Sneaky clocks: uncovering Einstein’s relativity in an interacting atomic playground

For over a century, physicists have grappled with one of the most profound questions in science: How do the rules of quantum mechanics, which govern the smallest particles, fit with the laws of general relativity, which describe the universe on the largest scales? 

The optical lattice clock, one of the most precise timekeeping devices, is becoming a powerful tool used to tackle this great challenge. Within an optical lattice clock, atoms are trapped in a “lattice” potential formed by laser beams and are manipulated with precise control of quantum coherence and interactions governed by quantum mechanics. Simultaneously, according to Einstein’s laws of general relativity, time moves slower in stronger gravitational fields. This effect, known as gravitational redshift, leads to a tiny shift of atoms’ internal energy levels depending on their position in gravitational fields, causing their “ticking”—the oscillations that define time in optical lattice clocks—to change. 

By measuring the tiny shifts of oscillation frequency in these ultra precise clocks, researchers are able to explore the influences of Einstein’s theory of relativity on quantum systems. While relativistic effects are well-understood for individual atoms, their role in many-body quantum systems, where atoms can interact and become entangled, remains largely unexplored.

Making a step forward in this direction, researchers led by JILA and NIST Fellows and University of Colorado Boulder physics professors Jun Ye and Ana Maria Rey—in collaboration with scientists at the Leibnitz University in Hanover, the Austrian Academy of Sciences, and the University of Innsbruck—proposed practical protocols to explore the effects of relativity, such as the gravitational redshift, on quantum entanglement and interactions in an optical atomic clock. Their work revealed that the interplay between gravitational effects and quantum interactions can lead to unexpected phenomena, such as atomic synchronization and quantum entanglement among particles. The results of this study were published in Physical Review Letters.

“One of our key findings is that interactions between atoms can help to lock them together so that now they behave as a unified system instead of ticking independently due to the gravitational redshift,” explains Dr. Anjun Chu, a former JILA graduate student, now a postdoctoral researcher at the University of Chicago and the paper’s first author. “This is really cool because it directly shows the interplay between quantum interactions and gravitational effects.”

“The interplay between general relativity [GR] and quantum entanglement has puzzled physicists for years,” Rey adds. “The challenge lies in the fact that GR corrections in most tabletop experiments are minuscule, making them extremely difficult to detect. However, atomic clocks are now reaching unprecedented precision, bringing these elusive effects within measurable range. Since these clocks simultaneously interrogate many atoms, they provide a unique platform to explore the intersection of GR and many-body quantum physics. In this work, we investigated a system where atoms interact by exchanging photons within an optical cavity. Interestingly, we found out that while individual interactions alone can have no direct effect on the ticking of the clock, their collective influence on the redshift can significantly modify the dynamics and even generate entanglement among the atoms which is very exciting.” 

Distinguishing Gravitational Effects

To explore this challenge, the team devised innovative protocols to observe how gravitational redshift interferes with quantum behavior. The first issue they focused on was to uniquely distinguish gravitational effects in an optical lattice clock from other noise sources contributing to the tiny frequency shifts. They utilized a technique called a dressing protocol, which involves manipulating the internal states of particles with laser light. While dressing protocols are a standard tool in quantum optics, this is one of the first instances of the protocol being used to fine-tune gravitational effects. 

The tunability is based on the mechanism known as mass-energy equivalence (from Einstein's famous equation E=mc²), which means that changes in a particle’s internal energy can subtly alter its mass. Based on this mechanism, an atom in the excited state has a slightly larger mass compared to the same atom in the ground state. The mass difference in gravitational potential energy is equivalent to gravitational redshift. The dressing protocol provides a flexible way to tune the mass difference, and thus the gravitational redshift, by controlling the particles to stay in a superposition of the two internal energy states. Instead of being strictly in the ground or excited state, the particles can be tuned to occupy both of the states simultaneously with a continuous change of occupation probability between these two levels. This technique provides unprecedented control of internal states, enabling the researchers to fine-tune the size of gravitational effects. 

In this way, the researchers could distinguish genuine gravitational redshift effects from other influences, like magnetic field gradients, within the system.

“By changing the superpositions of internal levels of the particles you're addressing, you can change how large the gravitational effects appear,” notes JILA graduate student Maya Miklos. “This is a really clever way to probe mass-energy equivalence at the quantum level.”

Seeing Synchronization and Entanglement

After providing a recipe to distinguish genuine gravitational effects, the researchers explored gravitational manifestations in quantum many-body dynamics. They made use of the photon-mediated interactions generated by placing the atoms in an optical cavity. 

If one atom is in an excited state, it can relax back to the ground state by emitting a photon into the cavity. This photon doesn’t necessarily escape the system but can be absorbed by another atom in the ground state, exciting it in turn. Such an exchange of energy—known as photon-mediated interactions—is key to making particles interact, even when they cannot physically touch each other. 

Such types of quantum interactions can compete with gravitational effects on individual atoms inside the cavity. Typically, particles positioned at different “heights” within a gravitational field experience slight differences in how they “tick” due to gravitational redshift. Without interactions between particles, the slight difference in oscillation frequencies will cause them to fall out of sync over time. 

However, when photon-mediated interactions were introduced, something remarkable happened: the particles began to synchronize, effectively “locking” their ticking together despite the differences in oscillation frequencies induced by gravity. 

“It’s fascinating,” Chu says. “You can think of each particle as its own little clock. But when they interact, they start to tick in unison, even though gravity is trying to pull their timing apart.” 

This synchronization showcased a fascinating interplay between gravitational effects and quantum interactions, where the latter can override the natural desynchronization caused by gravitational redshift.

This synchronization wasn’t just an oddity—it also led to the creation of quantum entanglement, a phenomenon where particles become interconnected, with the state of one instantly affecting the other. Remarkably, the researchers found that the speed of synchronization could also serve as an indirect measure of entanglement, offering an insight into quantifying the interplay between two effects. “Synchronization is the first phenomenon we can see that reveals this competition between gravitational redshift and quantum interactions,” adds JILA postdoctoral researcher Dr. Kyungtae Kim. “It’s a window into how these two forces balance each other.”

Advancing Physics Research

While this study revealed the initial interactions between these two fields of physics, the protocols developed could help refine experimental techniques, making them even more precise—with applications ranging from quantum computing to fundamental physics experiments. 

“Detecting this GR-facilitated entanglement would be a groundbreaking achievement, and our theoretical calculations suggest that it is within reach of current or near-term experiments,” says Rey. 

Future experiments could explore how particles behave under different conditions or how interactions can amplify gravitational effects, bringing us closer to unifying the two great pillars of modern physics.

This research was supported by the Sloan Foundation, the Simons Foundation and the Heising-Simons Foundation along with the JILA PFC. 

---

---