Eric Hessels at York University

Barium Monofluoride Embedded in an Argon Solid: Understanding a System That Could be Used for an Ultraprecise Measurement of the Electric Dipole Moment of the Electron

Hessels Figure 1: Contour figure from arXiv:2211.14804 (2022)
Figure 1: Contour figure from arXiv:2211.14804 (2022)

Hessels Figure 2: The geometry for the most energetically favorable substitution of BaF in the FCC argon solid, with the BaF aligned along the 111 axis and substituting for four Ar atoms.
Figure 2: The geometry for the most energetically favorable substitution of BaF in the FCC argon solid, with the BaF aligned along the 111 axis and substituting for four Ar atoms. The remaining Ar atoms have their positions only slightly perturbed by the BaF molecules.

Hessels Figure 3: Our cryogenic apparatus
Figure 3: Our cryogenic apparatus


We have studied methods for creating argon solids doped with barium monofluoride (BaF). Two methods were used to produce BaF molecules: an electrospray source followed by mass selection using a quadrupole mass spectrometer and a helium-buffer-gas-cooled laser ablation source. The latter allowed for the production of large numbers of BaF molecules, and these were observed using laser absorption spectroscopy and by directing the molecules into a residual gas analyzer. When a combination of these molecules and a stream of argon gas is incident onto a cryogenic sapphire substrate, the desired doped solid is produced. Initial studies of annealing of this solid and observation of laser-induced fluorescence have been performed. Future measurements will require a higher purity source of BaF, which will be obtained by deflecting the BaF molecules away from the other ablation products. Extensive modelling has led to two viable options for this deflection, namely electrostatic deflection (using the large electric dipole moment of the BaF molecule) or laser light forces. Understanding of the local environment of the BaF molecule embedded in an argon crystal has been advanced by precise relativistic all-electron quantum-mechanical coupled-cluster calculations of BaF-Ar interaction binding energies for a range of BaF-Ar separations and angles. These calculations have been used to find the most favorable number of argon atoms for which the BaF substitutes (four), the position of the BaF molecule relative to the FCC crystal and the positions of the neighbouring argon atoms. The modes of motion of the BaF molecule can also be deduced.

This work is moving us to a more complete understanding of a BaF doped Ar solid and towards an ultraprecise measurement of the electron electric dipole moment using this system.

Big scientific questions addressed

The larger goal of this research is to make an ultraprecise measurement of the electron’s electric dipole moment (eEDM) using the favorable properties of polar molecules embedded in an argon solid. These favorable properties include large numbers of cold, stationary molecules in a small volume and fixed molecular alignment without an external electric field. This system could have the potential to improve eEDM measurements by several orders of magnitude. CP violation larger than that found in the Standard Model is necessary to explain the matter-antimatter asymmetry implied by the existence of our universe, and extensions to the Standard Model that provide the extra violation also predict a larger eEDM. Thus precise eEDM measurements will continue to guide theoretical work to extend the Standard Model and help to answer one of the most fundamental open questions in physics.

Researchers Whose Research Profited from these Funds
  1. Eric Hessels (faculty member)

  2. Marko Horbatsch (faculty member)

  3. Rene Fournier (faculty member)

  4. Matthew George (faculty member)

  5. Cody Storry (faculty member)

  6. Katrina Carver (undergraduate student)

  7. Ethan Brooks (undergraduate student)

  8. Nadav Gasner (undergraduate student)

  9. Quinton Weyrich (undergraduate student)

  10. Nick Gourley (undergraduate student)

  11. Hin Man Yau (graduate student)

  12. Zachary Corriveau (graduate student)

  13. Neil McCall (graduate student)

  14. Jorge Perez Garcia (graduate student)

  15. Taylor Skinner (graduate student)

  16. Anita Ragyanszki (postdoc)

  17. Alain Marsman (postdoc)

  18. Daniel Heinrich (postdoc)

  19. Ricardo Lambo (postdoc)

  20. Greg Koyanagi (research associate)

  21. Ushieja De Zoysa Senaratne (research associate)

All of these personnel (except for faculty members) have been financially supported by the CFP/Templeton grant. The faculty members listed have supervised the supported personnel.

Notable scientific progress was enabled by the CFP Templeton grant?

The grant provided the ability to pay personnel to design and build a complex ultrahigh-vacuum cryogenic apparatus in which a helium-buffer-gas-cooled laser ablation source created a beam of BaF molecules (by mixing ablated Ba with SF6 gas). These molecules, along with a flow of argon gas, were incident on a temperature-controlled cryogenic sapphire surface to produce a BaF doped Ar solid.

To monitor the output of this source, it was sent directly into a residual gas analyzer, where counting techniques could be used to measure the intensity of the source, as well as to monitor impurities from the source.

A novel idea for an electrostatic mirror (that allows for specular reflections) has been developed. A deflection is necessary to separate our BaF molecules from the other ablation products. An electrostatic deflector that can allow for this separation within our present apparatus has been designed and is presently being constructed.

An alternative deflection method involves laser light forces. These forces have been evaluated for our BaF molecule using computationally-intensive density-matrix calculations. A scheme that allows for a large force has been developed and will soon be submitted for publication.

To understand the interaction of the BaF molecule with Ar, precise relativistic all-electron quantum-mechanical coupled-cluster calculations of BaF-Ar interaction binding energies are obtained for a range of BaF-Ar separations and angles. These calculations are extrapolated to a complete basis set and our methods are tested against known properties of BaF, Ba, Ba+ and Ar. The result gives a precise potential surface for describing BaF-Ar interactions. The work has just been submitted for publication and can be found at arXiv:2211.14804.

Using this potential surface, we are able to model the environment of a BaF molecule within an Ar solid. We find that having the BaF substitute for four Ar atoms is strongly energetically favoured compared to other numbers of Ar atoms. We can also predict the positions of the BaF molecule and neighbouring Ar atoms, as well as investigate the modes of motion for the BaF molecule.

The BaF doped Ar solid has been studied using laser-induced fluorescence. After annealing, the BaF spectrum shows substructure (with a separation of 20 cm-1), and we believe that this substructure is due zero or one quanta of BaF center-of-mass oscillatory motion being excited while the molecule is transferred to the electronically excited state.

We have built up a system to allow x-rays to be incident onto our solids. We will use the x-ray-induced fluorescence from the solid (which gives separate signatures for each impurity) to measure the purity of our solid.

Notable scientific progress that was Triggered, Launched or Enabled that Can be Reasonably Expected in the Next Couple of Years?

We expect to have continued improved understanding of our doped solid.

On the calculation side, we expect to be able to model the behaviour of excited states of our molecule within an argon solid. Additionally, we expect to be able to do dynamical simulations that show how the solid grows as each Ar atom or BaF molecule arrives onto its surface.

On the experimental side, we will continue to study the properties of our doped solid. We will demonstrate electrostatic (and, if necessary, laser-induced) deflections that separate the BaF from the other ablation products. We will demonstrate the steps necessary to make an eEDM measurement, namely optical pumping, rf transitions between ground-state hyperfine levels and cycling-transition fluorescence detection.

Full citations and whether support was properly acknowledged

Although several papers are currently in preparation (see below), only one has been submitted for publication to date:

"Accurate calculation of the interaction of a barium monofluoride molecule with an argon atom: A step towards using matrix isolation of BaF for determining the electron electric dipole moment," GK Koyanagi, RL Lambo, A Ragyanszki, R Fournier, M Horbatsch and EA Hessels. Submitted to the Journal arXiv:2211.14804 (2022). (a copy of this paper is attached)

Note added: A second paper has just been posted to the arXiv: RL Lambo, GK Koyanagi, A Ragyanszki, M Horbatsch, R Fournier and EA Hessels. ”Calculation of the local environment of a barium monofluoride molecule in an argon matrix: A step towards using matrix-isolated BaF for determining the electron electric dipole moment”. Submitted to Molecular Physics (2022) arxiv:2212.09232

The fact that only one paper has been submitted at this time is a result of two factors:

  1. Some delays due to COVID19, which led to a complete shutdown and then restricted access to our laboratory and

  2. The nature of the research. This grant was awarded as we were starting a brand new venture towards performing a precision measurement using molecules embedded into a solid. This is a largely unexplored area of research, and we had to start much of the work from scratch both experimentally and theoretically. It has taken some years to now get to a point where we are getting results on both fronts. The current grant has been instrumental in this progress.

Resulting publications reasonably expected in the next couple of years

Four papers are in preparation at the moment and should be submitted within the next six months:

  1. A paper detailing our laser deflection schemes. From extensive density-matrix modeling, we have come up with two schemes (one based on laser pulses and one inspired by the Metcalf and Eyler work on bichromatic forces) that allow for very large forces and therefore large deflections of BaF molecules.

  2. A paper detailing our electrostatic mirror for molecules. We have developed a method that gives specular reflection of molecules (to within microradians). The apparatus needed to demonstrate the method is almost complete.

  3. A paper detailing the calculated positions and fundamental vibrational modes for the BaF:Ar system. This work will allow us to understand the local environment for the ground state of BaF in an Ar solid.

  4. A paper describing our experimental results for laser-induced fluorescence for BaF in an Ar solid.

Within the next two years, we will:

  1. Expand the work of arXiv:2211.14804 (2022) to BaF-Ne and BaF-He interactions. The first will allow for an understanding of the results of the EDMcubed work at the University of Toronto (SJ Li, R Anderson and AC Vutha BaF molecules trapped in neon ice arXiv:2207.07279 (2022)), and the latter will allow for a better understanding of our buffergas- cooled source.

  2. Expand the work of (3) above to neon.

  3. Expand the work of arXiv:2211.14804 (2022) to excited states.

  4. A paper on measuring the purity of solids using x-ray-induced fluorescence.

  5. A paper of the purity of BaF obtained using deflection of our BaF molecules.

  6. Papers on each step of a future eEDM measurement, as they are demonstrated in the doped solid.

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