Researchers have been able to “look” inside atomic nuclei thanks to a new type of quantum entanglement.

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Physicists at the Brookhaven National Laboratory report that they have been able to very accurately map the location of elementary particles found in the core of atomic nuclei. Their work is based on a new way to use the Relativistic Heavy Ion Collider (RHIC) and a new kind of quantum entanglement never seen before.

The atomic nucleus consists of protons and neutrons, which themselves consist of elementary particles, quarks, interconnected by gluons. Through a series of quantum fluctuations, photons interact with gluons, creating an intermediate particle (“rho”), which immediately decays into two charged “pions” (or pi-mesons), denoted π+ and π-. The speed and angles at which these π+ and π particles collide with the STAR detector at the RHIC provide information that allows very accurate mapping of the location of gluons in the nucleus.

“This method is similar to how doctors use positron emission tomography (PET) to see what is happening inside the brain and other parts of the body,” says James Daniel Brandenburg, a member of the STAR-collaboration. The difference is that here we are talking about displaying characteristics on a femtometer scale (i.e. 10-15 meters)! The researchers not only gained a unique insight into the interior of atoms, but also witnessed a whole new kind of entanglement between π+ and π particles.


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Two-dimensional representation of the distribution of gluons

The RHIC (Relativistic Heavy Ion Collider) is a particle accelerator designed to study collisions between heavy ions (copper, gold, uranium, etc.) at relativistic speeds. Basically, it was designed to study the primordial form of matter (the one that existed at the very beginning of the universe), but it can also produce collisions between protons to study their structure. Several different detectors, including STAR, allow you to record the results of collisions.

To study elementary particles, scientists collide with the nuclei of heavy atoms moving in opposite directions around the collider at a speed close to the speed of light. The intensity of collisions is such that it can “melt” the boundaries between individual protons and neutrons, exposing their elementary components: quarks and gluons.

But nuclear physicists also want to know how quarks and gluons behave and organize themselves inside atomic nuclei to form protons and neutrons.

But recent work by the STAR Collaboration on polarized photon collisions has suggested a way to use these light particles to understand the interior of nuclei. “We have demonstrated that these photons are polarized and their electric field radiates outward from the center of the ion. And now we are using this tool, polarized light, to efficiently image high-energy nuclei,” says Zhangbu Xu, a physicist at the Brookhaven Laboratory and a member of the STAR collaboration.

Until now, scientists have not had the opportunity to know the direction of polarization of photons. Therefore, the measured gluon density was an average calculated as a function of the distance from the center of the nucleus. But the quantum interference observed between π+ and π- particles makes it possible to measure the direction of polarization very accurately. This allows physicists to explore the distribution of gluons in two dimensions: along the direction of the photon, but also perpendicular to it.

The first entanglement between dissimilar particles

While old measurements gave the impression that the nucleus was too large compared to what theoretical models and measurements of the charge distribution in the nucleus predicted, this new 2D image helped shed light on this mystery. It turns out that the momentum and energy of the photons themselves merge with the momentum and energy of the gluons. Thus, a one-dimensional measurement necessarily gave a result distorted by the influence of photons.

Specifically, the sum of the momenta of two pions gives the momentum of their parent rho particle and other information, which includes the distribution of gluons and the effect of photon blocking. To determine the distribution of gluons, scientists measure the angle between the π+ or π- trajectory and the rho particle’s trajectory. The closer this angle is to 90°, the less the photon effect is applied. By tracking pions from rho particles moving at different angles and with different energies, the scientists were able to map the distribution of gluons throughout the nucleus.

The closer the angle (Φ) between the π trajectory (pink and blue) and the rho particle trajectory (purple) to 90°, the clearer the scientists’ “vision” of the distribution of gluons. As each rho decays, the pion wave functions (+ and -) of each decay interfere and reinforce each other. © Brookhaven National Laboratory

“Now we can make an image where we can actually discern the gluon density at a given angle and radius. The images are so clear that we can even start to see the difference between where the protons are and where the neutrons are inside these big nuclei,” says Brandenburg. And, of course, these images are more consistent with theoretical predictions.

But this is only possible due to the fact that π+ and π- particles, although they have different charges, are entangled. “This is the very first experimental observation of entanglement between dissimilar particles,” the physicist emphasizes.

When two ions collide with each other without colliding, the photons that surround them interact with the gluons: then it is as if these interactions produce two rho particles (one in each nucleus). As each rho particle decays into π+ and π-, the wavefunction of the negative pion of one interferes with the wavefunction of the negative pion of the other. When the resulting boosted wavefunction reaches the STAR detector, it sees π-. The same thing happens with the wave functions of the two π+.

“Interference occurs between two wave functions of identical particles, but without entanglement between two dissimilar particles – π+ and π- – this interference does not materialize,” explains Wangmei Zha, STAR fellow at the University of Science and Technology. China. If the two particles were not entangled, the two wave functions would have a random phase and would not interfere; therefore, the researchers could not determine the direction of polarization of the photons and therefore could not make measurements.

The following experiments, carried out at the RHIC, as well as at the electron-ion collider currently under construction, will make it possible to study the distribution of gluons inside atomic nuclei in more detail and test other possible quantum interference scenarios.

STAR Collaboration, Science Advances.

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