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Round 1 Funding Summary

With funds from the Templeton Foundation

Awarded January 2021

Ulrich Jentschura (Missouri S&T)	Accurate Quantum Field Theory Under External Conditions

The proposal Accurate Quantum Field Theory under External Conditions has the following parts:

1. Electron g factor in a finite-space volume. One of the most pressing questions concerning the further development of the quantum electrodynamic (QED) theory concerns the influence of external conditions (the geometry of the Penning trap) on the very well-known g factor measurements; these have recently been carried out with unprecedented accuracy. The evaluation of the geometry-dependent “dressed” correction to the g factor is an important cornerstone of the current project.
2. Quantum electrodynamic bound-state calculations. Subtle quantum field-theoretical effects in-fluence the spectrum of bound systems, and may play a role in explanations of the so-called proton radius puzzle. Namely, during the last decade, several measurements of transition frequencies in muonic bound systems have led, after the subtraction of all non-nuclear effects, to proton (and deuteron) radii significantly discrepant from the corresponding experiments in electronic systems. The puzzle continues to intrigue physicists over a number of subdisciplines, and represents one of the most pressing questions to answer in regard to our understanding of fundamental forces. This puzzle has recently been reinforced by a measurement of the deuteron radius, which also is discrepant in between electronic and muonic bound systems. The discrepancy inspires the evaluation, and re-evaluation, of a number of higher-order quantum electrodynamics (QED) corrections in bound systems, conceivably with the help of advanced numerical methods.
3. Particle physics and atomic theory. We aim to confront a number of recently proposed low- energy extensions of the standard model with high-precision atomic spectroscopic data. One example is a recently proposed X boson with a mass of about 16.7MeV, as an explanation for a recently seen excess of electron-positron pairs in the decay of 8Be. Recent advances in this area must urgently be complemented by a further thorough analysis; it would be very interesting to confirm the conjectured existence of a “fifth force” by an independent atomic physics experiment.
4. Dirac theory in curved space-time. Recently, the PI has been involved in a series of investigations on Dirac particles embedded in curved space-times. Bound states have been the focus of the investigations. On large distance scales, one probably cannot expect “quantum corrections” to the Einstein equivalence principle. However, the question is whether the same statement holds true on atomic length scales. Does the internal structure of the atom lead to corrections to the frequency shifts of atomic transitions in the gravitational potentials, such as the one generated by the Earth? Are there nontrivial corrections due to these combined effects, for relativistic geodesy? These questions can only be answered in combining quantum mechanics, and field theory, with general relativity. Very recently, a number of correction terms have been identified which imply limitations (violations!?) of Einstein’s equivalence principle. These need to mapped out with regard to conceivable experiments in the future.
5. Atom-surface interactions and non-contact friction. Recently calculated long-range tails in atom-wall interactions have been shown to mimic parity-violating terms, which have otherwise been conjectured to exist in extensions of the Standard Model that involve Lorentz-symmetry breaking. Our proposal aims to map out conceivable confirmations of these effects in high-precision experiments, improving our understanding of fundamental aspects of quantized fields in dressed environments. The proposal combines atomic theory and quantum-field theory, as well as general relativity, in the low-energy domain, in order to address fundamentally important questions and pressing current experimental-theoretical discrepancies. Service activities of the applicant (such as membership in the Editorial Board of Physical Review A for the period of 2013–2016) profit from the broad spectrum of physical questions investigated by the PI in the past, and this past experience will prove useful for the challenging calculations which lie ahead. Since 2016, the PI has been a member of the Editorial Board of the journal Atoms [MDPI publishing].

John Doyle (Harvard)	Laser Cooled Symmetric Top Molecules for Electron EDM Measurements

The standard theory of particle physics, known as the Standard Model (SM), successfully accounts for every laboratory experiment probing microscopic fundamental physics. However, it completely fails to explain two huge questions about the Universe, both of which arise from the simplest astronomical observations. First, what is the particle nature of dark matter? Second, how is it that, throughout the Universe, matter completely dominates over anti-matter? Time-reversal (T) violating eects that are not in the SM are needed to explain the matter/anti-matter asymmetry. (T-violation is characterized by a dierence in the laws of physics when time goes backward.) Similarly, a new, beyond-the-SM, particle is needed to explain the dark matter. The best theoretical explanations that solve both problems also generically invoke T-violating physics that produces a distortion to the shape of elementary particles like electrons, causing them to be no longer perfectly round. This distortion could be observed as an electric dipole moment (EDM). Most theories beyond the SM would be ruled out if an EDM were not found at high precision. Likewise, these theories would be put on sound experimental footing if one were found. The best electron EDM searches currently use diatomic molecules, with triatomic molecules on the horizon. We are now exploring new methods that use a new class of much more complex molecules as EDM probes.

Recent experimental progress on the laser cooling of molecules, originating and accomplished in our and others' labs, underpin what can reasonably be called a revolution in molecular physics. We have successfully laser cooled CaF and SrOH molecules. Drawing upon the insights acquired during our experimental work with SrOH, we theorize that we can laser cool larger polyatomic molecules, including ones containing heavy nuclei useful for EDM searches. A dramatically improved EDM experiment can be done by using ultra-cold samples of such EDM sensitive molecules because they can be held for very long times in the pristine environment of a trap made of light. Long interaction times with the molecules dramatically improve the probe for the subtle eects of an EDM. Experiments pursuing this goal are currently underway with relatively simple molecules, but we now envision major advantages of molecules that behave as perfect spinning tops, called symmetric top molecules. Our proposal is the in-depth study of the properties of such molecules for EDM experiments. The long-range goal is to employ the molecule that we propose to study, YbOCH3, in a next-generation EDM experiment and thus move much closer to, and perhaps answer, the fundamental questions of dark matter and the matter/anti-matter asymmetry of the universe.

Shimon Kolkowitz (UW - Madison)	A Multiplexed Optical Lattice Clock to Search for New Physics

Optical lattice clocks are currently the most stable and accurate timekeepers in the world, with accuracies and precisions equivalent to neither losing nor gaining a second over the entire 14- billion-year age of the universe. This unprecedented level of precision offers sensitivity to new and exotic physics with tabletop-scale experiments. Here we propose a novel design for an optical lattice clock dedicated to searches for new physics. We will build a first-of-its-kind "multiplexed" clock that will consist of two strontium optical lattice clocks in one. This novel apparatus will enable differential comparisons between the two internal atomic clocks at much higher levels of precision than can be achieved with independent clocks. We will then apply this new apparatus to study several of the central outstanding questions in fundamental physics.

A unified field theory that can describe gravity and all other fundamental forces is believed to require Einstein’s theories of relativity to fail at some scale, and many of the beyond SM theories proposed in attempts to account for dark energy require modifications to relativity. It is therefore natural to ask whether gravity behaves as Einstein predicted, as all previous tests have indicated, or whether a deviation from the expected behavior can be observed in a previously unexplored regime. Optical atomic clocks offer an attractive tool to explore this question, thanks to their remarkable frequency precision, and the sensitivity of comparisons between clocks in different frames to relative differences in the passage of proper time. Our multiplexed optical lattice clock will have the capability to reposition the relative height of the two clocks with respect to gravity, and to rapidly accelerate both clocks together or independently. We will use these features to probe relativity by testing its predictions in two new regimes: the gravitational redshift due to Earth’s gravity at the millimeter scale, and the special relativistic analogue to the gravitational redshift in accelerating reference frames, testing the Accelerated Clock Principle in the process. By combining these two measurements we will perform a novel test of the Einstein equivalence principle.

The overwhelming evidence for the existence of dark matter and dark energy and the observed imbalance between matter and antimatter hint at the existence of as yet undiscovered particles and interactions. Isotope shift measurements of atomic clock transitions offer a precision probe of new physics beyond the Standard Model without requiring precise calculations of internal atomic structure. Our strontium multiplexed optical lattice clock is well suited for isotope shift measurements. The same lasers can be used for cooling, trapping, and clock interrogation of both isotopes. Clock laser noise and environmental perturbations will then be shared between the two isotopes, offering longer coherent interrogation times and enhanced differential stability. We will perform a simultaneous differential isotope shift comparison between ⁸⁸Sr and ⁸⁷Sr in the multiplexed OLC with improved stability relative to interleaved or independent clock isotope shift measurements. This will include a detailed systematic evaluation of the sources of differential frequency shifts between the two isotopes.

Finally, as a potential future research direction we note the prospects for using the multiplexed optical lattice clock to test the achievable limits of searches for dark matter candidates using clocks. Certain proposed dark matter candidates such as ultra-light scaler dark matter and topological dark matter are expected to cause a transient or oscillatory relative frequency shift between two spatially separated clocks, or between two nearby clocks utilizing transitions with different sensetivities to changes in α which would be revealed through a clock comparison. Beyond the scope of the proposed program, we envision that our apparatus can be used to probe the achievable limits of clock-based dark matter detectors.

David Demille (Yale)	Probing New Physics via Nuclear Spin-Dependent Parity Violation

Atoms and molecules are composed of electrons, protons and neutrons. The protons and neutrons are bound together tightly into nuclei by one of Nature’s four fundamental forces, the strong force. The negatively charged electrons are bound to the positively charged nuclei by another fundamental force, the electromagnetic force. Within both the nuclei and the atoms, the other two fundamental forces—gravity and the weak force—also affect how they are bound. The effect of gravity within these systems is far too small to detect. However, the effect of the weak force is large enough to measure.

The primary goal of this project is to measure certain effects of the weak force that have to date been poorly measured, and then compare them to the theoretically expected size of these effects. Discrepancies between measured and predicted outcomes could signal the existence of a new, previously undiscovered force with properties similar to those of the weak force. In addition, we will test whether the weak force is constant over the duration of our experiment, or instead oscillates or drifts over time. Such a time variation could be caused by certain types of a cosmological “background field” that permeates all of space. Fields of this type have been proposed as a possible constituent of “dark matter”. Dark matter is a substance of unknown composition that causes galaxies to be bound together more strongly than expected, if only the gravitational attraction between visible stars were at play.

The weak force has a critical difference from all other known forces: its strength depends on the handedness of the configuration of particles on which it acts. Put differently, the weak force breaks the symmetry between mirror-image configurations; in the language of quantum physics, this is known as violation of parity symmetry. In our experiment, we use this feature of parity violation to distinguish the tiny effect of the weak force from the much larger effects of electromagnetic and strong forces. In particular, we measure changes in the energy difference between two quantized states in a diatomic molecule, when we put the molecules in configurations of electric and magnetic fields of different handedness. Our experimental approach uses the properties of diatomic molecules, together with a very precisely controlled magnetic field, to greatly amplify the measurable effect of this parity-violating energy change. Compared to prior experiments studying the weak force using atoms instead of molecules, this amplification makes it possible to measure particular aspects of the weak force that were previously difficult to observe.

In addition to violating parity, the weak force has another important difference from the other forces. In particular, each type of particle has two independent types of charges. One of these weak-force charges, known as the vector weak charge, is exactly analogous to the electromagnetic charge. The other, however has no analogue in the other forces. This extra weak-force charge, known as the axial charge, is linked to the angular momentum of each particle—the property known in quantum mechanics as “spin”.

Our experiment will specifically measure the product of two weak force charges: the electron’s vector charge and the axial charge of nuclei. This particular combination is predicted to be accidentally small in the Standard Model of particle physics. This small effect has been measured in only one nucleus, in one experiment, to date—and the results of that measurement disagree with theoretical predictions. In addition, the axial charge of protons and neutrons is significantly modified in the presence of the strong force. These modifications are difficult to measure or to predict with high accuracy. Our experiment will shed important new light on the interplay between weak and strong forces.

Our specific initial goal is to measure the axial weak charge of the ¹³⁷Ba and ¹³⁵Ba nuclei, in the molecule BaF. These will be the first measurements of the axial weak charge of nuclei whose spin comes mostly from neutrons. Once measurements of Ba nuclei are complete, we will apply out method to other nuclei, where the energy shifts are smaller but theoretical predictions for the size of the axial charge are more reliable, so that the possibility to detect the effect of new forces is enhanced.

Tanya Zelevinsky (Columbia)	Molecular Lattice Clock for Fundamental Physics

There is a growing connection between AMO science and fundamental physics. The techniques of quantum state control are leading to a new generation of table-top experiments that can offer a glimpse of new physics over an extensive range of length scales, energies, and types of fundamental interactions. The unprecedented reach of these experiments arises from an immaculate control of atomic and molecular quantum states and their environmental influences. Fundamental insights gained from AMO physics experiments include tight constraints on time-reversal-symmetry violating physics, measurements of fundamental constants and their stability, searches for dark energy and dark matter, tests of general relativity, searches for new forces, and rigorous tests of QED. Among many types of such experiments, atomic clocks play a special role as extremely precise scientific measurement tools, contributing to diverse scientific questions such as dark energy, gravitational waves, and high-precision many-body physics. While microwave and optical atomic clocks are based on different types of electronic transitions, molecules possess a significantly more extensive set of internal degrees of freedom than atoms. A clock based on molecular physics such as vibrations can access new fundamental measurements that are out of reach for atomic clocks. In addition, molecules with their variety of transition mechanisms present opportunities for self-normalized or systematics-cancelling clocks. Significant progress has recently taken place in molecular quantum state control. This makes possible state-of-the-art clocks that utilize ultracold molecules, where motional degradation of precision and accuracy is nearly eliminated. We propose the development of a vibrational molecular lattice clock and its first scientific applications, including tests of ultrashort-range gravity.

Tightly trapping ultracold neutral molecules in an optical lattice affords a large signal-to-noise ratio while eliminating motional effects that lead to rapid decoherence. Our recent work resulted in a molecularclock quality factor Q of nearly a trillion, matching the best atomic clocks of just over a decade ago. A large share of this success stems from realizing molecular state-insensitive (magic) trapping. This starting point makes the clock already applicable to a new class of high-precision measurements. The primary scientific application is for the most precise measurement of an interatomic force. Combined with stateof-the-art quantum chemistry theory that is being developed concurrently, this clock-based measurement should lead to the best limit on non-Newtonian gravity at the nanometer scale, while providing tests of molecular QED. The molecular clock will also yield a model-independent measurement of temporal stability of the electron-to-proton mass ratio. Further improvement in Q is contingent on understanding two-photon molecular photodissociation processes, which intellectually connects the molecular clock with the field of ultracold chemistry. As an added benefit, the ultralong molecule-light coherence times are highly relevant to quantum-information and many-body experiments with molecular qubits.

The proposed molecular clock makes broad connections between the fields of metrology, ultracold molecules, and fundamental physics. Tests of Newton’s law at ultrashort range link this work to gravity, and the concept can be easily understood by the general public. Constraints on drifts of fundamental constants contribute to our basic understanding of the fabric of the universe. To accomplish the stated goals, the project must make close connections with the growing field of ultracold chemistry. And beating the limitations on molecule-light coherence times will advance the progress of ultracold-molecule based qubits.

Eric Hessels (York)	Electron Electric Dipole Measurement Using Molecules in a Matrix

Collider physics is at an impasse: the Large Hadron Collider has not discovered any new physics beyond the Standard Model, and there is no theoretical consensus on whether a possible higher-energy collider will discover anything new either. Fortunately, it is not necessary to create real particles in a collision to study them. One can take advantage of a consequence of quantum field theory: a cloud of virtual particles of every mass and description, including hitherto undiscovered particles, swarm around each real particle. Very high precision measurements of the properties of this virtual cloud can probe for new physics at energy scales far beyond the reach of particle colliders.

One compelling reason to search for new physics is matter-antimatter asymmetry: the universe appears to be exclusively made up of matter, whereas our best physics theories predict that significant amounts of antimatter should also exist. This puzzling absence of antimatter can be explained if there is some undiscovered new source of microscopic time-reversal symmetry (T) violation. An unambiguous way to probe for T-violating new physics is to look for a permanent electric dipole moment (EDM) of fundamental particles such as electrons or quarks. An EDM is an asymmetry between the distributions of positive and negative virtual particles in the cloud around a real particle, oriented along its spin. Evidence of new particles or fundamental interactions responsible for the matter-antimatter asymmetry of the universe could be discovered by precision EDM search experiments. Conversely, the non-observation of an EDM rules out all theories that predict EDM values larger than the experimental upper bound.

Recent experiments using polar diatomic molecules have pushed the upper bound on the electron EDM (eEDM or d_e) down to |d_e| < 1.1x10^-29 e cm, ruling out a number of supersymmetric theories in the process. Nevertheless, an enormous range of new physics theories still remain viable, almost all of which tantalizingly predict the existence of an eEDM within 2 to 4 orders of magnitude of the current experimental limit. The aim of the proposed experiment is to discover the eEDM, or to definitively rule out all of these theories, by making a significant improvement in the measurement precision.

A large leap in precision requires a radical new technique. In particular, compared to all other previous efforts, a much larger number of polar molecules need to be precisely measured. This proposal describes our intent to perform an eEDM search using a large ensemble of polar molecules frozen into a rare-gas matrix. The matrix fixes the orientation and position of the molecules. Trapping molecules in this way improves the measurement time (and therefore the precision) of the experiment, but also freezes molecular motion and removes the need for an electric field to align the molecules, thereby eliminating many classes of potential systematic errors. An ensemble of oriented molecules in a rare-gas solid is also naturally equipped with excellent co-magnetometers to suppress errors from magnetic field fluctuations, allowing simple groundstate polar molecules to be used in an advanced eEDM experiment. The combination of these features yields an eEDM measurement method that is capable of probing new physics up to the peta-electron-volt energy scale.

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