Fundamental Symmetries with Polyatomic Molecules

We use polyatomic molecules to realize quantum control via laser cooling and trapping while maintaining large polarizability and properties favorable for precision measurements of fundamental symmetries.

Precision sensing of fundamental particle and nuclear physics

Sensing fundamental physics with molecules typically involve measuring phases that accumulate as the molecule coherently precession in some superposition state.  This means that the sensitivity of these experiments is linear in the time that the molecules spends precessing, which is called the precession time or coherence time.  It turns out that the longest precession that that you can reasonably achieve with a molecular beam, even a cryogenic beam like a CBGB, is a few milliseconds.  In the ultracold world, coherence times of seconds can be realized with cold and controlled quantum samples.  Ultracold molecules therefore have the potential to increase sensitivity to new physics by many orders of magnitude, into the PeV regime.  This will require methods to realize extreme quantum coherence in molecules, which the atomic physics community has been using successfully for decades.  Adapting their methods to molecules is therefore a key ingredient for these experiments.

Click here to read a review about the quantum sensing applications of polyatomic molecules.

Laser-Cooling Molecules

Laser cooling works by using repeatedly scattering photons to apply forces on atoms or molecules.  Since photons have momentum, if an atom or molecule absorbs and then re-emits a photon, it will receive a momentum kick - in other words, it experiences a force.  However, the momentum kick is very tiny, so typically hundreds of thousands of photon scatters are needed to reduce the velocity of a typical gas-phase atom to the ultracold regime.  If you want to learn more about laser cooling, consider taking Physics 137A!

The problem with molecules is that they have internal vibrational modes that can be excited when a molecule receives a momentum kick.  Because laser cooling schemes generally address only a single quantum state per laser, exciting these internal modes is effectively loss of molecules.  This is a serious problem since a "typical" molecule can only scatter "a few" photons before the molecule is effectively gone. 

There are a number of clever tricks that enable laser cooling for certain molecules.  A critical ingredient is using a molecule with electronic structure that is largely decoupled from the vibrational modes of the molecule.  This can be achieved, for example, by using an alkaline earth atom with a single ionic bond to an electronegative bonding partner, such as F or OH.  Alkaline earth atoms have an s2 valence configuration, so when they bond monovalently, one electron in an s orbital remains localized on the metal.  This electron looks very much like it is bound to a single atom, and can therefore be excited via strong optical transitions.  Furthermore, the bonding induces some orbital hybridization with excited p states that actually push the electron cloud away from the bonding region, which decouples the optical excitation from the mechanical modes of the molecule.

Figure: Electronic structure of molecules with a single alkaline earth atom with an ionic, monovalent chemical bond.  Orbital hybridization induced by the bond push the electron cloud away from the bonding region, which decouples the electronic and mechanical degrees of freedom in both the ground (X) and excited (A) states.

Polyatomic Molecules

Laser cooling and high polarizability conflict in diatomics because both features have to come from very specific electronic structure on the heavy atom, and these requirements are at odds.  On the other hand, polyatomic molecules, with at least three atoms, offer laser cooling and high polarizability.  Like in diatomics, a heavy metal atom with suitable electronic structure and bonding can provide photon cycling and laser cooling; unlike diatomics, internal co-magnetometers can arise from degenerate vibrational or rotational motions that exist only in molecules with at least three atoms.

Figure: degenerate bending modes in a linear triatomic molecule give rise to states with vibrational angular momentum that can be easily polarized in electric fields.  Here the orange atom is a heavy metal center with new physics sensitivity and favorable laser-cooling properties, such as Sr, Yb, or Ra.

These degenerate mechanical modes give to "parity doublets" which enable high polarizability in small fields, as well as tricks to engineer systematic robustness via tuning of electromagnetic moments and access to internal co-magnetometer states.  These features are therefore a generic feature of linear and symmetric top polyatomic molecules that do not depend on the electronic properties of their constituent atoms.  

Figure: Electric field shifts of the bending mode in the YbOH molecule, from one of our papers.  This plot shows that we can reach the linear, polarized Stark regime in ~100 V/cm, compared to ~10,000 V/cm for laser-coolable diatomics.  This simplifies experimental requirements, and gives access to two states where the molecule is aligned or anti-aligned with the lab field, offering a powerful opportunity for systematics rejection via internal co-magnetometers.  Furthremore, these states have tunable electromagnetic moments which can suppress decoherence.

Similarly, the laser cooling properties only depend on the electronic properties, and in general not the bonding partners (for suitably chosen ligands.)  We can therefore construct molecules with laser-coolable metal centers, such as MOH or MOCH3, where M = Sr, Yb, or Ra for example, that can be laser-cooled, have co-magnetometers, and are sensitive to a wide range of new symmetry violating physics, such as nuclear magnetic quadrupole moments and permanent EDMs.

Figure: The metal center (orange) can cycle photons without exciting internal modes, independent of the bonding partners, under a wide range of conditions.  Here we show a symmetric top molecule, where the polarizable states arise from low energy rotation of the molecule about the symmetry axis.

Want to know more?

Please be in touch if you have any questions!  Here is some suggested reading for more information as well.

Our original proposal:

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

A review of quantum sensing with polyatomic molecules:

• Polyatomic Molecules as Quantum Sensors for Fundamental Physics
  Nicholas R. Hutzler
  Quantum Science and Technology 5, 044011 (2020)

Some great reviews of laser cooling (not written by us):

• Direct Laser Cooling of Polyatomic Molecules
  Benjamin L. Augenbraun, Loic Anderegg, Christian Hallas, Zack D. Lasner, Nathaniel B. Vilas, John M. Doyle
  arXiv:2302.10161

• Laser cooled molecules
  N. J. Fitch, M. R. Tarbutt
  Adv. At. Mol. Opt. Phys. 70, 157-262 (2021)