 35 - 26908 ± 55 3

Experiment Experimental Fit Theory +687 cm-1 0.10 0.5 CaH+ CaD+ v' = 1 v' = 2 v' = 3 v' = 1 0.08 0.4 )

1 0.06 0.3 - v' = 2 v' = 4 s v' = 0 v' = 3 m ( 0.04 0.2 Γ v' = 0 0.02 0.1

0 0 2.40×104 2.45×104 2.50×104 2.55×104 2.60×104 2.65×104 2.70×104 2.40×104 2.45×104 2.50×104 2.55×104 2.60×104 2.65×104 2.70×104 ν (cm-1)

FIG. 3. Comparisons of the experimental and ab initio-predicted spectra for each isotopologue. The optimized parameters 0 include G1(v ), B1,v0 , and µv→v0 . Relative heights of theoretical vibronic peaks are governed by CASPT2 transition dipole moments scaled to fit the experimental v0 = 2 peak, while peak shapes come from the Boltzmann rotational state distribution 298 K. anomalies prompted a reassignment of the vibrational potential. To maintain the assumption that the inter- energy levels within the 21Σ manifold. nuclear potentials of CaH+ and CaD+ are similar, the The new assignment of vibrational quantum numbers, energy surfaces of the ab initio-calculated 11Σ and 21Σ shown in Table I, reflects a 687 cm−1 departure from states must be separated by an additional 687 cm−1. ab initio calculations. This shift manifests as a 687 This sizable departure from ab initio calculations is −1 cm increase in T (1)−E0. Roughly a vibrational quan- currently unexplained. Deviations could be due to the + tum in CaH , the revision is greater than the 100 - 150 frozen core electron approximation of CASPT2 or non- −1 cm error window afforded by the mismatch of calcu- adiabatic effects. The latter effect is expected to be + 1 lated and measured dissociation asymptotes for Ca (3d ) small based on estimations from other diatomic hydrides. 1 and H(1s ). This revised assignment, however, features LiH vibrational levels show a 10 cm−1 isotopic electronic 0 observable vibrational peaks through v = 4 and good shift28,29 and the KH, KD system also features correc- agreement for both isotopologues. tions around 10 cm−1.22,24 The disparity in experimental and calculated peak heights may be explained after further study of electronic levels relevant to the dissociation B. Experimental Parameters pathway. In addition, the different rates for CaH+ and

With the new CaH+ and CaD+ peak assignments, we determined the spectroscopic constants of the excited Previous ν' Assignment state by ﬁtting both theory and experimental values to a 4 1 2 3 4 5 6 second-order model of vibrational energy levels. Vibronic 2.70×10 transitions to v0 of the 21Σ state were modeled with the 2.65×104 equation 2.60×104 ) 1 0 1 0 1 2 - 0 4 vv = T (1) + ω1(v + ) − ωχ1(v + ) − E0 (2) m 2.55×10 c

2 2 (

ν where T (1) is the potential minimum of the 21Σ state, 2.50×104 + + and E0 is the zero-point energy of the ground state. The CaH CaD + + 2.45×104 Experiment Experiment parameters T (1), ω1, and ωχ1 for both CaH and CaD Revised: +687 cm-1 Revised: +687 cm-1 are varied to fit experimental data points by quadratic Previous: -50 cm-1 Previous: -50 cm-1 2.40×104 regression. Regression curves of theory predictions and 0 1 2 3 4 5 experimental fits were plotted (see Fig. 4) to obtain the Revised v' Assignment constants listed in Table II. Since CaH+ ground state 18 + + information is limited, the E0 energy is confined to the FIG. 4. The vibronic transitions of CaH and CaD and their ab initio prediction. associated fits using Eqn. 2. Theoretical and experimental −1 The spectroscopic constants agree reasonably with the- values are separated by 687 cm on average. Spectroscopic ory, however we notice a large shift of the excited state constants of each species may be found in Table II. 4

University Research Initiative award W911NF-14-1-0378. TABLE II. Molecular constants for the 11Σ → 21Σ vibronic + + We also acknowledge the National Science Foundation transitions of CaH and CaD based on the revised peak award PHY-1404388. Thanks to Colin Trout for his in- assignments. All values are in cm−1. put on the manuscript. CaH+ CaH+ CaD+ CaD+ Experimental CASPT2 Experimental CASPT2 ω1 795 ± 12 803 ± 3 537 ± 102 574 ± 1 ωχ1 11.5 ± 3.0 8.0 ± 0.7 0 ± 20 3.5 ± 0.1 T (1) 24978 ± 10 24226 ± 2 24973 ± 108 24223 ± 1 E0 - 739 - 526

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