Princeton scientists measure quantum correlations between molecules for the first time

Physicists are increasingly using ultracold molecules to study quantum states of matter. Many researchers contend that molecules have advantages over other alternatives, such as trapped ions, atoms or photons. These advantages suggest that molecular systems will play important roles in emerging quantum technologies. But, for a while now, research into molecular systems has advanced only so far because of long-standing challenges in preparing, controlling and observing molecules in a quantum regime.  

Now, as chronicled in a recent paper in the journal Nature, Princeton researchers have achieved a major breakthrough by microscopically studying molecular gases at a level never before achieved by previous research. The Princeton team, led by Waseem Bakr, associate professor of physics, was able to cool molecules down to ultracold temperatures, load them into an artificial crystal of light known as an optical lattice, and study their collective quantum behavior with high spatial resolution such that each individual molecule could be observed.  

“We prepared the molecules in the gas in a well-defined internal and motional quantum state. The strong interactions between the molecules gave rise to subtle quantum correlations which we were able to detect for the first time,” said Bakr.  

This experiment has profound implications for fundamental physics research, such as the study of many-body physics, which looks at the emergent behavior of ensembles of interacting quantum particles. The research also might accelerate the development of large-scale quantum computer systems. 

In the quest to build large-scale quantum systems, both for quantum computing and for more general scientific applications, researchers have used a variety of different alternatives — everything from trapped ions and atoms to electrons confined in “quantum dots.” The goal is to transform these various alternatives into what are called qubits, which are the building blocks of a quantum computer system. Quantum computers have much greater computing power and capacity — exponentially greater — than classical computer systems, and can solve problems classical computers have difficulty solving.  

Although so far no single type of qubit has emerged as the front runner, Bakr and his team believe that molecular systems, while less explored than other platforms, hold particular promise.

One important advantage of using molecules in experimental settings — and especially as potential qubits — is the fact that molecules can store quantum information in an abundance of new ways not available to single atoms. For example, even for a simple molecule made of just two atoms, which can be visualized as a tiny dumbbell, quantum information can be stored in the rotational motion of the dumbbell or the shaking of its constituent atoms relative to each other. Another advantage of molecules is that they often have long-range interactions; they can interact with other molecules many sites away in an optical lattice, whereas atoms, for example, can only interact if they occupy the same site.

When using molecules to study many-body physics, these advantages are expected to enable researchers to explore fascinating new quantum phases of matter in these synthetic systems. However, a major problem, which Bakr and his team have been able to overcome in this experiment, is the microscopic characterization of these quantum states.

“The ability to probe the gas at the level of individual molecules is the novel aspect of our research,” said Bakr. “When you’re able to look at individual molecules, you can extract a lot more information about the many-body system.”  

What Bakr means by extracting more information is the ability to observe and document the subtle correlations that characterize molecules in a quantum state — for example, correlations of their positions in the lattice or their rotational states.  

“Researchers had prepared molecules in the ultracold regime before, but they couldn’t measure their correlations because they couldn’t see the single molecules,” said Jason Rosenberg, a graduate student in Princeton’s Department of Physics and the co-lead author of the paper. “By seeing each individual molecule, we can really characterize and explore the different quantum phases that are expected to emerge.”  

While researchers have been studying many-body physics with atomic quantum gases for over two decades, molecular quantum gases have been much harder to tame. Unlike atoms, molecules can store energy by vibrating and rotating in many different ways. These various excitations are known as “degrees of freedom” — and their abundance is the characteristic that makes molecules difficult to control and manipulate experimentally.  

“In order to study molecules in a quantum regime, we need to control all their degrees of freedom and place them in a well-defined quantum mechanical state,” said Bakr.  

The researchers accomplished this precise level of control by first cooling two atomic gases of sodium and rubidium down to incredibly low temperatures that are measured in nanokelvins, or temperatures one-billionth of a degree Kelvin. At these ultracold temperatures, each of the two gases transition into a state of matter known as a Bose-Einstein condensate. In this ultracold environment, the researchers coax the atoms into pairing up into sodium-rubidium molecules in a well-defined internal quantum state. Then they use lasers to transfer the molecules into their absolute ground state where all rotations and vibrations of the molecules are frozen.

To maintain the quantum behavior of the molecules, they are isolated in a vacuum chamber and held in an optical lattice made of standing waves of light.  

“We interfere a set of laser beams together and, from this, we create a corrugated landscape resembling an ‘egg carton’ in which the molecules sit,” said Rosenberg.

In the experiment, the researchers captured about one hundred molecules in this “egg carton” lattice. Then the researchers pushed the system out of equilibrium — and tracked what happened in the strongly interacting system. 

“We gave the system a sudden ‘nudge,’” said Lysander Christakis, a graduate student and co-lead author of the paper. “We allowed the molecules to interact and build up quantum entanglement. This entanglement is reflected in subtle correlations, and the ability to probe the system at this microscopic level allows us to reveal these correlations — and learn about them.”    

Left: Members of the Princeton research team. Front row (from left to right) Dr. Zoe Yan, Lysander Christakis, Jason Rosenberg. Back row (from left to right) Ravin Raj, Prof. Waseem Bakr, Prof. David Huse.  Photo by Richard Soden, Department of Physics

Right: The researchers used a novel microscopy apparatus to probe the quantum state of individual ultracold molecules in an optical lattice and measure quantum correlations arising from interactions between them. Image created by Lysander Christakis, Department of Physics

Entanglement is one of the most fascinating — and perplexing — properties of many-body quantum states. It describes a property of the subatomic world in which quantum elements — whether molecules, electrons, photons, or whatever — become inextricably linked with each other no matter the distance separating them. Entanglement is especially significant in quantum computing because it acts as a sort of computational multiplier. It is the crucial ingredient underlying the exponential speedup in solving problems with quantum computers.

The unparalleled control the researchers achieved in preparing and detecting the molecules has clear implications for quantum computing. But the researchers emphasize that, ultimately, the experiment is not necessarily about creating the most advanced qubits. Rather, it is, most importantly, a huge step forward in fundamental physics research.  

“This research opens up a lot of possibilities to study really interesting problems in many-body physics,” said Christakis. “What we’ve demonstrated here is a complete platform for using ultracold molecules as a system to study complex quantum phenomena.”  

Rosenberg concurred. “In this experiment, the molecules were frozen into individual sites on the lattice and quantum information was only stored in the rotational states of the molecules. Moving forward, it will be exciting to explore a whole other realm of interesting phenomena that appear when you allow the molecules to ‘hop’ from site to site. Our research has opened the door to investigating ever more exotic states of matter that can be prepared with these molecules, and now we can characterize them very well,” he concluded.  

Other members of the Princeton team are graduate student Ravin Raj, post-doc Dr. Zoe Yan, undergraduate Sungjae Chi and theorists Alan Morningstar and Prof. David Huse. The research was supported by the National Science Foundation and the Packard Foundation.

The study, “Probing site-resolved correlations in a spin system of ultracold molecules,” by Lysander Christakis, Jason S. Rosenberg, Ravin Raj, Sungjae Chi, Alan Morningstar, David A. Huse, Zoe Z. Yan and Waseem S. Bakr was published online in the journal Nature on Feb. 1, 2023 (DOI: 10.1038/s41586-022-05558-4.