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Optical pumping of barium monofluoride (BaF) within a cryogenic neon matrix is demonstrated. Interestingly, with an applied magnetic field of 2~G, optical pumping is found to be considerably more efficient for a laser beam with right-circular polarization compared to left-circular polarization. Calculations show that the higher efficiency is due to a constructive versus destructive interference and is dependent on the orientation of the BaF molecule relative to the magnetic field direction. The effect leads to orientation-dependent optical pumping within the matrix. As optical pumping is the first step used in our planned electron electric-dipole moment (eEDM) measurement, we intend to exploit this property to obtain the selection of molecular orientations that is required for an eEDM measurement., Comment: 9 pages, 5 figures

A method for specular reflection of polar molecules is proposed. Electrostatatic potentials and forces are calculated for a low-field-seeking molecule near a series of long cylindrical electrodes of radius $r$ with dc potentials of $+V$ and $-V$ applied to alternate electrodes. A center-to-center separation of $2.9\,r$ leads to remarkably flat equipotential surfaces and thus to a nearly planar mirror for specular reflection of the polar molecules, with the angle of reflection equalling the angle of incidence to an accuracy approaching a microradian. This mirror can be used to redirect cryogenic molecular beams. Separating barium monofluoride (BaF) molecules created in a helium-buffer-gas laser-ablation source from other ablation products is a necessary step to producing a pure sample of matrix-isolated BaF, as is required by the EDM$^3$ collaboration for implementing a precise measurement of the electron electric dipole moment. The design and modelling for the BaF deflector based on this electrode geometry is presented., Comment: 5 pages, 5 figures

A cryogenic neon solid doped with barium monofluoride (BaF) is created on a cryogenic substrate using a stream of Ne gas and a high-intensity beam of BaF molecules produced in a cryogenic helium-buffer-gas laser-ablation source. The apparatus is designed for eventual use in a measurement of the electron electric dipole moment (eEDM). Laser-induced fluorescence is observed from transitions up to the $B\,^2\Sigma_{1/2}$ state. The number of BaF molecules found to be present in the solid and addressable with this laser transition is approximately 10$^{10}$ per mm$^3$, which is of the same order as the total number of BaF molecules that impact the substrate during the hour of growth time for the solid. As a result, an eventual eEDM measurement could have continual access to an accumulation of an hour's worth of molecules (all of which are contained within a 1-mm$^3$ volume and are thermalized into the ground state), compared to beam experiments which study the molecules from a single ablation during the millisecond-timescale of their passage through a much larger-scale measurement apparatus. The number of BaF molecules observed in the doped solid matches the target value for our planned eEDM measurement., Comment: 9 pages, 6 figures

Increasing accuracy of the theory and experiment of the $n$$=$$2$ $^3$P fine structure of helium has allowed for increasingly-precise tests of quantum electrodynamics (QED), determinations of the fine-structure constant $\alpha$, and limitations on possible beyond-the-Standard-Model physics. Here we present a 2~part-per-billion (ppb) measurement of the $J$$=$$1$-to-$J$$=$$0$ interval. The measurement is performed using frequency-offset separated-oscillatory-fields. Our result of $29\,616\,955\,018(60)$~Hz represents a landmark for helium fine-structure measurements, and, for the first time, will allow for a 1-ppb determination of the fine-structure constant when QED theory for the interval is improved., Comment: 6 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1807.07923

The local environment of a barium monofluoride (BaF) molecule embedded in a neon matrix is studied theoretically. The energy of the BaF-Ne triatomic system is calculated with a scalar relativistic Hamiltonian, using coupled-cluster theory at the CCSD(T) level for $1625$ positions of the Ne atom relative to the BaF molecule. The calculations are repeated with increasing basis sets (from double to quintuple zeta), and are extrapolated to estimate the complete-basis-set limit. Using the potential obtained from these calculations, it is determined that substituting a BaF molecule for ten Ne atoms is favoured compared to substitutions for other numbers of Ne atoms. The equilibrium position and orientation of the BaF molecule and the displacement of its nearby Ne neighbours are determined. The potential barriers that prevent the BaF molecule from migrating and rotating are calculated. These barriers are essential for the EDM$^3$ collaboration, which is using BaF molecules embedded in a noble-gas solid to perform a precision measurement of the electron electric dipole moment., Comment: 6 figures. arXiv admin note: text overlap with arXiv:2211.14804, arXiv:2212.09232

A full density-matrix simulation is performed for optical deflection of a barium monofluoride ($^{138}$Ba$^{19}$F) beam using the bichromatic force, which employs pairs of counter-propagating laser beams that are offset in frequency. We show that the force is sufficient to separate BaF molecules from the other products generated in a helium-buffer-gas-cooled ablation source. For our simulations, the density-matrix and force equations are numerically integrated during the entire time that the molecules pass through a laser beam to ensure that effects of the evolution of the Doppler shift and of the optical intensity and phase at the position of the molecule are properly included. The results of this work are compared to those of a deflection scheme (Phys. Rev. A 107, 032811 (2023)) which uses $\pi$ pulses to drive frequency-resolved transitions. This work is part of an effort by the EDM$^3$ collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Separation of BaF molecules will aid in producing a sufficiently pure solid., Comment: 8 pages, 5 figures

A full density-matrix simulation is performed for optical deflection of a barium monofluoride (BaF) beam. Pairs of counter-propagating laser pulses are used for stimulated absorption followed by stimulated emission. The scheme produces a force which is nearly an order of magnitude larger than that obtainable using continuous-wave laser deflection, and yields a force-to-spontaneous-decay ratio which is more than an order of magnitude larger. The large reduction in spontaneous decay is key to optical deflection of molecules, where branching ratios to other vibrational states do not allow for cycling transitions. This work is part of an effort by the EDM$^3$ collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Deflection of BaF molecules will separate them from the other ablation products coming from a buffer-gas-cooled ablation source, before embedding them into the argon solid. Our simulations show that sufficiently large deflections for this separation are feasible., Comment: 7 pages, 6 figures

The local environment of a barium monofluoride (BaF) molecule embedded in an argon matrix is calculated. A substitution of a BaF molecule for four Ar atoms is found to be strongly favoured compared to substitutions for other numbers of Ar atoms. The equilibrium positions of the BaF molecule and its nearby Ar neighbours are found by minimizing the total energy. The potential barrier that prevents the migration of the BaF molecule within the solid and the barrier that prevents its rotation are calculated. At the cryogenic temperatures used by the EDM$^3$ collaboration, these barriers are sufficiently large to fix the position and orientation of the molecule. Knowledge of the local environment of matrix-isolated BaF molecules is essential for the EDM$^3$ collaboration, which is using them in a precision measurement of the electron electric dipole moment., Comment: 6 pages, 3 figures. As published, with typos corrected in tables

Calculations of the BaF-Ar triatomic system are performed with a relativistic Hamiltonian and coupled cluster theory at the CCSD(T) level for 1386 positions of the Ar atom relative to the BaF molecule. Calculations are repeated with increasing basis sets (double-, triple-, quadruple- and quintuple-zeta), and these are extrapolated to estimate the complete-basis-set limit. The resulting energies provide a potential energy for the interaction of an Ar atom with a BaF molecule. A fit is presented that parametrizes this potential. This work is needed for an understanding of the position, modes of motion and energy shifts of BaF isolated in an Ar matrix. This understanding will guide the EDM$^3$ collaboration in its pursuit of a precision measurement of the electron electric dipole moment using BaF isolated in a cryogenic Ar matrix.

High-accuracy spectroscopic comparisons of trapped antihydrogen atoms ($\overline{\text{H}}$) and hydrogen atoms ($\text{H}$) promise to stringently test the fundamental CPT symmetry invariance of the standard model of particle physics. ATRAP's nested Penning-Ioffe trap was developed for such studies. The first of its unique features is that its magnetic Ioffe trap for $\overline{\text{H}}$ atoms can be switched between quadrupole and octupole symmetries. The second is that it allows laser and microwave access perpendicular to the central axis of the traps., Comment: 20 pages, 33 figures, submitted to NIM A

For decades, improved theory and experiment of the $n=2$ $^3$P fine structure of helium have allowed for increasingly-precise tests of quantum electrodynamics, determinations of the fine-structure constant $\alpha$, and limitations on possible beyond-the-Standard-Model physics. Here we use the new frequency-offset separated-oscillatory-fields (FOSOF) technique to measure the $2^3$P$_2\!\!\to\!2^3$P$_1$ interval. Our result of $2\,291\,176\,590(25)$~Hz represents a major step forward in precision for helium fine-structure measurements.

Because molecules can have their orientation locked when embedded into a solid rare-gas matrix, their hyperfine structure is strongly perturbed relative to the freely rotating molecule. The addition of an electric field further perturbs the structure, and fields parallel and antiparallel to the molecular orientation result in different shifts of the hyperfine structure. These shifts enable the selective detection of molecules with different orientations relative to the axes of a rare-gas crystal, which will be an important ingredient of an improved electron electric dipole moment measurement using large ensembles of polar molecules trapped in rare-gas matrices.

We evaluate a number of systematic effects that are important for an experimental microwave measurement of the $n$$=$$2$ S-to-P intervals in atomic hydrogen. The analysis is important for both re-evaluating the best existing measurement [Lundeen and Pipkin, PRL 46, 232 (1981)] of the 2S$_{1/2}$-to-2P$_{1/2}$ Lamb shift, and for a new measurement that is ongoing in our laboratory. This work is part of a larger program to understand the several-standard-deviation discrepancies between various methods for determining the proton charge radius.

We propose a very sensitive method for measuring the electric dipole moment of the electron using polar molecules embedded in a cryogenic solid matrix of inert-gas atoms. The polar molecules can be oriented in the $\hat{\rm{z}}$ direction by an applied electric field, as has recently been demonstrated by Park, et al. [Angewandte Chemie {\bf 129}, 1066 (2017)]. The trapped molecules are prepared into a state which has its electron spin perpendicular to $\hat{\rm{z}}$, and a magnetic field along $\hat{\rm{z}}$ causes precession of this spin. An electron electric dipole moment $d_e$ would affect this precession due to the up to 100~GV/cm effective electric field produced by the polar molecule. The large number of polar molecules that can be embedded in a matrix, along with the expected long coherence times for the precession, allows for the possibility of measuring $d_e$ to an accuracy that surpasses current measurements by many orders of magnitude. Because the matrix can inhibit molecular rotations and lock the orientation of the polar molecules, it may not be necessary to have an electric field present during the precession. The proposed technique can be applied using a variety of polar molecules and inert gases, which, along with other experimental variables, should allow for careful study of systematic uncertainties in the measurement.

The resonant line shape from driving a transition between two states, $|\rm{a}\rangle$ and $|\rm{b}\rangle$, can be distorted due to a quantum-mechanical interference effect involving a resonance between two different states, $|\rm{c}\rangle$ and $|\rm{d}\rangle$, if $|\rm{c}\rangle$ has a decay path to $|\rm{a}\rangle$ and $|\rm{d}\rangle$ has a decay path to $|\rm{b}\rangle$. This interference can cause a shift of the measured resonance, despite the fact that the two resonances do not have a common initial or final state. As an example, we demonstrate that such a shift affects measurements of the atomic hydrogen 2S$_{1/2}$-to-2P$_{1/2}$ Lamb-shift transition due to 3S-to-3P transitions if the 3S$_{1/2}$ state has some initial population., Comment: 4 figures

We present tables for the bound-state energies for atomic hydrogen. The tabulated energies include the hyperfine structure, and thus this work extends the work of Rev. Mod. Phys. {\bf 84}, 1527 (2012), which excludes hyperfine structure. The tabulation includes corrections of the hyperfine structure due to the anomalous moment of the electron, due to the finite mass of the proton, and due to off-diagonal matrix elements of the hyperfine Hamiltonian. These corrections are treated incorrectly in most other works. Simple formulas valid for all quantum numbers are presented for the hyperfine corrections. The tabulated energies have uncertainties of less than 1 kHz for all states. This accuracy is possible because of the recent precision measurement [Nature, {\bf 466}, 213 (2010); Science, {\bf 339}, 417] of the proton radius. The effect of this new radius on the energy levels is also tabulated, and the energies are compared to precision measurements of atomic hydrogen energy intervals.

Precisely measured electron-proton elastic scattering cross sections [Phys. Rev. Lett. {\bf 105}, 242002 (2010)] are reanalyzed to evaluate their strength for determining the rms charge radius ($R_{\rm E}$) of the proton. More than half of the cross sections at lowest $Q^2$ are fit using two single-parameter form-factor models, with the first based on a dipole parametrization, and the second on a linear fit to a conformal-mapping variable. These low-$Q^2$ fits extrapolate the slope of the form factor to $Q^2$=0 and determine $R_{\rm E}$ values of approximately 0.84 and 0.89~fm, respectively. Fits spanning all $Q^2$, in which the single constants are replaced with cubic splines at larger $Q^2$, lead to similar results for $R_{\rm E}$. We conclude that the scattering data is consistent with $R_{\rm E}$ ranging from at least 0.84 to 0.89~fm, and therefore cannot resolve the discrepancy between determinations of $R_{\rm E}$ made using muonic and electronic hydrogen-atom spectroscopy.

\DeclareRobustCommand{\pbar}{\HepAntiParticle{p}{}{}\xspace} \DeclareRobustCommand{\p}{\HepParticle{p}{}{}\xspace} \DeclareRobustCommand{\mup}{$\mu_{p}${}{}\xspace} \DeclareRobustCommand{\mupbar}{$\mu_{\pbar}${}{}\xspace} \DeclareRobustCommand{\muN}{$\mu_N${}{}\xspace For the first time a single trapped \pbar is used to measure the \pbar magnetic moment ${\bm\mu}_{\pbar}$. The moment ${\bm\mu}_{\pbar} = \mu_{\pbar} {\bm S}/(\hbar/2)$ is given in terms of its spin ${\bm S}$ and the nuclear magneton (\muN) by $\mu_{\pbar}/\mu_N = -2.792\,845 \pm 0.000\,012$. The 4.4 parts per million (ppm) uncertainty is 680 times smaller than previously realized. Comparing to the proton moment measured using the same method and trap electrodes gives $\mu_{\pbar}/\mu_p = -1.000\,000 \pm 0.000\,005$ to 5 ppm, for a proton moment ${\bm{\mu}}_{p} = \mu_{p} {\bm S}/(\hbar/2)$, consistent with the prediction of the CPT theorem., Comment: 4 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1201.3038

Antihydrogen atoms are confined in an Ioffe trap for 15 to 1000 seconds -- long enough to ensure that they reach their ground state. Though reproducibility challenges remain in making large numbers of cold antiprotons and positrons interact, 5 +/- 1 simultaneously-confined ground state atoms are produced and observed on average, substantially more than previously reported. Increases in the number of simultaneously trapped antithydrogen atoms are critical if laser-cooling of trapped antihydrogen is to be demonstrated, and spectroscopic studies at interesting levels of precision are to be carried out.