# Assignment of excited-state bond lengths using branching-ratio measurements:The B$^2\Sigma^+$ state of BaH molecules

Ian Lane, Keith Moore, Rees McNally, Tanya Zelevinsky

Research output: Contribution to journalArticle

### Abstract

Vibrational branching ratios in the B$^2\Sigma^+$ -- X$^2\Sigma^+$ and A$^2\Pi$ -- X$^2\Sigma^+$ optical-cycling transitions of BaH molecules are investigated using spectroscopic measurements and {\it ab initio} calculations. The experimental values are determined using fluorescence and absorption detection. The observed branching ratios have a very sensitive dependence on the difference in the equilibrium bond length between the excited and ground state, $\Delta r_e$: a 1 pm (.5\%) displacement can have a 25\% effect on the branching ratios but only a 1\% effect on the lifetime. The measurements are combined with theoretical calculations to reveal a clear preference for one particular set of published spectroscopic values for the B$^2\Sigma^+$ state ($\Delta r_e^{B-X}$ = 5.733 pm), while a larger bond length difference ($\Delta r_e^{B-X} = 6.3-6.7$ pm) would match the branching ratio data even better. By contrast, the observed branching ratio for the A$^2\Pi_{3/2}$ -- X$^2\Sigma^+$ transition is in excellent agreement with both the {\it ab initio} result and the spectroscopically measured bond lengths. This shows that care must be taken when estimating branching ratios for molecular laser cooling candidates, as small errors in bond length measurements can have outsize effects on the suitability for laser cooling. Additionally, our new calculations agree more closely with experimental values of the B$^2\Sigma^+$ state lifetime and spin-rotation constant, and revise the predicted lifetime of the H$^2\Delta$ state
to 9.5 $\mu$s.
Language English 022506 14 Physical Review A - Atomic, Molecular, and Optical Physics 100 02 Accepted - 15 Jul 2019

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laser cooling
life (durability)
excitation
molecules
estimating
fluorescence
cycles
ground state

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title = "Assignment of excited-state bond lengths using branching-ratio measurements:The B$^2\Sigma^+$ state of BaH molecules",
abstract = "Vibrational branching ratios in the B$^2\Sigma^+$ -- X$^2\Sigma^+$ and A$^2\Pi$ -- X$^2\Sigma^+$ optical-cycling transitions of BaH molecules are investigated using spectroscopic measurements and {\it ab initio} calculations. The experimental values are determined using fluorescence and absorption detection. The observed branching ratios have a very sensitive dependence on the difference in the equilibrium bond length between the excited and ground state, $\Delta r_e$: a 1 pm (.5\{\%}) displacement can have a 25\{\%} effect on the branching ratios but only a 1\{\%} effect on the lifetime. The measurements are combined with theoretical calculations to reveal a clear preference for one particular set of published spectroscopic values for the B$^2\Sigma^+$ state ($\Delta r_e^{B-X}$ = 5.733 pm), while a larger bond length difference ($\Delta r_e^{B-X} = 6.3-6.7$ pm) would match the branching ratio data even better. By contrast, the observed branching ratio for the A$^2\Pi_{3/2}$ -- X$^2\Sigma^+$ transition is in excellent agreement with both the {\it ab initio} result and the spectroscopically measured bond lengths. This shows that care must be taken when estimating branching ratios for molecular laser cooling candidates, as small errors in bond length measurements can have outsize effects on the suitability for laser cooling. Additionally, our new calculations agree more closely with experimental values of the B$^2\Sigma^+$ state lifetime and spin-rotation constant, and revise the predicted lifetime of the H$^2\Delta$ stateto 9.5 $\mu$s.",
author = "Ian Lane and Keith Moore and Rees McNally and Tanya Zelevinsky",
year = "2019",
month = "7",
day = "15",
language = "English",
volume = "100",
journal = "Physical Review A (Atomic, Molecular, and Optical Physics)",
issn = "1050-2947",
publisher = "American Physical Society",
number = "02",

}

Assignment of excited-state bond lengths using branching-ratio measurements:The B$^2\Sigma^+$ state of BaH molecules. / Lane, Ian; Moore, Keith; McNally, Rees; Zelevinsky, Tanya.

In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 100, No. 02, 022506, 15.07.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Assignment of excited-state bond lengths using branching-ratio measurements:The B$^2\Sigma^+$ state of BaH molecules

AU - Lane, Ian

AU - Moore, Keith

AU - McNally, Rees

AU - Zelevinsky, Tanya

PY - 2019/7/15

Y1 - 2019/7/15

N2 - Vibrational branching ratios in the B$^2\Sigma^+$ -- X$^2\Sigma^+$ and A$^2\Pi$ -- X$^2\Sigma^+$ optical-cycling transitions of BaH molecules are investigated using spectroscopic measurements and {\it ab initio} calculations. The experimental values are determined using fluorescence and absorption detection. The observed branching ratios have a very sensitive dependence on the difference in the equilibrium bond length between the excited and ground state, $\Delta r_e$: a 1 pm (.5\%) displacement can have a 25\% effect on the branching ratios but only a 1\% effect on the lifetime. The measurements are combined with theoretical calculations to reveal a clear preference for one particular set of published spectroscopic values for the B$^2\Sigma^+$ state ($\Delta r_e^{B-X}$ = 5.733 pm), while a larger bond length difference ($\Delta r_e^{B-X} = 6.3-6.7$ pm) would match the branching ratio data even better. By contrast, the observed branching ratio for the A$^2\Pi_{3/2}$ -- X$^2\Sigma^+$ transition is in excellent agreement with both the {\it ab initio} result and the spectroscopically measured bond lengths. This shows that care must be taken when estimating branching ratios for molecular laser cooling candidates, as small errors in bond length measurements can have outsize effects on the suitability for laser cooling. Additionally, our new calculations agree more closely with experimental values of the B$^2\Sigma^+$ state lifetime and spin-rotation constant, and revise the predicted lifetime of the H$^2\Delta$ stateto 9.5 $\mu$s.

AB - Vibrational branching ratios in the B$^2\Sigma^+$ -- X$^2\Sigma^+$ and A$^2\Pi$ -- X$^2\Sigma^+$ optical-cycling transitions of BaH molecules are investigated using spectroscopic measurements and {\it ab initio} calculations. The experimental values are determined using fluorescence and absorption detection. The observed branching ratios have a very sensitive dependence on the difference in the equilibrium bond length between the excited and ground state, $\Delta r_e$: a 1 pm (.5\%) displacement can have a 25\% effect on the branching ratios but only a 1\% effect on the lifetime. The measurements are combined with theoretical calculations to reveal a clear preference for one particular set of published spectroscopic values for the B$^2\Sigma^+$ state ($\Delta r_e^{B-X}$ = 5.733 pm), while a larger bond length difference ($\Delta r_e^{B-X} = 6.3-6.7$ pm) would match the branching ratio data even better. By contrast, the observed branching ratio for the A$^2\Pi_{3/2}$ -- X$^2\Sigma^+$ transition is in excellent agreement with both the {\it ab initio} result and the spectroscopically measured bond lengths. This shows that care must be taken when estimating branching ratios for molecular laser cooling candidates, as small errors in bond length measurements can have outsize effects on the suitability for laser cooling. Additionally, our new calculations agree more closely with experimental values of the B$^2\Sigma^+$ state lifetime and spin-rotation constant, and revise the predicted lifetime of the H$^2\Delta$ stateto 9.5 $\mu$s.

M3 - Article

VL - 100

JO - Physical Review A (Atomic, Molecular, and Optical Physics)

T2 - Physical Review A (Atomic, Molecular, and Optical Physics)

JF - Physical Review A (Atomic, Molecular, and Optical Physics)

SN - 1050-2947

IS - 02

M1 - 022506

ER -