Nuclear Physicists Can "See" Inside Atomic Nuclei Thanks to a New Type of Entanglement

First-ever observation of quantum interference between dissimilar particles offers new approach for mapping distribution of gluons in atomic nuclei—and potentially more.

Nuclear physicists have found a new way to use the Relativistic Heavy Ion Collider (RHIC)—a particle collider at the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory—to see the shape and details inside atomic nuclei. A novel type of quantum entanglement that has never been seen before and light particles that surround gold ions as they speed around the collider are the components of the method.

The light particles, or photons, interact with gluons—glue-like particles that hold quarks together inside protons and neutrons of nuclei—through a series of quantum fluctuations. These interactions lead to the production of an intermediate particle, which swiftly decays into two "pions" with various charges (p). The scientists can track back to gain key information about the photon and use that to map out the arrangement of gluons within the nucleus with more accuracy than ever before by measuring the velocity and angles at which these p+ and p- particles strike RHIC's STAR detector.

According to former Brookhaven Lab physicist James Daniel Brandenburg, a member of the STAR collaboration who joined The Ohio State University as an assistant professor in January 2023, "this method is similar to the way doctors use positron emission tomography (PET scans) to see what's happening inside the brain and other body parts." However, in this instance, we're discussing mapping out features on the scale of femtometers, or quadrillionths of a metre, or the size of a single proton.

The discovery of an entirely new type of quantum interference that enables their observations, according to the STAR physicists, is even more astounding.

According to Brookhaven physicist and STAR collaborator Zhangbu Xu, "we measure two outgoing particles and clearly their charges are different—they are different particles—but we see interference patterns that indicate these particles are entangled, or in sync with one another, even though they are distinguishable particles."

That discovery may have applications well beyond the lofty goal of mapping out the building blocks of matter.

For instance, entanglement—a sort of "awareness" and interaction of physically separated particles—is being explored by numerous scientists, including those who will share the 2022 Nobel Prize in Physics. One objective is to build computers and communication devices that are much more powerful than what we have now. However, the majority of entanglement observations to far have used photons or identical electrons, including a recent showing of interference of lasers with different wavelengths.

According to Brandenburg, "This is the first experimental observation of entanglement between different particles."

Shining a light on gluons

RHIC is a DOE Office of Science user resource that allows physicists to examine the quarks and gluons that make up protons and neutrons, the most fundamental components of nuclear matter. They achieve this by colliding heavy atomic nuclei, such as those of gold, that are moving around the collider at nearly the speed of light. Scientists can investigate the quarks and gluons as they existed in the very early universe—before protons and neutrons formed—by studying the intensity of these collisions between nuclei (also known as ions), which can "melt" the boundaries between individual protons and neutrons.

But nuclear physicists also want to know how quarks and gluons behave within atomic nuclei as they exist today—to better understand the force that holds these building blocks together.

There may be a method to leverage the "clouds" of photons that surround the moving ions in RHIC to get a view into the nucleus, according to a recent finding. The photons surrounding one gold ion can look inside the other ion if two gold ions pass one another very closely without interacting.

In that earlier research, we established that the photons in question are polarised, with the electric field emanating from the ion's nucleus outward. And right now, we employ that tool—polarized light—to successfully examine the high-energy nuclei.

The quantum interference observed between the p⁺ and p^– in the newly analyzed data makes it possible to measure the photons’ polarization direction very precisely. That in turn lets physicists look at the gluon distribution both along the direction of the photon’s motion and perpendicular to it.

That two-dimensional imaging turns out to be very important.

“All past measurements, where we didn’t know the polarization direction, measured the density of gluons as an average—as a function of the distance from the center of the nucleus,” Brandenburg said. “That’s a one-dimensional image.”

Those measurements all came out making the nucleus look too big when compared with what was predicted by theoretical models and measurements of the distribution of charge in the nucleus.

"We were able to resolve the 20-year enigma of why this occurs with this 2D imaging technology," Brandenburg added.

According to the new findings, the momentum and energy of the photons themselves are mixed up with the gluons'. These photon impacts cause a picture to be warped when measuring only along the photon's direction (or when measuring without knowing what that direction is). However, measuring transversely prevents photon blurring.

The density of gluons at a specific angle and radius may now be clearly seen in a photograph, according to Brandenburg. The photos are so clear that we can even begin to distinguish between the locations of protons and neutrons inside these massive nuclei.

The new pictures match up qualitatively with the theoretical predictions using gluon distribution, as well as the measurements of electric charge distribution within the nuclei, the scientists say.

Details of the measurements

To understand how the physicists make these 2D measurements, let’s step back to the particle generated by the photon-gluon interaction. It’s called a rho, and it decays very quickly—in less than four septillionths of a second—into the p⁺ and p^–. The sum of the momenta of those two pions gives physicists the momentum of the parent rho particle—and information that includes the gluon distribution and the photon blurring effect.

To extract just the gluon distribution, the scientists measure the angle between the path of either the p⁺ or p^– and the rho’s trajectory. The closer that angle is to 90 degrees, the less blurring you get from the photon probe. By tracking pions that come from rho particles moving at a range of angles and energies, the scientists can map out the gluon distribution across the entire nucleus.

Now for the quantum quirkiness that makes the measurements possible—the evidence that the p⁺ and p^– particles striking the STAR detector result from interference patterns produced by the entanglement of these two dissimilar oppositely charged particles.

Remember that all of the particles we are discussing exist both as waves and as physical objects. The mathematical "wavefunctions" that define the crests and troughs of particle waves can interfere to strengthen or cancel one another, like ripples on the surface of a pond radiating outward when they strike a rock.

It appears as though two rho particles, one in each nucleus, are produced when photons surrounding two near-miss speeding ions contact with gluons inside the nuclei. The wavefunction of the negative pion from one rho decay interferes with the wavefunction of the negative pion from the other as each rho decays into a p+ and p-. The STAR detector detects one p- when the reinforced wavefunction hits it. The detector detects one p+ when the wavefunctions of the two positively charged pions behave similarly.

One of the original proponents of this explanation, Wangmei Zha, a STAR collaborator at the University of Science and Technology of China, stated that the interference is between two wavefunctions of the same particles, but that it would not exist without the entanglement between the two dissimilar particles, the p+ and p-. This is how quantum mechanics is strange.

The rhos might just be twisted. The experts disagree. It is impossible for the rho particle wavefunctions to interact before they degrade to p+ and p- since their origin is 20 times farther away than the maximum distance they can travel in their brief lifetime. However, despite reaching the detector metres apart, the p+ and p- wavefunctions from each rho decay maintain the quantum information of their parent particles; their crests and troughs are in phase, indicating that they are "knowing of one other."

The two p+ (or p-) wavefunctions would have a random phase if the p+ and p- were not entangled, without any discernible interference impact, according to Chi Yang, a STAR colleague from Shandong University in China who also oversaw the work that led to this finding. We wouldn't be able to perform these precise measurements or discern any orientation connected to photon polarization.

Future measurements at RHIC with heavier particles and different lifetimes—and at an Electron-Ion Collider (EIC) being built at Brookhaven—will probe more detailed distributions of gluons inside nuclei and test other possible quantum interference scenarios.