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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.

We report a method for the precision measurement of the oscillator strengths and the branching ratios of the decay channels of the $6d7p$ $^3F_2$ state in $^{226}$Ra. This method exploits a set of metastable states present in Ra, allowing a measurement of the oscillator strengths that does not require knowledge of the number of atoms in the atomic beam. We measure the oscillator strengths and the branching ratios for decays to the $7s6d$ $^3D_1$, $7s6d$ $^3D_2$, and $7s6d$ $^1D_2$ states and constrain the branching ratio to the $7s6d$ $^3D_3$ state to be less than 0.4$\%$ (68$\%$ confidence limit). The lifetime of the $^3F_2$ state is determined to be $15 \pm 4$ ns., Comment: 6 pages, 4 figures. Submitted to Physical Review A

Optical trapping techniques are an efficient way to probe limited quantities of rare isotopes. In order to achieve the highest possible measurement precision, it is critical to optimize the optical trapping efficiency. This work presents the development of a three-dimensional semi-classical Monte Carlo simulation of the optical trapping process and its application to optimizing the optical trapping efficiency of Radium for use in the search of the permanent electric dipole moment of $^{225}$Ra. The simulation includes an effusive-oven atomic beam source, transverse cooling and Zeeman slowing of an atomic beam, a three-dimensional magneto-optical trap, and additional processes such as collisions with residual gas molecules. We benchmark the simulation against a well-characterized $^{88}$Sr optical trap before applying it to the $^{225}$Ra optical trap. The simulation reproduces the relative gains in optical trapping efficiency measured in both the $^{88}$Sr and $^{225}$Ra optical traps. The measured and simulated values of the overall optical trapping efficiencies for $^{88}$Sr are in agreement; however, they differ by a factor of $30$ for $^{225}$Ra. Studies of several potential imperfections in the apparatus or systematic effects, such as atomic beam source misalignment and laser frequency noise, show only limited effects on the simulated trapping efficiency for $^{225}$Ra. We rule out any one systematic effect as the sole cause of the discrepancy between the simulated and measured $^{225}$Ra optical trapping efficiencies; but, we do expect that a combination of systematic effects contribute to this discrepancy. The accurate relative gains predicted by the simulation prove that it is useful for testing planned upgrades to the apparatus., Comment: 13 pages, 9 figures, submitted to Physical Review A

The radioactive radium-225 ($^{225}$Ra) atom is a favorable case to search for a permanent electric dipole moment (EDM). Due to its strong nuclear octupole deformation and large atomic mass, $^{225}$Ra is particularly sensitive to interactions in the nuclear medium that violate both time-reversal symmetry and parity. We have developed a cold-atom technique to study the spin precession of $^{225}$Ra atoms held in an optical dipole trap, and demonstrated the principle of this method by completing the first measurement of its atomic EDM, reaching an upper limit of $|$$d$($^{225}$Ra)$|$ $<$ $5.0\!\times\!10^{-22}$ $e \cdot$cm (95$\%$ confidence).

SU(N) symmetry can emerge in a quantum system with N single-particle spin states when spin is decoupled from inter-particle interactions. So far, only indirect evidence for this symmetry exists, and the scattering parameters remain largely unknown. Here we report the first spectroscopic observation of SU(N=10) symmetry in Sr-87 using the state-of-the-art measurement precision offered by an ultra-stable laser. By encoding the electronic orbital degree of freedom in two clock states, while keeping the system open to 10 nuclear spin sublevels, we probe the non-equilibrium two-orbital SU(N) magnetism via Ramsey spectroscopy of atoms confined in an array of two-dimensional optical traps. We study the spin-orbital quantum dynamics and determine all relevant interaction parameters. This work prepares for using alkaline-earth atoms as test-beds for iconic orbital models., Comment: 4 figures, 1 tables

We present a unifying theoretical framework that describes recently observed many-body effects during the interrogation of an optical lattice clock operated with thousands of fermionic alkaline earth atoms. The framework is based on a many-body master equation that accounts for the interplay between elastic and inelastic p-wave and s-wave interactions, finite temperature effects and excitation inhomogeneity during the quantum dynamics of the interrogated atoms. Solutions of the master equation in different parameter regimes are presented and compared. It is shown that a general solution can be obtained by using the so called Truncated Wigner Approximation which is applied in our case in the context of an open quantum system. We use the developed framework to model the density shift and decay of the fringes observed during Ramsey spectroscopy in the JILA 87Sr and NIST 171Yb optical lattice clocks. The developed framework opens a suitable path for dealing with a variety of strongly-correlated and driven open-quantum spin systems., Comment: 36 pages, 19 figures

The exquisite control exhibited over quantum states of individual particles has revolutionized the field of precision measurement, as exemplified by the most accurate atomic clock realized in single trapped ions. Whereas many-atom lattice clocks have shown advantages in measurement precision over trapped-ion clocks, their accuracy has remained 20 times worse. Here we demonstrate, for the first time, that a many-atom system achieves accuracy (6x10^{-18}) better than a single ion-based clock, with vastly reduced averaging times (3000 s). This is the first time a single clock has achieved the best performance in all three key ingredients necessary for consideration as a primary standard - stability, reproducibility, and accuracy. This work paves the way for future experiments to integrate many-body quantum state engineering into the frontiers of quantum metrology, creating exciting opportunities to advance precision beyond the standard quantum limit. Improved frequency standards will have impact to a wide range of fields from the realization of the SI units, the development of quantum sensors, to precision tests of the fundamental laws of nature., Comment: Nature, in press

Strongly interacting quantum many-body systems are fundamentally compelling and ubiquitous in science. However, their complexity generally prevents exact solutions of their dynamics. Precisely engineered ultracold atomic gases are emerging as a powerful tool to unravel these challenging physical problems. Here we present a new laboratory for the study of many-body effects: strongly interacting two-level systems formed by the clock states in ${}^{87}$Sr, which are used to realize a neutral atom optical clock that performs at the highest level of optical-atomic coherence and with precision near the limit set by quantum fluctuations. Our measurements of the collective spin evolution reveal signatures of many-body dynamics, including beyond-mean-field effects. We derive a many-body Hamiltonian that describes the experimental observation of severely distorted lineshapes, atomic spin coherence decay, density-dependent frequency shifts, and correlated quantum spin noise. These investigations open the door to exploring quantum many-body effects and entanglement in quantum systems with optical energy splittings, using highly coherent and precisely controlled optical lattice clocks., Comment: 21 pages, 6 figures

Many-particle optical lattice clocks have the potential for unprecedented measurement precision and stability due to their low quantum projection noise. However, this potential has so far never been realized because clock stability has been limited by frequency noise of optical local oscillators. By synchronously probing two 87Sr lattice systems using a laser with a thermal noise floor of 1e-15, we remove classically correlated laser noise from the intercomparison, but this does not demonstrate independent clock performance. With an improved optical oscillator that has a 1e-16 thermal noise floor, we demonstrate an order of magnitude improvement over the best reported stability of any independent clock, achieving a fractional instability of 1e-17 in 1000 s of averaging time for synchronous or asynchronous comparisons. This result is within a factor of 2 of the combined quantum projection noise limit for a 160 ms probe time with ~10^3 atoms in each clock. We further demonstrate that even at this high precision, the overall systematic uncertainty of our clock is not limited by atomic interactions. For the second Sr clock, which has a cavity-enhanced lattice, the atomic-density-dependent frequency shift is evaluated to be -3.11e-17 with an uncertainty of 8.2e-19., Comment: Final published version

Echelle spectra of HD 183143 [B7Iae, E(B-V) = 1.27] were obtained on three nights, at a resolving power R = 38,000 and with a signal-to-noise ratio ~1000 at 6400 A in the final, combined spectrum. A catalog is presented of 414 diffuse interstellar bands (DIBs) measured between 3900 and 8100 A in this spectrum. The central wavelengths, the widths (FWHM), and the equivalent widths of nearly all of the bands are tabulated, along with the minimum uncertainties in the latter. Among the 414 bands, 135 (or 33%) were not reported in four previous, modern surveys of the DIBs in the spectra of various stars, including HD 183143. The principal result of this study is that the great majority of the bands in the catalog are very weak and fairly narrow. Typical equivalent widths amount to a few mA, and the bandwidths (FWHM) are most often near 0.7 A. No preferred wavenumber spacings among the 414 bands are identified which could provide clues to the identities of the large molecules thought to cause the DIBs. At generally comparable detection limits in both spectra, the population of DIBs observed toward HD 183143 is systematically redder, broader, and stronger than that seen toward HD 204827 (Paper II). In addition, interstellar lines of C2 molecules have not been detected toward HD 183143, while a very high value of N(C2)/E(B-V) is observed toward HD 204827. Therefore, either the abundances of the large molecules presumed to give rise to the DIBs, or the physical conditions in the absorbing clouds, or both, must differ significantly between the two cases., Comment: Additional data and figures available at http://dibdata.org. To appear as Astrophysical Journal, 705, 32-45 (Nov. 1, 2009)

Two anomalously weak transitions within the $2 ^3{\rm S}_1~-~3 ^3{\rm P}_J$ manifolds in $^3$He have been identified. Their transition strengths are measured to be 1,000 times weaker than that of the strongest transition in the same group. This dramatic suppression of transition strengths is due to the dominance of the hyperfine interaction over the fine structure interaction. An alternative selection rule based on \textit{IS}-coupling (where the nuclear spin is first coupled to the total electron spin) is proposed. This provides qualitative understanding of the transition strengths. It is shown that the small deviations from the \textit{IS}-coupling model are fully accounted for by an exact diagonalization of the strongly interacting states., Comment: 4 Pages, 2 figures, 1 table. Accepted for publication in PRL

Echelle spectra of the double-lined spectroscopic binary HD 204827 were obtained on five nights, at a resolving power R = 38,000 and with a S/N ratio = 750 near 6000 A in the final, combined spectrum. The stars show E(B-V) = 1.11 and spectral types near O9.5V and B0.5III. A catalog is presented of 380 diffuse interstellar bands (DIBs) measured between 3900 and 8100 A in the stars' spectrum. The central wavelengths, the widths (FWHM), and the equivalent widths of nearly all of the bands are tabulated, along with the minimum uncertainties in the latter. The reliable removal of very weak stellar lines from the catalog, and of some stellar lines from the less severe blends with DIBs, is made generally easy by the highly variable radial velocities of both stars. The principal result of this investigation is that the great majority of the bands in the catalog are very weak and relatively narrow. Typical equivalent widths amount to a few mA, and the band widths (FWHM) are most often near 0.55 A. Therefore, most of these DIBs can be detected only in spectra obtained at a resolving power and a S/N ratio at least comparable to those used here. In addition, the anomalous interstellar reddening and the very high value of the ratio N(C2)/E(B-V) seen toward HD 204827 indicate that the physical conditions in one or more of the several interstellar clouds seen in this direction differ significantly from those found toward the prototypical DIB target HD 183143, for example. Probably primarily for these reasons, 113 of the 380 bands, or 30%, were not detected in four previous, modern surveys of the DIBs seen in the spectra of stars other than HD 204827. Both the tabulated data for the DIBs and a plot of our spectrum of HD 204827 are available online at http://dibdata.org, Comment: 85 pages (17 of text, 14 of tables, 54 of figures). To appear in the Astrophysical Journal