Caltech scientists have found a fast and efficient way to add up large numbers of Feynman diagrams, the simple drawings physicists use to represent particle interactions. The new method has already enabled the researchers to solve a longstanding problem in the materials science and physics worlds known as the polaron problem, giving scientists and engineers a way to predict how electrons will flow in certain materials, both conventional and quantum.
Feynman diagrams
In the 1940s, physicist Richard Feynman first proposed a way to represent the various interactions that take place between electrons, photons, and other fundamental particles using 2D drawings that involve straight and wavy lines intersecting at vertices. Though they look simple, these Feynman diagrams allow scientists to calculate the probability that a particular collision, or scattering, will take place between particles.
Since particles can interact in many ways, many different diagrams are needed to depict every possible interaction. And each diagram represents a mathematical expression. Therefore, by summing all the possible diagrams, scientists can arrive at quantitative values related to particular interactions and scattering probabilities.
«Summing all Feynman diagrams with quantitative accuracy is a holy grail in theoretical physics», says Marco Bernardi, professor of applied physics, physics, and materials science at Caltech. «We have attacked the polaron problem by adding up all the diagrams for the so-called electron-phonon interaction, essentially up to an infinite order».
The polaron problem
In a paper published in Nature Physics, the Caltech team uses its new method to precisely compute the strength of electron-phonon interactions and to predict associated effects quantitatively. The lead author of the paper is graduate student Yao Luo, a member of Bernardi’s group.
For some materials, such as simple metals, the electrons moving inside the crystal structure will interact only weakly with its atomic vibrations. For such materials, scientists can use a method called perturbation theory to describe the interactions that occur between electrons and phonons, which can be thought of as «units» of atomic vibration.
Perturbation theory is a good approximation in these systems because each successive order or interaction becomes decreasingly important. That means that computing only one or a few Feynman diagrams—a calculation that can be done routinely—is sufficient to obtain accurate electron-phonon interactions in these materials.
But for many other materials, electrons interact much more strongly with the atomic lattice, forming entangled electron-phonon states known as polarons. Polarons are electrons accompanied by the lattice distortion they induce. They form in a wide range of materials including insulators, semiconductors, materials used in electronics or energy devices, as well as many quantum materials.
For example, an electron placed in a material with ionic bonds will distort the surrounding lattice and form a localized polaron state, resulting in decreased mobility due to the strong electron-phonon interaction. Scientists can study these polaron states by measuring how conductive the electrons are or how they distort the atomic lattice around them.
Perturbation theory does not work for these materials because each successive order is more important than the last. «It’s basically a nightmare in terms of scaling», says Bernardi. «If you can calculate the lowest order, it’s very likely that you cannot do the second order, and the third order will just be impossible».
Diagrammatic Monte Carlo (DMC)
Scientists have searched for a way to add up all the Feynman diagrams that describe the many, many ways that the electrons in such a material can interact with atomic vibrations. Thus far such calculations have been dominated by methods where scientists can tune certain parameters to match an experiment.
«But when you do that, you don’t know whether you’ve actually understood the mechanism or not», says Bernardi. Instead, his group focuses on solving problems from «first principles», meaning beginning with nothing more than the positions of atoms within a material and using the equations of quantum mechanics.
Caltech researchers are addressing this problem by applying a technique called diagrammatic Monte Carlo (DMC), in which an algorithm randomly samples spots within the space of all Feynman diagrams for a system, but with some guidance in terms of the most important places to sample.
«We set up some rules to move effectively, with high agility, within the space of Feynman diagrams», explains Bernardi. The Caltech team overcame the enormous amount of computing that would have normally been required to use DMC to study real materials with first principle methods by relying on a technique they reported last year that compresses the matrices that represent electron-phonon interactions.
Another major advance is nearly removing the so-called «sign problem» in electron-phonon DMC using a clever technique that views diagrams as products of tensors, mathematical objects expressed as multi-dimensional matrices.
«The clever diagram sampling, sign-problem removal, and electron-phonon matrix compression are the three key pieces of the puzzle that have enabled this paradigm shift in the polaron problem», says Bernardi.
In the new paper, the researchers have applied DMC calculations in diverse systems that contain polarons, including lithium fluoride, titanium dioxide, and strontium titanate. The scientists say their work opens up a wide range of predictions that are relevant to experiments that people are conducting on both conventional and quantum materials—including electrical transport, spectroscopy, superconductivity, and other properties in materials that have strong electron-phonon coupling.
«We have successfully described polarons in materials using DMC, but the method we developed could also help study strong interactions between light and matter, or even provide the blueprint to efficiently add up Feynman diagrams in entirely different physical theories», says Bernardi.
Protecting quantum spins from noise with a laser beam
Researchers have discovered a simple yet powerful way to protect atoms from losing information—a key challenge in developing reliable quantum technologies.
By shining a single, carefully tuned laser beam on a gas of atoms, they managed to keep the atoms’ internal spins synchronized, dramatically reducing the rate at which information is lost. In quantum sensors and memory systems, atoms often lose their magnetic orientation—or «spin»—when they collide with each other or the walls of their container.
This phenomenon, known as spin relaxation, severely limits the performance and stability of such devices. Traditional methods to counteract it have required operating in extremely low magnetic fields and using bulky magnetic shielding.
The new method sidesteps those constraints entirely. Instead of magnetically shielding the system, it uses light to subtly shift atomic energy levels, aligning the spins of the atoms and keeping them in sync, even as they move and collide. This creates a more resilient spin state that is naturally protected from decoherence.
In lab experiments with warm cesium vapor, the technique reduced spin decay by a factor of 10 and significantly improved magnetic sensitivity. This breakthrough demonstrates that a single beam of light can extend the coherence time of atomic spins, opening the door to more compact, accurate, and robust quantum sensors, magnetometers, and memory devices.
A team of physicists from the Hebrew University’s Department of Applied Physics and Center for Nanoscience and Nanotechnology, in collaboration with the School of Applied and Engineering Physics at Cornell University, has unveiled a powerful new method to shield atomic spins from environmental «noise»—a major step toward improving the precision and durability of technologies like quantum sensors and navigation systems.
The study, «Optical Protection of Alkali-Metal Atoms from Spin Relaxation», by Avraham Berrebi, Mark Dikopoltsev, Prof. Ori Katz (Hebrew University), and Prof. Or Katz (Cornell University), has been published in Physical Review Letters and can potentially revolutionize fields that depend on magnetic sensing and atomic coherence.