The strange behaviors of high-temperature superconductors—materials that conduct electricity without resistance above the boiling point of liquid nitrogen—and other systems with unusual magnetic properties have fascinated scientists for decades. While researchers have developed mathematical models for these systems, much of the underlying quantum dynamics and phases remain a mystery because of the immense computational difficulty of solving these models.
In a new study published in Science, researchers from JILA, led by JILA and NIST Fellows and University of Colorado Boulder physics professors Jun Ye and Ana Maria Rey and JILA and CU Boulder physics professor John Bohn, used ultracold molecules to realize these models with an unprecedented level of control. Their work bridges the fields of atomic, molecular, and optical (AMO) physics with condensed matter physics, opening new doors for quantum simulations and advances in quantum technologies.
“It is very exciting that experiments with polar molecules are now reaching the point where these models can be implemented in the lab,” Rey says. “While currently, we are exploring dynamics at low filling fractions where theory effort can still have some predicting capabilities, very soon experiments will reach dense regimes intractable by theory, fulfilling the dream of quantum simulation.”
A Decade in the Making
JILA has long been celebrated as a hub where experimentalists and theorists collaborate to tackle some of the most challenging questions in physics. Indeed, over two decades of collaboration among JILA researchers, first with the experimentalists Ye and the late JILA Fellow Deborah Jin, later joined by theory colleagues Rey and Bohn, pioneered ultracold molecule research and laid the foundation for this work.
In this study, the researchers from Ye’s experimental group collaborated with theorists in Rey’s and Bohn’s groups to understand the data from several new experiments exploring different regimes of molecular motion and dipolar interactions.
“We wanted to understand how motion and magnetism are coupled in quantum systems,” says Annette Carroll, a JILA graduate student in the Ye laboratory and the paper’s first author. “The molecules offer a unique platform to study this interplay, thanks to their long-range dipolar interactions.”
These dipolar interactions were key to the experiment’s success. While neutral atoms have been widely used in quantum studies due to their ease of cooling and control, their typical short-range interactions often limit their ability to simulate magnetism. Ultracold molecules, with their natural long-range dipolar interactions, offer a richer platform for exploring exotic quantum phases but are more complicated to control.
Focusing on Framework
In the experiment, an array of ultracold potassium-rubidium molecules were used to emulate the behavior of electrons in a solid state crystal. Electrons tunnel between nearby ion cores in a crystal at a rate “t”.
To imitate the fact that electrons are like tiny magnets, which can point in two directions, spin up or spin down, molecules were prepared in two accessible internal (rotational) states. Electrons are charged particles and see each other at a distance, but due to the ion cores and other electrons in the system, they strongly screen each other, and effectively, one electron only sees another electron when they are at the same lattice site. In this setup, two nearby molecules (simulating electrons), one with spin up and one with spin down, can flip their spins but to do that, for example, the spin up electron needs to hop into the site where the down electron is, interact just for a glimpse to reduce the large energy cost to be at the same site, and then hop back to its original site now as a spin down.
This process is called superexchange and happens at a rate “J.” The behavior of electrons hopping and exchanging their spins is called “t-J” model and it is believed to have all the necessary ingredients to explain the emergence of high temperature superconductivity. But, this is not yet well understood.
“Polar molecules have the advantage that they carry a dipole moment, and this means that two molecules can exchange the spins far from the distance without needing to move where the other is. This has great consequences,” elaborates Rey. “It allows us to simulate the ‘t-J’ model in a broader parameter regime since the exchange rate J can be controlled in the lab. It opens exciting opportunities for the exploration of magnetism and superconductivity in new regimes.”
“The t-J model captures the interplay between motion and spin interactions,” adds Sean Muleady, a former JILA graduate student in Rey’s theory group now at the Joint Center for Quantum Information and Computer Science (QuICS) and the Joint Quantum Institute (JQI), who was also involved in this study. “These dynamics are critical to understanding phenomena like magnetism in strongly-correlated systems and, in certain regimes, even superconductivity. But studying these effects in real materials is notoriously difficult.”
To overcome these challenges, Rey, Muleady, and postdoctoral researcher David Wellnitz worked with Bohn and his graduate student Reuben Wang to develop mathematical tools to simulate the spin dynamics of moving dipolar particles within different lattice arrangements set up by the researchers within Ye’s experimental group.
“Using dipolar interactions adds an entirely new dimension,” says Bohn. “This is a more generalized version of the t-J model, incorporating features that condensed matter physicists could only theorize about.”
Combining Theory and Experiment
For the researchers in Ye’s laboratory, the team focused on ultracold potassium-rubidium molecules trapped in an optical lattice—a grid of laser light designed to confine the molecules to specific locations. This lattice structure served as a simulated crystal, mimicking the confinement of electrons in real materials. By applying electric fields, the researchers precisely controlled the strength and nature of the molecules’ dipolar interactions and, by tuning the strength of the optical lattice, tuned their ability to move within the lattice.
The experimentalists studied the dynamics between two distinct motional extremes: one where the molecules were “frozen” in place and another where they could move freely within two-dimensional planes without any transverse lattice confinement. By tuning the transverse lattice depth between these two extremes, the researchers explored a large range of behaviors governed by the t-J model, from interactions between frozen spins to dynamic coupling between spin and motion. In all setups, the researchers prepared the molecules in a superposition of rotational states, simulating magnetic spins all pointing in the same direction, and measured how quickly the spins lost their initial magnetization because of their interactions.
Interpreting these behaviors, however, required an equally flexible theoretical approach. Two theoretical groups, led by JILA Fellows Ana Maria Rey and John Bohn, collaborated to combine their unique expertise. Rey’s group specialized in lattice-based models, while Bohn’s group brought insights into molecular collisions and scattering processes.
“These were two very different schools of thought,” says Muleady. “Bringing them together was critical because the experiment operates in a middle ground that neither approach alone could fully describe.”
The collaboration resulted in novel theoretical frameworks that bridged the gap between frozen and dynamic motional regimes, enabling a comprehensive interpretation of the experimental data.
Connecting Magnetism and Motion
Through their collaboration, the team made several significant discoveries, including that the spins stayed aligned much longer at a particular electric field when the interaction between the spins is independent of their orientation. Observing coherence in this context is crucial because the spins maintain their alignment over time, which is rare. Long coherence times are important for preserving quantum entanglement, a behavior where particles’ quantum states are interdependent.
“At this special point, the spins of the molecules align perfectly, leading to slower decay of quantum coherence than at any other point,” explains Cal Miller, a JILA graduate student in the Ye group. “This is something that had been theorized but never observed in an experiment until now.”
This finding confirmed theoretical predictions about the behavior of spin systems and demonstrated the precise tunability of interactions between molecules.
However, the experimentalists observed other dynamics that required new theoretical modeling. The researchers systematically explored how the coherence between the spins depends on molecular motion, developing for the first time a model of how collisions between molecules allowed to move freely within 2D layers lead to the decoherence of the spins.
“At first, we couldn’t explain why the decoherence behaved this way,” explains Junyu Lin, a postdoctoral researcher in Ye’s group. “It took many discussions. Finally, when we saw the model from Reuben and John, and it matched our data, we thought: ‘Oh, that’s the mechanism.”
Moreover, when the molecules were allowed to move freely, the researchers observed a striking new phenomenon in the spin alignment.
“We saw a fascinating ‘stretched exponential’ behavior in the decay of spin alignment,” says Wang. “It’s a result of the molecules’ motion and their spin alignment—a combination that’s difficult to describe using traditional methods.”
The key understanding from the work is how motion, which can be regulated by optical lattices, affects the magnetization dynamics of strongly interacting dipoles. The researchers observed more complex spin orientation dynamics by allowing the molecules to move. The coupling between spin and motion modifies the rate at which interacting spins evolve.
Pushing New Frontiers in Experiment and Theory
Understanding these experimental discoveries would not have been possible without the team's new advances in theoretical modeling.
“This project pushed our tools to the limit,” explains Wellnitz. “We had to develop new methods to bridge the gap between systems where molecules are frozen and those where they’re moving freely.”
The collaboration also highlighted the challenges and rewards of interdisciplinary research within theoretical physics.
“One of the most exciting parts of this work was finding a shared language between the different theoretical approaches,” says Muleady. “Each group brought something unique to the table, and the experiment provided a real-world test for our models.”
For the experimentalists, these results may bring new interest to the t-J model from multiple different subfields of physics.
“While the condensed matter community is already interested in this model, I think the AMO community will also be more interested in our work because we’re approaching things differently,” adds Lin.
While the results of this study have uncovered vital information about the rich dynamics of long-range interacting spin systems, the researchers are already looking toward the project’s next steps.
For the experimentalists, future work will focus on achieving even colder temperatures and higher densities of molecules.
“We’re working toward regimes where the molecules’ interactions are strong enough to create new quantum phases,” says Carroll. “These are the conditions where we might observe rich phenomena like superfluidity.”
For others, the results of this project suggest major implications for the future development of quantum devices.
“By advancing our understanding of spin-motion coupling, this work could inform the design of new quantum technologies,” notes Wellnitz. “It’s an exciting time to be in this field.”
This research is supported by the National Science Foundation, the US Department of Energy's Office of Science, National Quantum Information Science Research Centers, the Quantum Systems Accelerator, the Air Force Office and Office of Science and Research, and the JILA Physics Frontier Center.
Written by Kenna Hughes-Castleberry, JILA Science Communicator