Nuclear MQM

We are searching for symmetry-violating nuclear magnetic quadrupole moments (MQMs) in heavy, deformed nuclei as a probe for new particles and forces.

As discussed in the research overview, atoms and molecules are powerful systems to search for fundamental symmetry violations involving their subatomic constituents.  We are currently interested in using polar molecules to study symmetry violation inside the nucleus itself.  This symmetry violation can come things like permanent EDMs of protons, nucleons, or quarks, new nuclear forces, the strong force, and more.  These symmetry-violating effects would arise from new physics beyond the Standard Model, and therefore shed light on the asymmetry between matter and anti-matter in the universe.

We are running an experiment to search for the MQM of the Yb-173 Nucleus using the 173YbOH molecule.  This molecule combines large intrinsic sensitivity due to the large mass and quadrupolar deformation of the Yb-173 nucleus, combined with the advantages of symmetry-lowered polyatomic molecular states which offer high polarizability, robustness against systematic errors, and the ability to engineer coherence.

Nuclear Magnetic Quadrupole Moments (MQMs)

A permanent EDM violates CP symmetry, so we could search for CP violation in the nucleus by searching for a permanent EDM of the nucleus.  However, that is not the only permanent electromagnetic moment whose existence would violate CP, and there are advantages for looking at other, higher electromagnetic moments.  For example, a permanent magnetic quadrupole moment (MQM) would violate CP symmetry, and therefore have the same important implications should one be discovered. 

Very similar to the case of a permanent EDM, the very existence of a particle with an MQM would violate P, T, and CP symmetries.  In the figure below, we show a particle with an intrinsic spin indicated by the black arrow, and a magnetic quadrupole moment, which we can classically picture as two currents flowing in opposite directions, indicated by the orange arrows.  Because the particle and its mirror image are distinguishable - notice the relative orientation of the black and orange arrows - only one of the two possible configurations can exist, indicating violation of P symmetry.  A similar argument shows that T symmetry is also violated, and therefore CP, which is the symmetry we want to study in order to understand the matter/anti-matter asymmetry.

Figure: A particle with a permanent MQM would violate P symmetry.  Notice the different relative orientation between the black arrow (spin) and orange arrows (magnetic quadrupole).

In order for a particle to have a MQM, it must have spin of at least 1; it turns out that the interaction of spin 0 or spin 1/2 particles with an electromagnetic field cannot be sufficiently complex to accommodate a quadrupole moment, either electric or magnetic.  This rules out electrons, protons, and neutrons, but nuclei can have spin of 1 and higher, and are therefore candidates for MQM searches.

MQMs in Deformed Nuclei, and New Physics

A nuclear MQM would arise from symmetry-violating effects inside the nucleus.  As an example, consider a nucleus with a single nucleon in a valence nuclear shell, as shown in the figure below.  If the nucleus has a spin indicated by the black arrow, and the valence nucleon has a permanent EDM (which violates CP), then the nucleus will have a CP-violating MQM.

Figure: an orbiting EDM creates an MQM.  Such a situation could arise from a nucleus with a valence nucleon that posses a permanent EDM, though it turns out to not generally be the dominant contribution to nuclear MQMs.

This example is hopefully intuitive, but not particularly exciting - if the MQM simply comes from a proton or neutron EDM, why not just measure the latter?  The reason is that new CP violating physics could be present in internuclear forces that would not act on individual nucleons.  This makes nuclear MQM searches, along with other nuclear symmetry violations such as Nuclear Schiff Moments (NSMs), sensitive to entirely new sectors of physics beyond the Standard Model, such as pion-mediated symmetry violating forces.

Furthermore, nuclear MQMs are significantly enhanced in heavy nuclei with quadrupole deformations.  When a nucleus is deformed, nucleons in nominally filled shells can contribute to observable effects, leading to collective enhancements of the MQM that enhance sensitivity to new physics.  Specifically, we are interested in nuclei with a large quadrupole deformation, characterized by the parameter β2, shown schematically in the figure below.  Nuclei with a large β2 parameter include isotopes of Yb, Ta, Th, Hf, and others.  This enhancement of the nuclear MQM through collective effects induced by nuclear deformation provides a number of advantages over directly searching for permanent nuclear EDMs; however, the two approaches generally complement each other in terms of sensitivity to new physics.

Figure: A nucleus with a quadrupolar deformation (orange) versus a spherical nucleus (gray).

Measuring Nuclear MQMs in Polar Molecules

To measure an electromagnetic moment, we need to place the particle of interest into a strong electromagnetic field.  As with permanent EDMs, the largest accessible fields are inside molecules.  By performing precision measurements of spin precession in molecules with heavy, quadrupole-deformed nuclei, such as YbOH, we can search for new physics on the TeV scale - and beyond - in a low energy setting.  Many of the tricks used to search for the electron EDM - cryogenic buffer gas beams, heavy polar molecules, internal co-magnetometers, etc. - are immediately applicable to search for nuclear symmetry violation, and therefore provide a way to realize sensitive and robust searches for nuclear symmetry violation above the TeV scale.

Relevant Publications

• Engineering field-insensitive molecular clock transitions for symmetry violation searches
  Phys. Rev. Lett. 131, 183003 (2023) 

• Optical cycling in polyatomic molecules with complex hyperfine structure
  Phys. Rev. A 108, 012813 (2023)  

• Characterizing the Fundamental Bending Vibration of a Linear Polyatomic Molecule for Symmetry Violation Searches
  New J. Phys. 25, 073014 (2023) 

• Fine and hyperfine interactions in 171YbOH and 173YbOH
  J. Chem Phys. 154, 244309 (2021)

• Enhanced Molecular Yield from a Cryogenic Buffer Gas Beam Source via Excited State Chemistry
  New J. Phys. 22, 022002 (2020)

• Enhanced P,T-violating nuclear magnetic quadrupole moment effects in laser-coolable molecules
  J. Chem. Phys. 152, 084303 (2020)

• Precision Measurement of Time-Reversal Symmetry Violation with Laser-Cooled Polyatomic Molecules
  Phys. Rev. Lett. 119, 133002 (2017) 

Photos

Support and Acknowledgements

This work  has received support from a National Science Foundation CAREER Award, and Heising-Simons Foundation, and a NIST Precision Measurement Grant.