Search

Motivated by the idea of using simple macroscopic examples to illustrate the physics of complex systems, we modify a historic experimental setup in which interacting floating magnets spontaneously self-assemble into ordered clusters. By making the cluster components mechanically stable against their natural tendency to flip and coalesce, we can monitor the torque experienced by individual magnets through the macroscopic tilt angles they acquire when exposed to non-collinear external fields. A mathematical model that reproduces the empirical observations is introduced, enabling us to go beyond the experimental cases considered. The model confirms the existence of alternative orderings as the number of objects increases. Furthermore, a simpler and more mathematically transparent version of our model enables us to establish the conditions under which the cluster structure is stable and when it will collapse. We argue that our simple experimental setup combined with the accompanying models may be useful to describe general features seen in systems composed of mutually repulsive particles in the presence of modulating confining fields., Comment: 14 pages, 8 figures, submitted to PRE

Relativistic exact two-component coupled-cluster calculations of molecular sensitivity factors for nuclear Schiff moments (NSMs) are reported. We focus on molecules containing heavy nuclei, especially octupole-deformed nuclei. Analytic relativistic coupled-cluster gradient techniques are used and serve as useful tools for identifying candidate molecules that sensitively probe for physics beyond the Standard Model in the hadronic sector. Notably, these tools enable straightforward ``black-box'' calculations. Two competing chemical mechanisms that contribute to the NSM are analyzed, illuminating the physics of ligand effects on NSM sensitivity factors.

Despite the ubiquity of ice, a molecular-resolution image of ice crystallized from liquid water or the resulting defect structure has never been obtained. Here, we report the stabilization and angstrom-resolution electron imaging of ice Ih crystallized from liquid water. We combine lattice mapping with molecular dynamics simulations to reveal that ice formation is highly tolerant to nanoscale defects such as misoriented subdomains and trapped gas bubbles, which are stabilized by molecular-scale structural motifs. Importantly, bubble surfaces adopt low-energy nanofacets and create negligible strain fields in the surrounding crystal. These bubbles can dynamically nucleate, grow, migrate, dissolve, and coalesce under electron irradiation and be monitored in situ near a steady state. This work opens the door to understanding water crystallization behaviors at an unprecedented spatial resolution., Comment: 15 pages, 4 figures, and 1 table. Supplementary Materials: 35 pages, 25 figures, and 9 tables. Updated to resolve the equation typesetting issue and a panel ordering error in Fig. 1

Working in an abstract, homotopy type theory based axiomatization of the higher Zariski-topos called synthetic algebraic geometry, we show that the Picard group of projective n-space is the integers, the automorphism group of projective n-space is PGL(n+1) and morphisms between projective standard spaces are given by homogenous polynomials in the usual way.

We present a formalization of quasi-compact and quasi-separated schemes (qcqs-schemes) in the Cubical Agda proof assistant. We follow Grothendieck's functor of points approach, which defines schemes, the quintessential notion of modern algebraic geometry, as certain well-behaved functors from commutative rings to sets. This approach is often regarded as conceptually simpler than the standard approach of defining schemes as locally ringed spaces, but to our knowledge it has not yet been adopted in formalizations of algebraic geometry. We build upon a previous formalization of the so-called Zariski lattice associated to a commutative ring in order to define the notion of compact open subfunctor. This allows for a concise definition of qcqs-schemes, streamlining the usual presentation as e.g. given in the standard textbook of Demazure and Gabriel. It also lets us obtain a fully constructive proof that compact open subfunctors of affine schemes are qcqs-schemes., Comment: 18 pages

Closed-shell atoms and molecules such as Hg or TlF provide some of the best low-energy tests of hadronic $\mathcal{CP}$-violation which is considered to be a necessary ingredient to explain the observed excess of matter over antimatter in our universe. $\mathcal{CP}$-violation is, however, expected to be strongly enhanced in octupole deformed nuclei such as $^{225}$Ra. Recently, closed-shell radium-containing symmetric-top molecular ions were cooled sympathetically in a Coulomb crystal [M. Fan et al., Phys. Rev. Lett. 126, 023002 (2021)] and shown to be well-suited for precision spectroscopy in the search for fundamental physics [P. Yu and N. R. Hutzler, Phys. Rev. Lett. 126, 023003 (2021)]. In closed-shell molecules hadronic $\mathcal{CP}$-violation contributes to a net electric dipole moment (EDM) that violates parity and time-reversal symmetry ($\mathcal{P,T}$), which is the target of measurements. To interpret experiments, it is indispensable to know the electronic structure enhancement parameters for the various sources of $\mathcal{P,T}$-violation which contribute to the net $\mathcal{P,T}$-odd EDM. In this paper we employ relativistic Hartree--Fock and density functional theory calculations to determine relevant parameters for interpretation of possible EDM measurements in RaOCH$_3^+$, RaSH$^+$, RaCH$_3^+$, RaCN$^+$, and RaNC$^+$ and perform accurate relativistic coupled cluster calculations of the Schiff moment enhancement in RaSH$^+$ to gauge the quality of the density functional theory approach. Finally, we project to bounds on various fundamental $\mathcal{P,T}$-odd parameters that could be achievable from an experiment with RaOCH$_3^+$ in the near future and asses the complementarity of this experiment to experiments with Hg and TlF., Comment: Updated references, corrected Wm values for RaCH3+, RaCN+ and RaNC+ in Table VII and in the supplement

We present a novel technique to probe electroweak nuclear properties by measuring parity violation (PV) in single molecular ions in a Penning trap. The trap's strong magnetic field Zeeman shifts opposite-parity rotational and hyperfine molecular states into near degeneracy. The weak interaction-induced mixing between these degenerate states can be larger than in atoms by more than twelve orders of magnitude, thereby vastly amplifying PV effects. The single molecule sensitivity would be suitable for applications to nuclei across the nuclear chart, including rare and unstable nuclei., Comment: 8 pages, 3 figures, 1 table

We propose to use atoms and molecules as quantum sensors of axion-mediated monopole-dipole forces. We show that electron spin precession experiments using atomic and molecular beams are well-suited for axion searches thanks to the presence of co-magnetometer states and single-shot temporal resolution. Experimental strategies to detect axion gradients from localised sources and the earth are presented, taking ACME III as a prototype example. Other possibilities including atomic beams, and laser-cooled atoms and molecules are discussed., Comment: 9 pages, 2 figures. Comments welcome. V2: matches published version. Appendix on axion co-magnetometry added

We propose a method to measure time-reversal symmetry violation in molecules that overcomes the standard quantum limit while leveraging decoherence-free subspaces to mitigate sensitivity to classical noise. The protocol does not require an external electric field, and the entangled states have no first-order sensitivity to static electromagnetic fields as they involve superpositions with zero average lab-frame projection of spins and dipoles. This protocol can be applied with trapped neutral or ionic species, and can be implemented using methods which have been demonstrated experimentally., Comment: 7+11 pages, 3+3 figures

We propose to sympathetically slow and cool polar molecules in a cold, low-density beam using laser-cooled Rydberg atoms. The elastic collision cross sections between molecules and Rydberg atoms are large enough to efficiently thermalize the molecules even in a low density environment. Molecules traveling at 100 m/s can be stopped in under 30 collisions with little inelastic loss. Our method does not require photon scattering from the molecules and can be generically applied to complex species for applications in precision measurement, quantum information science, and controlled chemistry., Comment: 8 pages, 3 figures

This is a foundation for algebraic geometry, developed internal to the Zariski topos, building on the work of Kock and Blechschmidt. The Zariski topos consists of sheaves on the site opposite to the category of finitely presented algebras over a fixed ring, with the Zariski topology, i.e. generating covers are given by localization maps $A\to A_{f_1}$ for finitely many elements $f_1,\dots,f_n$ that generate the ideal $(1)=A\subseteq A$. We use homotopy type theory together with three axioms as the internal language of a (higher) Zariski topos. One of our main contributions is the use of higher types -- in the homotopical sense -- to define and reason about cohomology. Actually computing cohomology groups, seems to need a principle along the lines of our ``Zariski local choice'' axiom, which we justify as well as the other axioms using a cubical model of homotopy type theory., Comment: 39 pages

A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.

We have developed and demonstrated a scheme to achieve rotationally-closed photon cycling in polyatomic molecules with complex hyperfine structure and sensitivity to hadronic symmetry violation, specifically $^{171}$YbOH and $^{173}$YbOH. We calculate rotational branching ratios for spontaneous decay and identify repumping schemes which use electro-optical modulators (EOMs) to address the hyperfine structure. We demonstrate our scheme by cycling photons in a molecular beam and verify that we have achieved rotationally-closed cycling by measuring optical pumping into unaddressed vibrational states. Our work makes progress along the path toward utilizing photon cycling for state preparation, readout, and laser cooling in precision measurements of polyatomic molecules with complex hyperfine structure., Comment: 10 pages, 7 figures

Molecules are a powerful platform to probe fundamental symmetry violations beyond the Standard Model, as they offer both large amplification factors and robustness against systematic errors. As experimental sensitivities improve, it is important to develop new methods to suppress sensitivity to external electromagnetic fields, as limits on the ability to control these fields are a major experimental concern. Here we show that sensitivity to both external magnetic and electric fields can be simultaneously suppressed using engineered radio frequency, microwave, or two-photon transitions that maintain large amplification of CP-violating effects. By performing a clock measurement on these transitions, CP-violating observables including the electron electric dipole moment, nuclear Schiff moment, and magnetic quadrupole moment can be measured with suppression of external field sensitivity of $\gtrsim$100 generically, and even more in many cases. Furthermore, the method is compatible with traditional Ramsey measurements, offers internal co-magnetometry, and is useful for systems with large angular momentum commonly present in molecular searches for nuclear CP-violation.

This whitepaper presents the research priorities decided on by attendees of the 2022 Town Meeting for Fundamental Symmetries, Neutrons and Neutrinos, which took place December 13-15, 2022 in Chapel Hill, NC, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 275 scientists registered for the meeting. The whitepaper makes a number of explicit recommendations and justifies them in detail.

Molecular laser cooling and trapping requires addressing all spontaneous decays to excited vibrational states that occur at the $\gtrsim 10^{-4} - 10^{-5}$ level, which is accomplished by driving repumping transitions out of these states. However, the transitions must first be identified spectroscopically at high-resolution. A typical approach is to prepare molecules in excited vibrational states via optical cycling and pumping, which requires multiple high-power lasers. Here, we demonstrate a general method to perform this spectroscopy without the need for optical cycling. We produce molecules in excited vibrational states by using optically-driven chemical reactions in a cryogenic buffer gas cell, and implement frequency-modulated absorption to perform direct, sensitive, high-resolution spectroscopy. We demonstrate this technique by measuring the spectrum of the $\tilde{A}^2\Pi_{1/2}(1,0,0)-\tilde{X}^2\Sigma^+(3,0,0)$ band in $^{174}$YbOH. We identify the specific vibrational repump transitions needed for photon cycling, and combine our data with previous measurements of the $\tilde{A}^2\Pi_{1/2}(1,0,0)-\tilde{X}^2\Sigma^+(0,0,0)$ band to determine all of the relevant spectral constants of the $\tilde{X}^2\Sigma^+(3,0,0)$ state. This technique achieves high signal-to-noise, can be further improved to measure increasingly high-lying vibrational states, and is applicable to other molecular species favorable for laser cooling., Comment: 14 pages, 5 figures

A non-resonant cavity to build up laser intensity is modeled, developed and tested. It can be used for overlapping multiple lasers of different wavelengths, increasing their intensities by over an order of magnitude while maintaining good uniformity. It is simple to set up, has flexible optical characteristics, and is robust against perturbations. The intensity buildup requires no resonances, and the wavelength dependence of the performance is limited only by the mirror coatings. The cavity can be used in applications requiring a spatially-constrained intensity buildup, for example in atomic and molecular traps., Comment: 15 pages, 11 figures

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Ultracold polyatomic molecules are promising candidates for experiments in quantum science, quantum sensing, ultracold chemistry, and precision measurements of physics beyond the Standard Model. A key, yet unrealized, requirement of these experiments is the ability to achieve full quantum control over the complex internal structure of the molecules. Here, we establish coherent control of individual quantum states in a polyatomic molecule, calcium monohydroxide (CaOH), and use these techniques to demonstrate a method for searching for the electron electric dipole moment (eEDM). Optically trapped, ultracold CaOH molecules are prepared in a single quantum state, polarized in an electric field, and coherently transferred into an eEDM sensitive state where an electron spin precession measurement is performed. To extend the coherence time of the measurement, we utilize eEDM sensitive states with tunable, near-zero magnetic field sensitivity. The spin precession coherence time is limited by AC Stark shifts and uncontrolled magnetic fields. These results establish a path for eEDM searches with trapped polyatomic molecules, towards orders-of-magnitude improved experimental sensitivity to time-reversal-violating physics.

Polyatomic molecules have been identified as sensitive probes of charge-parity violating and parity-violating physics beyond the Standard Model (BSM). For example, many linear triatomic molecules are both laser-coolable and have parity doublets in the ground electronic $\tilde{X} {}^2\Sigma^+ (010)$ state arising from the bending vibration, both features that can greatly aid BSM searches. Understanding the $\tilde{X} {}^2\Sigma^+ (010)$ state is a crucial prerequisite to precision measurements with linear polyatomic molecules. Here, we characterize fundamental bending vibration of ${}^{174}$YbOH using high-resolution optical spectroscopy on the nominally forbidden $\tilde{X} {}^2\Sigma^+ (010) \rightarrow \tilde{A} {}^2\Pi_{1/2} (000)$ transition at 588 nm. We assign 39 transitions originating from the lowest rotational levels of the $\tilde{X} {}^2\Sigma^+ (010)$ state, and accurately model the state's structure with an effective Hamiltonian using best-fit parameters. Additionally, we perform Stark and Zeeman spectroscopy on the $\tilde{X} {}^2\Sigma^+ (010)$ state and fit the molecule-frame dipole moment to $D_\mathrm{mol}=2.16(1)$ D and the effective electron $g$-factor to $g_S=2.07(2)$. Further, we use an empirical model to explain observed anomalous line intensities in terms of interference from spin-orbit and vibronic perturbations in the excited $\tilde{A} {}^2\Pi_{1/2} (000)$ state. Our work is an essential step toward searches for BSM physics in YbOH and other linear polyatomic molecules., Comment: 26 pages, 7 figures

High energy physics aims to understand the fundamental laws of particles and their interactions at both the largest and smallest scales of the universe. This typically means probing very high energies or large distances or using high-intensity beams, which often requires large-scale experiments. A complementary approach is offered through high-precision measurements in small- and mid-scale size experiments, often at lower energies. The field of such high-precision experiments has seen tremendous progress and importance for particle physics for at least two reasons. First, they exploit synergies to adjacent areas of particle physics and benefit by many recent advances in experimental techniques. Together with intensified phenomenological explorations, these advances led to the realization that challenges associated with weak couplings or the expected suppression factors from the mass scale of new physics can be overcome with such methods. Second, many of these measurements add a new set of particle physics phenomena and observables that can be reached compared to the more conventional methodologies using high energies. Combining high-precision, smaller-scale measurements with the large-scale efforts therefore casts a wider and tighter net for possible effects originating from physics beyond the Standard Model. This report presents a broad set of small-scale research projects that could provide key new precision measurements in the areas of electric dipole moments, magnetic dipole moments, fermion flavor violation, tests of spacetime symmetries, and tests with gravity. The growing impact of these high-precision studies in high energy physics and the complementary input they provide compared to large-scale efforts warrants strong support over the next decades. In particular, EDM searches are expected to improve sensitivities by four or more orders of magnitude in the next decade or two., Comment: Snowmass 2021 Community Study on the Future of Particle Physics, Rare Processes and Precision Measurements Frontier, Topical Group RF3 Report v2: 3 additional references and one co-author added

Advanced in situ techniques based on electrons and X-rays are increasingly used to gain insights into fundamental materials dynamics in liquid media. Yet, ionizing radiation changes the solution chemistry. In this work, we show that ionizing radiation decouples the acidity from autoprotolysis. Consequently, pH is insufficient to capture the acidity of water-based systems under irradiation. Via radiolysis simulations, we provide a more conclusive description of the acid-base interplay. Finally, we demonstrate that acidity can be tailored by adjusting the dose rate and adding pH-irrelevant species. This opens up a huge parameter landscape for studies involving ionizing radiation., Comment: 21 pages, 9 figures (main: 8 pages, 3 figures + SI: 13 pages, 6 figures)

High-precision tests of fundamental symmetries are looking for the parity- (P), time-reversal- (T) violating electric dipole moment of the electron (eEDM) as proof of physics beyond the Standard Model. Particularly, in polyatomic molecules, the complex vibrational and rotational structure gives the possibility to reach high enhancement of the P, T-odd effects in moderate electric fields. Additionally, it is possible to increase the statistical sensitivity by using laser cooling. In this work, we calculate the P, T-odd electronic structure parameters $W_\mathrm{d}$ and $W_\mathrm{s}$ for the promising candidates BaCH$_3$ and YbCH$_3$ for the interpretation of future experiments. We employ high-accuracy relativistic coupled cluster methods and systematically evaluate the uncertainties of our computational approach. Compared to other Ba- and Yb-containing molecules, BaCH$_3$ and YbCH$_3$ exhibit larger $W_\mathrm{d}$ and $W_\mathrm{s}$ associated to increased covalent character of the M--C bond. The calculated values are $3.22\pm 0.11 \times 10^{24}\frac{h\text{Hz}}{e\text{cm}}$ and $13.80\pm 0.35 \times 10^{24}\frac{h\text{Hz}}{e\text{cm}}$ for $W_\mathrm{d}$, and $8.42\pm0.29$~$h$kHz and $45.35\pm1.15$~$h$kHz for $W_\mathrm{s}$, in BaCH$_3$ and YbCH$_3$, respectively. The robust, accurate, and cost-effective computational scheme reported in this work makes our results suitable for extracting the relevant fundamental properties from future measurements and also can be used to explore other polyatomic molecules sensitive to various violations of fundamental symmetries.

We regard a geometric theory classified by a topos as a syntactic presentation for the topos and develop tools for finding such presentations. Extensions of geometric theories, which can add axioms, symbols and sorts, are treated as objects in their own right, to be able to build up complex theories from parts. The role of equivalence extensions, which leave the theory the same up to Morita equivalence, is investigated. Motivated by the question what the big Zariski topos of a non-affine scheme classifies, we show how to construct a syntactic presentation for a topos if syntactic presentations for a covering family of open subtoposes are given. For this, we introduce conditional theory extensions that require part of the data a model is made of only under some condition given in the form of a closed geometric formula. We also give a general definition for systems of interdependent theory extensions, to be able to talk about compatible syntactic presentations not only for the open subtoposes in a given cover but also for their finite intersections. An important concept for finding classified theories of toposes in concrete situations is that of theories of presheaf type. We develop several techniques for extending a theory while preserving the presheaf type property, and give a list of examples of simple extensions which can destroy it. Finally, we determine a syntactic presentation of the big crystalline topos of a scheme. In the case of an affine scheme, this is accomplished by showing that the biggest part of the classified theory is of presheaf type and transforming the site defining the crystalline topos into the canonical presheaf site for this theory, while the remaining axioms induce the Zariski topology. Then we can apply our results on gluing classifying toposes to obtain a classified theory even in the non-affine case.

Optical control of polyatomic molecules promises new opportunities in precision metrology, fundamental chemistry, quantum information, and many-body science. Contemporary experimental and theoretical efforts have mostly focused on cycling photons via excitation of a single electron localized to an alkaline earth (group 2)-like metal center. In this manuscript, we consider pathways towards optical cycling in polyatomic molecules with multi-electron degrees of freedom, which arise from two or more cycling electrons localized to $p$-block post-transition metal and metalloid (group 13, 14, and 15) centers. We characterize the electronic structure and rovibrational branching of several prototypical candidates using ab initio quantum chemical methods. Despite increased internal complexity and challenging design parameters, we find several molecules possessing quasi-closed photon cycling schemes with highly diagonal, visible and near-infrared transitions. Furthermore, we identify new heuristics for engineering optically controllable and laser-coolable polyatomic molecules with multi-electron cycling centers. Our results help elucidate the interplay between hybridization, repulsion, and ionicity in optically active species and provide a first step towards using polyatomic molecules with complex electronic structure as a resource for quantum science and measurement., Comment: 29 pages, 11 figures, 5 tables, and 6 supplemental data tables

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework., Comment: Contribution to Snowmass 2021; updated with community edits and endorsements

A wide range of quantum sensing technologies are rapidly being integrated into the experimental portfolio of the high energy physics community. Here we focus on sensing with atomic interferometers; mechanical devices read out with optical or microwave fields; precision spectroscopic methods with atomic, nuclear, and molecular systems; and trapped atoms and ions. We give a variety of detection targets relevant to particle physics for which these systems are uniquely poised to contribute. This includes experiments at the precision frontier like measurements of the electron dipole moment and electromagnetic fine structure constant and searches for fifth forces and modifications of Newton's law of gravity at micron-to-millimeter scales. It also includes experiments relevant to the cosmic frontier, especially searches for gravitional waves and a wide variety of dark matter candidates spanning heavy, WIMP-scale, light, and ultra-light mass ranges. We emphasize here the need for more developments both in sensor technology and integration into the broader particle physics community., Comment: contribution to Snowmass 2021 18 pages, 3 figures; updated author list and references, fixed typos

We propose and study a method of optical crosstalk suppression for silicon photomultipliers (SiPMs) using optical filters. We demonstrate that attaching absorptive visible bandpass filters to the SiPM can substantially reduce the optical crosstalk. Measurements suggest that the absorption of near infrared light is important to achieve this suppression. The proposed technique can be easily applied to suppress the optical crosstalk in SiPMs in cases where filtering near infrared light is compatible with the application.

The odd isotopologues of ytterbium monohydroxide, $^{171,173}$YbOH, have been identified as promising molecules in which to measure parity (P) and time reversal (T) violating physics. Here we characterize the $\tilde{A}^{2}\Pi_{1/2}(0,0,0)-\tilde{X}^2\Sigma^+(0,0,0)$ band near 577 nm for these odd isotopologues. Both laser-induced fluorescence (LIF) excitation spectra of a supersonic molecular beam sample and absorption spectra of a cryogenic buffer-gas cooled sample were recorded. Additionally, a novel spectroscopic technique based on laser-enhanced chemical reactions is demonstrated and utilized in the absorption measurements. This technique is especially powerful for disentangling congested spectra. An effective Hamiltonian model is used to extract the fine and hyperfine parameters for the $\tilde{A}^{2}\Pi_{1/2}(0,0,0)$ and $\tilde{X}^2\Sigma^+(0,0,0)$ states. A comparison of the determined $\tilde{X}^2\Sigma^+(0,0,0)$ hyperfine parameters with recently predicted values (M. Denis, et al., J. Chem. Phys. $\bf{152}$, 084303 (2020), K. Gaul and R. Berger, Phys. Rev. A $\bf{101}$, 012508 (2020), J. Liu et al., J. Chem. Phys. $\bf{154}$, 064110 (2021)) is made. The measured hyperfine parameters provide experimental confirmation of the computational methods used to compute the P,T-violating coupling constants $W_d$ and $W_M$, which correlate P,T-violating physics to P,T-violating energy shifts in the molecule. The dependence of the fine and hyperfine parameters of the $\tilde{A}^{2}\Pi_{1/2}(0,0,0)$ and $\tilde{X}^2\Sigma^+(0,0,0)$ states for all isotopologues of YbOH are discussed and a comparison to isoelectronic YbF is made., Comment: 54 pages, 7 figures