The YbF molecule is a sensitive system for measuring the electron’s electric dipole moment. The precision of this measurement can be improved by direct laser cooling of the molecules to ultracold temperature. However, low-lying electronic states arising from excitation of a 4f electron may hinder laser cooling. One set of these “4f hole” states lies below the A2Π1/2 excited state used for laser cooling, and radiative decay to these intermediate levels, even with branching ratios as small as 10−5, can be a hindrance. Other 4f hole states lie very close to the A2Π1/2 state, and a perturbation results in states of mixed character that are involved in the laser cooling cycle. This perturbation may enhance the loss of molecules to states outside of the laser cooling cycle. We model the perturbation of the A2Π1/2 state to determine the strength of the coupling between the states, the de-perturbed potential energy curves, and the radiative branching ratios to various vibrational levels of the ground state, X2Σ+. We use electronic structure calculations to characterize the 4f hole states and the strengths of transitions between these states and the A2Π1/2 and X2Σ+ states. We identify a leak out of the cooling cycle with a branching ratio of roughly 5×10−4, dominated by the contribution of the ground state configuration in a 4f hole state. Finally, we assess the impact of these results for laser cooling of YbF and molecules with similar structure.
The YbF molecule is a sensitive system for measuring the electron’s electric dipole moment. The precision of this measurement can be improved by direct laser cooling of the molecules to ultracold temperature. However, low-lying electronic states arising from excitation of a 4f electron may hinder laser cooling. One set of these “4f hole” states lies below the A2Π1/2 excited state used for laser cooling, and radiative decay to these intermediate levels, even with branching ratios as small as 10−5, can be a hindrance. Other 4f hole states lie very close to the A2Π1/2 state, and a perturbation results in states of mixed character that are involved in the laser cooling cycle. This perturbation may enhance the loss of molecules to states outside of the laser cooling cycle. We model the perturbation of the A2Π1/2 state to determine the strength of the coupling between the states, the de-perturbed potential energy curves, and the radiative branching ratios to various vibrational levels of the ground state, X2Σ+. We use electronic structure calculations to characterize the 4f hole states and the strengths of transitions between these states and the A2Π1/2 and X2Σ+ states. We identify a leak out of the cooling cycle with a branching ratio of roughly 5×10−4, dominated by the contribution of the ground state configuration in a 4f hole state. Finally, we assess the impact of these results for laser cooling of YbF and molecules with similar structure.
Molecules containing a lanthanide atom have sets of electronic states arising from excitation of an inner-shell electron. These states have received little attention but are thought to play an important role in laser cooling of such molecules and may be a useful resource for testing fundamental physics. We study a series of inner-shell excited states in YbF using resonance-enhanced multiphoton ionization spectroscopy. We investigate the excited states of lowest energy, 8474, 9013, and 9090 cm−1 above the ground state, all corresponding to the configuration 4f136s2 F27/2 of the Yb+ ion. They are metastable, since they have no electric dipole allowed transitions to the ground state. We also characterize a state at 31 050 cm−1 that is easily excited from both the ground and metastable states, which makes it especially useful for this spectroscopic study. Finally, we study two states at 48 720 and 48 729 cm−1 , which are above the ionization limit and feature strong autoionizing resonances that prove useful for efficient detection of the molecules and for identifying the rotational quantum number of each line in the spectrum. We resolve the rotational structures of all these states and find that they can all be described by a very simple model based on Hund’s case (c). Our study provides information necessary for laser slowing and magneto-optical trapping of YbF, which is an important species for testing fundamental physics. We also consider whether the low-lying inner-shell states may themselves be useful as probes of the electron’s electric dipole moment or of varying fundamental constants, since they are long-lived states in a laser-coolable molecule featuring closely spaced levels of opposite parity. Published by the American Physical Society 2024
Cold molecules are attractive for a wide range of scientific applications, including quantum computation, the study of chemical reactions, and tests of fundamental physics. Laser cooling has proved to be an invaluable technique in the cooling of atoms. This technique was once thought to be infeasible for molecules, because it is difficult to find a closed cycling transition due to their vibrational structure. Recently, laser cooling of several diatomic species has been demonstrated. These molecules possess electronic transitions with highly diagonal Franck-Condon matrices, which make it possible to drive a quasi-closed cycling transition. Ytterbium fluoride (YbF) molecules are amenable to laser cooling and are especially interesting because they are used to measure the electron's electric dipole moment (eEDM). Measurements of the eEDM test the prediction of theories that extend the Standard Model of particle physics. The sensitivity of an eEDM experiment could be greatly increased by using ultracold molecules produced by direct laser cooling. This thesis presents work done towards producing a laser-cooled beam of YbF for an eEDM experiment. This work includes the construction of the cooling experiment, a novel method for efficiently combining laser beams of very similar frequencies, results of spectroscopic measurements to find the required transitions for laser cooling, the results of initial optical cycling experiments, and the first laser cooling results of YbF. Using a one-dimensional optical molasses, a beam of molecules is Doppler cooled in one transverse direction to a temperature of approximately 70 mK. Preliminary evidence of cooling to lower temperatures through a Sisyphus mechanism is also presented. Finally, paths towards improving the laser cooling are suggested. The work opens the door to improved measurements of the eEDM using ultracold YbF molecules.
We report radiation pressure slowing of YbF molecules to low velocity. In YbF, laser slowing is hindered by leaks out of the optical cycle attributed to low-lying metastable electronic states arising from inner-shell excitation. We bring this population back into the optical cycle once it has decayed to the electronic ground state using microwaves to couple the relevant rotational levels. We measure the scattering rate and closure of the optical cycle as repumps are added, and study the destabilization of dark states by a magnetic field and by polarization modulation, finding that both are helpful for maximizing the scattering rate. Starting from a beam with a mean speed of 80 m/s, and using frequency-broadened slowing light, we reduce the mean speed of the beam and produce a substantial flux in the low-velocity tail of the distribution. Slowing increases the fraction of molecules below 40 m/s from 0.4(1)% to 7.0(2)%, and the fraction below 30 m/s from zero to 3.2(1)%. The establishment of a nearly closed optical cycle and the production of molecules at low velocity are important steps toward trapping YbF molecules for future measurements of the electron's electric dipole moment.
This thesis investigates the suitability of BH molecules for laser cooling and describes progress towards the laser cooling of this molecule. We produce a molecular beam of BH and measure the branching ratios for the excited electronic state, A^{1}\Pi(v_{0}=0), to decay to the various vibrational states of the ground electronic state, X^{1}\Sigma. We verify that the branching ratio for the spin-forbidden transition to an intermediate triplet state is inconsequentially small. We measure the frequency of the lowest rotational transition of the X state, and the hyper fine structure in the relevant levels of both the X and A states, and determine the nuclear electric quadrupole and magnetic dipole coupling constants. We use a semiclassical model of the molecule-light interaction to investigate the expected cycling behaviour on the main cooling transition using light with modulated polarisation. The results of the model are compared with the effect of modulating the polarisation experimentally using an electro-optic modulator. In order to repump the population that leaks into the first vibrationally excited state, we have designed, built and tested a suitable repump laser and have demonstrated that we can drive the repump transition. We have also designed a Zeeman slower for slowing molecules to low velocity so that they can be trapped. Our results show that a relatively simple laser cooling scheme can be used to cool, slow and trap BH molecules.
A spin-orbit coupling electronic structure study of the AlZn molecule is conducted to investigate the molecular properties of the low-lying electronic states and their feasibility toward direct laser cooling. This study uses the complete active-space self-consistent field level of theory, followed by the multireference configuration interaction method with Davidson correction (+Q). The potential energy and dipole moment curves and the spectroscopic constants are computed for the low-lying doublet and quartet electronic states in the 2S+1Λ± and Ω(±) representations. The transition dipole moments, the Franck-Condon factors, the Einstein coefficient, the radiative lifetimes, the vibrational branching ratio, and the slowing distance are determined between the lowest spin-orbit bound electronic states. These results show that the molecule AlZn has a high potential for laser cooling through the X2Π1/2 → (2)2Π1/2 transition by utilizing four lasers at a wavelength in the ultraviolet region, reaching a sub-microkelvin temperature limit.
The electronic structure, including the spin–orbit coupling effect of the HfH molecule, has been studied to determine if it can be cooled through Doppler and Sysphus laser cooling techniques. The multi-reference configuration interaction plus Davidson correction (MRCI + Q) method has been used to calculate its potential energy curves (P.E.C.s) in the Ω(±) and 2s+1Ʌ(+/-) representation. The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment µe, and the dissociation energies De agree very well with previously published work. In addition, we present in this work twenty new doublet and quartet states in the Ω(±) representation. The electronic transition dipole moment curves (TDMCs) between the lowest-lying electronic states have been investigated for the Δ -Π, Π - ∑+ and Δ - Φ transitions among specific Ω(±) states. The Franck-Condon factors (FCFs), the Einstein coefficient of spontaneous emission Aν′ν, and the radiative lifetime τ have been computed for the investigated transitions. In addition, properties of the molecules' electronic and vibrational states, such as the static dipole moment curves (D.M.C.s), the ionic character fionic, and the rovibrational constants are calculated. We deduce from our results that the HfH molecule is indeed a laser-cooling candidate that can reach a temperature as low as the nK regime. We present a complementary scheme with suitable experimental parameters. These results can be of great interest to experimental spectroscopists interested in ultracold diatomic molecules and their applications.