# One Lab’s Quest to Build Space-Time Out of Quantum Particles

## Introduction

The prospects for directly testing a theory of quantum gravity are poor, to put it mildly. To probe the ultra-tiny Planck scale, where quantum gravitational effects appear, you would need a particle accelerator as big as the Milky Way galaxy. Likewise, black holes hold singularities that are governed by quantum gravity, but no black holes are particularly close by — and even if they were, we could never hope to see what’s inside. Quantum gravity was also at work in the first moments of the Big Bang, but direct signals from that era are long gone, leaving us to decipher subtle clues that first appeared hundreds of thousands of years later.

But in a small lab just outside Palo Alto, the Stanford University professor Monika Schleier-Smith and her team are trying a different way to test quantum gravity, without black holes or galaxy-size particle accelerators. Physicists have been suggesting for over a decade that gravity — and even space-time itself — may emerge from a strange quantum connection called entanglement. Schleier-Smith and her collaborators are reverse-engineering the process. By engineering highly entangled quantum systems in a tabletop experiment, Schleier-Smith hopes to produce something that looks and acts like the warped space-time predicted by Albert Einstein’s theory of general relativity.

In a paper posted in June, her team announced their first experimental step along this route: a system of atoms trapped by light, with connections made to order, finely controlled with magnetic fields. When tuned in the right way, the long-distance correlations in this system describe a treelike geometry, similar to ones seen in simple models of emergent space-time. Schleier-Smith and her colleagues hope to build on this work to create analogues to more complex geometries, including those of black holes. In the absence of new data from particle physics or cosmology — a state of affairs that could continue indefinitely — this could be the most promising route for putting the latest ideas about quantum gravity to the test.

## The Perils of Perfect Predictions

For five decades, the prevailing theory of particle physics, the Standard Model, has met with almost nothing but success — to the endless frustration of particle physicists. The problem lies in the fact that the Standard Model, despite its success, is clearly incomplete. It doesn’t include gravity, despite the long search for a theory of quantum gravity to replace general relativity. Nor can it explain dark matter or dark energy, which account for 95% of all the stuff in the universe. (The Standard Model also has trouble with the fact that neutrinos have mass — the sole particle physics phenomenon it has failed to predict.)

Moreover, the Standard Model itself dictates that beyond a certain threshold of high energy — one closely related to the Planck scale — it almost certainly fails.

## Introduction

Physicists are desperate for puzzling experimental data that might help to guide them as they build the Standard Model’s replacement. String theory, still the leading candidate to replace the Standard Model, has often been accused of being untestable. But one of the strangest features of string theory suggests a way to test some ideas about quantum gravity that don’t require impractical feats of galactic architecture.

String theory is filled with dualities — relations between different physical systems that share the same mathematical structure. Perhaps the most surprising and consequential of these dualities is a connection between a type of quantum theory in four dimensions without gravity, known as a conformal field theory (CFT), and a particular kind of five-dimensional space-time with gravity, known as an anti-de Sitter (AdS) space. This AdS/CFT correspondence, as it’s known, was first discovered in 1997 by the physicist Juan Maldacena, now at the Institute for Advanced Study.

Because the CFT has one fewer dimension than the AdS space, the former can be thought of as lying on the surface of the latter, like the two-dimensional skin of a three-dimensional apple. Yet the quantum theory on the surface still fully captures all the features of the volume inside — as if you could tell everything about the interior of an apple just by looking at its skin. This is an example of what physicists call holography: a lower-dimensional space giving rise to a higher-dimensional space, like a flat hologram producing a 3D image.

In the AdS/CFT correspondence, the interior or “bulk” space emerges from relationships between the quantum components on the surface. Specifically, the geometry of the bulk space is built from entanglement, the “spooky” quantum connections that infamously troubled Einstein. Neighboring regions of the bulk correspond to highly entangled portions of the surface. Distant regions of the bulk correspond to less entangled parts of the surface. If the surface has a simple and orderly set of entanglement relations, the corresponding bulk space will be empty. If the surface is chaotic, with all its parts entangled with all the others, the bulk will form a black hole.

The AdS/CFT correspondence is a deep and fruitful insight into the connections between quantum physics and general relativity. But it doesn’t actually describe the world we live in. Our universe isn’t a five-dimensional anti-de Sitter space — it’s an expanding four-dimensional space with a “flat” geometry.

## Introduction

So over the past few years, researchers have proposed another approach. Rather than starting from the bulk — our own universe — and looking for the kind of quantum entanglement pattern that could produce it, we can go the other way. Perhaps experimenters could build systems with interesting entanglements — like the CFT on the surface — and search for any analogues to space-time geometry and gravity that emerge.

That’s easier said than done. It’s not yet possible to build a system like any of the strongly interacting quantum systems known to have gravitational duals. But theorists have only mapped out a small fraction of possible systems — many others are too complex to study theoretically with existing mathematical tools. To see if any of those systems actually yield some kind of space-time geometry, the only option is to physically construct them in the lab and see if they also have a gravitational dual. “These experimental constructions might help us discover such systems,” said Maldacena. “There might be simpler systems than the ones we know about.” So quantum gravity theorists have turned to experts in building and controlling entanglement in quantum systems, like Schleier-Smith and her team.

## Quantum Gravity Meets Cold Atoms

“There’s something really just elegant about the theory of quantum mechanics that I’ve always loved,” said Schleier-Smith. “If you go into the lab, you’ll see there’s cables all over the place and all kinds of electronics we had to build and vacuum systems and messy-looking hardware. But at the end of the day, you can make a system that is clean and controlled in such a way that it does nicely map onto this sort of elegant theory that you can write down on paper.”

This messy elegance has been a hallmark of Schleier-Smith’s work since her graduate days at the Massachusetts Institute of Technology, where she used light to coax collections of atoms into particular entangled states and demonstrated how to use these quantum systems to build more precise atomic clocks. After MIT, she spent a few years at the Max Planck Institute of Quantum Optics in Garching, Germany, before landing at Stanford in 2013. A couple of years later, Brian Swingle, a theoretical physicist then at Stanford working on string theory, quantum gravity and other related subjects, reached out to her with an unusual question. “I wrote her an email saying, basically, ‘Can you reverse time in your lab?’” said Swingle. “And she said yes. And so we started talking.”

Swingle wanted to reverse time in order to study black holes and a quantum phenomenon known as scrambling. In quantum scrambling, information about a quantum system’s state is rapidly dispersed across a larger system, making it very hard to recover the original information. “Black holes are very good scramblers of information,” said Swingle. “They hide information very well.” When an object is dropped into a black hole, information about that object is rapidly hidden from the rest of the universe. Understanding how black holes obscure information about the objects that fall into them — and whether that information is merely hidden or actually destroyed — has been a major focus of theoretical physics since the 1970s.

In the AdS/CFT correspondence, a black hole in the bulk corresponds to a dense web of entanglement at the surface that scrambles incoming information very quickly. Swingle wanted to know what a fast-scrambling quantum system would look like in the lab, and he realized that in order to confirm scrambling was taking place as rapidly as possible, researchers would need to tightly control the quantum system in question, with the ability to perfectly reverse all interactions. “The sort of obvious way to do it required the ability to effectively fast forward and rewind the system,” said Swingle. “And that’s not something you can do in an everyday kind of experiment.” But Swingle knew Schleier-Smith’s lab might be able to control the entanglement between atoms carefully enough to perfectly reverse all their interactions, as if time were running backward. “If you have this nice, isolated, well-controlled, highly engineered quantum many-body system, then maybe you have a chance,” he said.

So Swingle reached out to Schleier-Smith and told her what he wanted to do. “He explained to me this conjecture that this process of scrambling — that there’s a fundamental speed limit to how fast that can happen,” said Schleier-Smith. “And that if you could build a quantum system in the lab that scrambles at this fundamental speed limit, then maybe that would be some kind of an analogue of a black hole.” Their conversations continued, and in 2016, Swingle and Schleier-Smith co-authored a paper, along with Patrick Hayden, another theorist at Stanford, and Gregory Bentsen, one of Schleier-Smith’s graduate students at the time, outlining a feasible method for creating and probing fast quantum scrambling in the lab.

That work left Schleier-Smith contemplating other quantum gravitational questions that her lab could investigate. “That made me think … maybe these are actually good platforms for being able to realize some toy models of quantum gravity that are hard to realize by other means,” she said. She started to consider a setup where pairs of atoms would be entangled together, and then each pair would itself be entangled with another pair, and so on, forming a kind of tree. “It seemed kind of far-fetched to actually do it, but at least I could sort of imagine on paper how you would design a system where you can do that,” she said. But she wasn’t sure if this actually corresponded to any known model of quantum gravity.

## Introduction

Intense and affable, Schleier-Smith has an infectious enthusiasm for her work, as her student Bentsen discovered. He had started his doctoral work at Stanford in theoretical physics, but Schleier-Smith managed to pull him into her group anyhow. “I sort of convinced him to do experiments,” she recalled, “but he maintained an interest in theory as well, and liked to chat with theorists around the department.” She discussed her new idea with Bentsen, who discussed it with Sean Hartnoll, another theorist at Stanford. Hartnoll in turn played matchmaker, connecting Schleier-Smith and Bentsen with Steven Gubser, a theorist at Princeton University. (Gubser later died in a rock-climbing accident.)

At the time, Gubser was working on a twist on the AdS/CFT correspondence. Rather than using the familiar kind of numbers that physicists generally use, he was using a set of alternative number systems known as the *p*-adic numbers. The key distinction between the *p*-adics and ordinary “real” numbers is the way the size of a number is defined. In the *p*-adics, a number’s size is determined by its prime factors. There’s a *p*-adic number system for each prime number: the 2-adics, the 3-adics, the 5-adics, and so on. In each *p*-adic number system, the more factors of *p* a number has, the smaller that number is. So, for example, in the 2-adics, 44 is much closer to 0 than it is to 45, because 44 has two factors of 2, while 45 doesn’t have any. But in the 3-adics, it’s the reverse; 45 is closer to 0 than to 44, because 45 has two factors of 3. Each *p*-adic number system can also be represented as a kind of tree, with each branch containing numbers that all have the same number of factors of *p*.

Using the *p*-adics, Gubser and others had discovered a remarkable fact about the AdS/CFT correspondence. If you rewrite the surface theory using the *p*-adic numbers rather than the reals, the bulk is replaced with a kind of infinite tree. Specifically, it’s a tree with infinite branches packed into a finite space, resembling the structure of the *p*-adic numbers themselves. The *p*-adics, Gubser wrote, are “naturally holographic.”

“The structure of *p*-adic numbers that [Gubser] told me about reminded me of the way Monika’s atoms interacted with each other,” said Hartnoll, “so I put them in touch.” Gubser co-authored a paper in 2019 with Schleier-Smith, Bentsen and others. In the paper, the team described how to get something resembling the *p*-adic tree to emerge from entangled atoms in an actual lab. With the plan in hand, Schleier-Smith and her team got to work.

## Building Space-Time in the Lab

Schleier-Smith’s lab at Stanford is a dense forest of mirrors, lenses and fiber-optic cables that surround a vacuum chamber at the center of the room. In that vacuum chamber, 18 tiny collections of rubidium atoms — about 10,000 to a group — are arranged in a line and cooled to phenomenally low temperatures, a fraction of a degree above absolute zero. A specially tuned laser and a magnetic field that increases from one end of the chamber to the other allow the experimenters to choose which groups of atoms become correlated with each other.

Using this lab setup, Schleier-Smith and her research group were able to get the two groups of atoms at the ends of the line just as correlated as neighboring groups were in the middle of the line, connecting the ends and turning the line into a circle of correlations. They then coaxed the collection of atoms into a treelike structure. All of this was accomplished without moving the atoms at all — the correlation “geometry” was wholly disconnected from the actual spatial geometry of the atoms.

While the tree structure formed by the interacting atoms in Schleier-Smith’s lab isn’t a full-blown realization of *p*-adic AdS/CFT, it’s “a first step towards holography in the laboratory,” said Hayden. Maldacena, the originator of the AdS/CFT correspondence, agrees: “I’m very excited about this,” he said. “Our subject has been always very theoretical, and so this contact with experiment will probably raise more questions.”

Hayden sees this as the way of the future. “Instead of trying to understand the emergence of space-time in our universe, let’s actually just make toy universes in the lab and study the emergence of space-time there,” he said. “And that sounds like a crazy thing to do, right? Like kind of mad-scientist kind of crazy, right? But I think it really is likely to be easier to do that than to directly test quantum gravity.”

Schleier-Smith is also optimistic about the future. “We’re still at the stage of getting more and more control, characterizing the quantum states that we have. But … I would love to get to that point where we don’t know what will happen,” she said. “And maybe we measure the correlations in the system, and we learn that there’s a geometric description, some holographic description that we didn’t know was there. That would be cool.”