Simulations hint at new strongly correlated states of matter in ultracold polar molecules

Bose-Einstein condensates (BECs) are fascinating states of matter that emerge when atoms or molecules are cooled to extremely low temperatures just slightly above absolute zero (0 K). In 2023, physicists at Columbia University realized BECs comprised of ultracold molecules for the very first time.

Building on their work, another research group at TU Wien and the Vienna Center for Quantum Science and Technology recently set out to investigate the behavior of these ultracold dipolar molecules, while also exploring the possibility that they could spontaneously organize themselves into new forms of matter. Their findings, published in Physical Review Letters, suggest that new correlated states could emerge in ultracold polar molecules, showing that these states could be probed in future experiments.

“BECs of ultracold polar molecules were a decade-long goal, but have only been realized experimentally very recently,” Matteo Ciardi, co-author of the paper, told Phys.org.

“From the beginning, our objective was to perform accurate simulations for realistic systems, to serve as future benchmarks for other numerical works and a useful comparison for experiments. It was also important that an analytical expression describing a realistic experimental potential, which we could directly use in our simulations, had just been published.”

Initially, Ciardi and his colleagues were planning to study molecules that were held in place by an external trap (i.e., a structure made of light). However, they subsequently decided to investigate states in which molecules might hold themselves together naturally, which are known as self-bound phases.

“Our work was motivated by our earlier research on weakly dipolar magnetic quantum gases and by the recent breakthroughs from two other groups who realized strongly dipolar molecular BECs,” said Tim Langen, co-author of the paper. “These developments opened exciting new possibilities, but it remains unclear what kinds of novel physical phenomena might emerge in this new regime.”

The primary objective of this recent study carried out by Ciardi, Langen, Kasper Rønning Pedersen, and Thomas Pohl was to identify new aspects of dipolar molecule physics that could soon be probed experimentally. In addition, they wished to shed light on how these aspects might manifest in ultracold molecules, where interactions are particularly strong.

“When I started my Ph.D. two years ago, dipolar BEC systems were studied with atoms, and the first BEC of polar molecules was not yet realized,” said Kasper Rønning Pedersen, co-author of the paper. “Atoms with large dipole moments are interesting because they can form exotic phases such as superfluid droplets and superfluids, and certain quantum effects are enhanced by the dipole strength.”

The dipole moments in atoms are magnetic and this poses limits on their size. In contrast, polar molecules can also have electric dipoles and their size can be significantly larger than that of atoms, which increases their complexity and can open new possibilities for the observation of new phases of matter.

“The problem with ultracold molecules is that since interactions are very strong, approximate methods usually employed for ultracold atoms become unreliable,” explained Ciardi.

“We thus turned to more sophisticated techniques, specifically Path Integral Monte Carlo, which was developed to make predictions for strongly correlated bosons such as superfluid Helium-4. The method requires extensive computational resources and is limited by the number of particles.

“Luckily, BECs of ultracold polar molecules have around 500–1500 particles, which is within the reach of simulations (especially contrasted with the ~100,000 particles usually involved in ultracold atom experiments).”

While Path Integral Monte Carlo allowed the researchers to reliably simulate BECs of ultracold polar molecules, the simulations they performed were still computationally heavy. To perform them, they thus had to employ advanced computing systems and even then, a single simulation run lasted up to several days.

“The dipole physics community has developed methods based on mean-field equations that work well for atoms,” said Pedersen.

“In addition to the dipole-dipole interaction, which dominates at large distances, atoms repel each other like billiard balls when they get very close. The way molecules interact shows many similarities, but the repulsive ‘wall’ works at larger distances, meaning that the molecules do not get as close to each other as atoms do. This is one reason why we needed to use the computationally heavy quantum Monte Carlo method for this study.”

The simulations performed by the researchers showed that ultracold polar molecules could form strongly correlated phases without requiring any external confinement. In particular, they hinted at the emergence of these self-bound phases in single-molecule crystals.

“Since the parameters we use are realistic (and more recent experiments in recent months are starting to approach those regions of the phase diagram) there is a strong implication that these phases can be realized in experiments soon,” said Ciardi.

The researchers found that ultracold polar molecules could form self-bound quantum droplets at lower interaction strengths than earlier works had predicted. These droplets could then transform into superfluid membranes, frictionless two-dimensional (2D) layers, and subsequently into a crystalline monolayer than remains bound together without the need to be confined.

“Our results demonstrate that strongly correlated new states of matter can indeed exist and be probed in ultracold molecular systems under realistic experimental conditions,” added Langen.

“This is particularly exciting because it bridges two worlds—the supersolid phases previously explored in magnetic Bose–Einstein condensates and the long-sought physics of helium systems, which has remained elusive for decades.”

This recent study could inform future experiments with ultracold dipolar molecules, which could potentially lead to the observation of the new states of matter that emerged in their simulations. In the meantime, the researchers plan to continue their analysis in the hope of uncovering any other phases that could be probed experimentally.

“The dipolar interactions studied in this paper already show very interesting properties, but they are only a specific case of a much wider range of potentials which can and are being used in experiments,” said Ciardi. “Our short-term goal is therefore to extend the analysis to more potentials and figure out what other phases can be expected in experiments.”

In his next studies, Ciardi particularly hopes to characterize other crystalline phases of ultracold polar molecules. Langen, on the other hand, who is an experimental physicist, is now working towards the realization of the states simulated with his colleagues in a laboratory setting.

“We are trying to realize these states by laser cooling molecules to ultracold temperatures,” Langen said. “This ongoing effort will allow us to bring our theoretical predictions to life and directly study their properties.”

“One cool thing about polar molecules is that we can control and modify the way they interact,” added Pedersen. “This is in contrast to, say, how electrons interact, which is fixed and given by nature. The interaction we chose to study in the paper is just one of many possibilities, meaning that there are a lot more out there to be explored.”

The researchers hope that their work will soon contribute to the discovery of new quantum phases of matter. They are now planning additional studies that will rely on their newly proposed experimental platform.

“For example, exotic strongly correlated crystalline phases that simultaneously feature superfluid properties have been conjectured more than 50 years ago but have not yet been found in nature,” said Thomas Pohl, who led the research project. “Our demonstration of ultracold molecular crystals with such widely tunable interactions, suggests that this could now become possible in the near future.”

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