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## Round 2 Funding Summapry

#### Awarded January 2021

Alexander Shushkov (Boston Univ.) The Search for Electron Spin coupling of Axion-like Matter

The nature of dark matter is one of the most important open problems in modern physics. Since dark matter has only been observed through its gravitational effects, there is a wide variety of possible dark matter candidates, and a large number of direct and indirect searches for dark matter interactions with standard model particles. The WIMP is a well-known candidate that has inspired a large number of ultra-sensitive experiments of increasing complexity and scale, but so far there has been no unambiguous detection, and fundamental backgrounds (neutrino floor) will soon start to limit the sensitivity of direct WIMP searches. It is important to broaden the search. Remarkably, recent developments in the fields of precision measurements and sensing have enabled a broad range of technologies that are finding applications in a variety of sensitive small-scale searches for ultralight dark matter candidates. Among these candidates, the axion is particularly well motivated, as it offers a solution to the strong-CP problem of the Standard Model.

This proposal describes a table-top direct experimental search for light axion-like dark matter, via the axion-electron interaction. This interaction creates an oscillating magnetization of a magnetic sample, with the oscillation frequency determined by the mass of the axion-like particle. Our approach is to search for such an oscillating magnetization, using SQUID magnetic sensors, coupled to the sample. Our recent work with a similar experimental apparatus has demonstrated the magnetic field sensitivity of 150 aT/$\sqrt{Hz}$, which is at the level of the most sensitive magnetic field measurement with any broadband magnetometer technology. This level of sensitivity will enable us to improve the best laboratory limits on the axion-electron interaction over more than three decades of mass, and approach the astrophysical bounds. In contrast to the astrophysical constraints, our results would not depend on details of stellar dynamics models. An important feature of our experimental design is the systematic rejection scheme, in which we will correlate the signals in three independent detection channels to distinguish between radiofrequency interference and the axion-like dark matter signal, which has to match a specific modulation pattern, produced by earth rotation, as it travels through the dark matter halo.

Our project is especially timely, given the recently-reported excess of low-energy recoil events in the XENON1T detector, with one of the leading models ascribing these events to the electron spin interaction of solar axions. Our goal is to reach the sensitivity at the level of the coupling strength necessary to explain these events, under the assumptions that the axion-like particles have mass  10 peV − 1 neV and constitute the dominant component of dark matter. Searches for ultra-light axion-like particles create an experimental window into physics at energy scales many orders of magnitude beyond that accessible at particle colliders. A discovery may solve several of the mysteries facing today’s physicists, including the nature of dark matter, the strong CP problem, and the energy scale of inflation, providing insights into the earliest epochs of the universe.

Dylan Yost (Colorado State) Search for an Anomalous Spin-Dependent Force through Hydrogen Spectroscopy

We propose a new measurement of the hydrogen 2s hyperfine interval, $E$HFS(2s), using a cryogenic beam, and optical excitation to the 2s metastable state. While this transition is already known with an uncertainty of only 4 x 10-8, we anticipate that with a new measurement a 4 x 10-9 uncertainty should be possible during the award period of this grant. Further, we believe that an uncertainty of 1 x 10-11 will be possible using the basic measurement principle outlined in this proposal.

In general, the hyperfine structure of hydrogen can be calculated to high precision using boundstate quantum electrodynamics (QED). Unfortunately, the structure of the proton introduces uncertainties into the theory that are currently much larger than the experimental uncertainties. However, by considering the combination $D21 = 8 E$HFS(2s) - EHFS(1s), where $E$HFS(1s) is the hyperfine interval of the ground state, it is possible to eliminate many of these theoretical uncertainties. With this, the theoretical value of D21 is determined primarily through 3rd and 4th order QED correction and has an uncertainty which is 18 times smaller than the experimental. The measurement we propose will drastically reduce the experimental uncertainty in D21 and stringently test bound-state QED predictions.

For the 1s and 2s states of hydrogen, the hyperfine structure arises due to the interaction of the magnetic moments arising from the electron and proton spin. Therefore, a deviation of our result from the theory could be an indication of an anomalous spin-dependent force. Such a force would lie outside of the Standard Model of particle physics and could be an indication of a new previously undetected low-mass (<1 keV) weakly-interacting particle.

To conduct our measurement, we will leverage our cryogenic (4 K) atomic hydrogen beam. We will excite a portion a portion of this beam to the metastable 2s state using high-power cavity-enhanced laser radiation at 243 nm. The 2s beam will then travel to a separate spectroscopy chamber where we will use Ramsey’s method of separated oscillatory fields (at $E$HFS(2s) = 178 MHz) to transfer population from the 2s F=0 state to the 2s F=1 state (the lower and upper hyperfine states respectively). Finally, we will detect the population transferred to the 2s F=1 to complete the measurement. The spectroscopy region will be carefully shielded from external fields to prevent systematic effects. In addition, precise control over the average velocity of the metastable beam will be used to eliminate line pulling due to a phase offsets in the 178 MHz RF fields.

While our initial goal will be an uncertainty of 4 x 10-9, we believe much higher precision is possible in principle by increasing the transit time of the atoms through the spectroscopy region. Therefore, we anticipate that this project will continue to test bound-state QED and search for anomalous spin-dependent forces for many years past this award period.

Andrei Derevianko (Univ. of Nevada-Reno) Resolving persistent inconsistencies in interpretation of atomic parity violation

Atomic parity violation (APV) is a powerful probe of the electroweak sector of the Standard Model of elementary particles. High-precision APV experiments measure the degree of violation of mirror symmetry in atomic systems. Theoretical interpretations search for a deviation of the measured APV signal from the Standard Model predictions. In the absence of the deviation, the interpretations place important constraints on a plethora of new, beyond the Standard Model, physics scenarios, such as grand unifed theories and dark matter models. The APV probes are often unique and complementary to those derived from particle colliders. Here, we propose to analyze so-far overlooked systematic corrections in interpretation of APV. These are the corrections to the so-called transition polarizability, a crucial quantity normalizing the measured APV signal. Careful evaluation of these corrections, proposed here, is anticipated to resolve several persistent inconsistencies in interpretation of APV.

1. There are sizable and unexplained differences in determination of transition polarizabilities in alternative approaches reported in the literature. These differences cloud the extraction of electroweak observables and thus preclude probing new physics at an improved level. We anticipate that our newly-introduced corrections will resolve these disagreements and improve the accuracy of the analysis.
2. We argue that with these overlooked corrections, the transition polarizability becomes a nuclear spin-dependent quantity. As such, it has a direct effect on extraction of the so-called nuclear anapole moment from APV experiments. The anapole moment of Cs-133 is the only anapole moment ever measured in nature; its currently extracted value is in a signifcant tension with nuclear theory of hadronic parity violation. We anticipate that computing the overlooked corrections to transition polarizabilities will modify the extracted value of the anapole moment and reconcile it with nuclear theory.
3. Our order-of-magnitude estimates support these expectations. The proposed computations require involved technical work in third order perturbation theory coupled with ab initio relativistic many-body perturbation theory. The proposed work is based on the PI's expertise in APV and high-precision atomic structure calculations.

Dalziel Wilson (Univ. of Arizona) Quantum optomechanical dark matter detectors

The aim of this project is to explore the possibility of detecting dark matter with a table-top optomechanical sensor, harnessing advances that have enabled optomechanical systems to operate in the quantum regime in recent years. Specifically, we will build a quantum-limited accelerometer based on the ultra-high-Q silicon nitride membrane coupled to a Fabry-Perot cavity, and use it to search for ultralight “dark photons” in the 10-11 - 10-9 eV/c2 mass range.

Dark matter is on the enduring scientific mysteries of our time. This project will advance knowledge by carving out new constraints for—or possibly detecting for the first time—ultralight dark matter, while serving as a demonstration for a new generation of laboratory-scale dark matter detectors based on quantum-limited mechanical systems. The target acceleration sensitivity (10-12 $g/\sqrt{Hz}$ at the 1 – 100 kHz frequencies) is unprecedented and will give access to the fundamental forces produced by a variety of dark matter or dark energy candidates, Casimir effect, and spontaneous waveform collapse, among others. Besides fundamental science, the project will address critical issues in the development of quantum sensors, such as scalability and decoherence.

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