Time-of-flight image of an atomic cloud of 6Li, where dark density depletions are quantum vortices. Credit: Kyuhwan Lee at SNU
The Kibble–Zurek (KZ) mechanism is a theoretical framework introduced by physicists Tom Kibble and Wojciech Zurek. This framework essentially describes the formation of topological defects during non-equilibrium phase transitions of systems.
Researchers from Seoul National University and the Korea Institute of Basic Science recently observed KZ scaling in a homogeneous, strongly interacting Fermi gas as it transitioned to a superfluid.
Their article, published in Physics of naturecould pave the way for new experimental efforts to probe this long-standing physical framework.
“Superfluidity and superconductivity have fascinated physicists for nearly a century,” Kyuhwan Lee, a co-author of the study, told Phys.org. “They are beautiful manifestations of quantum mechanics on a large scale.”
“Basically, when we have many interacting particles that are cold enough, they can flow collectively without any resistance. A natural question that arises from this is: how do superfluids arise, and what happens during the transition from a normal phase (in which they flow with resistance like most ordinary liquids) to a superfluid phase?”
In the 1980s, Zurek began to address this interesting research question experimentally, drawing on Kibble’s recent cosmological frameworks. Zurek suggested that studying the remnants of the phase transition of a physical system to a superfluid would provide interesting insights into how superfluids arise.
“In our experiment, the remnants are quantum vortices, a swirling flow with quantized angular momentum,” Lee said. “The central prediction, now also known as KZ scaling, is that the number of quantum vortices should scale as a power law with respect to the rate at which you go through the superfluid phase transition.”
“The faster the phase transition, the more quantum vortices we get because of the reduced time the superfluid has to adapt to external changes in the system’s parameters.”
Although KZ scaling is applicable to a wide range of systems, including superfluids, ferroelectrics, superconductors, ion traps, and Rydberg atom lattices, it has so far been observed primarily in a few of these systems. The main goal of the study by Lee and colleagues was to observe KZ scaling in a Fermi superfluid, which has so far proven particularly challenging.
“The real kicker here is that we observed the predicted KZ scaling behavior using both temperature and interaction strength as two separate control knobs,” Lee said.
An atomic cloud of 6Li. The typical cloud diameter is 350 µm. Credit: Kyuhwan Lee at SNU
The sample used by the researchers was an atomic cloud of 6The lithium samples were cooled to extremely low temperatures (a few tens of nano Kelvin). Their sample had a unique configuration, which they created using a spatial light modulator (SLM). Its configuration consisted of a spatially uniform atomic cloud with a disk geometry and a diameter of about 350 µm.
“To observe the KZ scaling behavior, we needed a spatially uniform sample with a large surface area,” Lee explains. “It had to be uniform because we wanted the superfluid phase transition to occur simultaneously throughout the sample.”
“If there are irregularities, phase transitions occur at different times in different locations, making observations difficult to compare to theoretical predictions. We also wanted the telescope to be large, so that we could observe a large number of quantum vortices and avoid finite-size effects.”
Another important factor the researchers considered when designing their experiment was the ability to tune the interactions in their experimental system. To tune the interatomic interactions, they exploited Feshbach magnetic resonance between 6Li atoms in their cloud.
“This gave us a new tool to study superfluid phase transition dynamics, instead of just using temperature as a control knob,” Lee said. “Armed with these exciting tools, we turned off either the temperature or the interaction force across the superfluid phase transition at varying rates.”
Whether by changing the temperature of their system or the strength of the interactions between atoms, Lee and his colleagues observed identical (i.e., universal) KZ-scaling behavior in their sample over a wide dynamic range. Their study thus successfully observed the KZ scale in a superfluid, something that had previously remained elusive.
“In cash 4“This is another representative example of a superfluid system, the typical time scale of phase transition dynamics was simply out of reach with conventional mechanical pressure quenches,” Lee said.
“In cash 3There were signatures of quantum vortex generation, which were made possible by fast nuclear reactions. Many unknown factors, however, made a direct comparison with the KZ scale difficult.
“In ultracold atomic gases, significant work has been done to verify the spontaneous generation of quantum vortices and unveil the static and dynamic scaling properties, but the typical sample configuration has made it difficult to capture the KZ scaling behavior.”
The recent work of this team of researchers constitutes a significant contribution to the study of the KZ scale in superfluids. Their most notable achievement was the observation of identical scaling behavior whether the team manipulated the temperature or the interactions in their sample.
“The concept of universality, which is now even taught in undergraduate statistical mechanics courses, allows us to understand complex systems in a very ‘economical’ way,” Lee said. “It’s really amazing that we can untangle a common feature in such complex phase transition dynamics.”
In their next studies, Lee and his colleagues plan to study in more detail the behavior observed in their experiments, which cannot be simply explained by the KZ mechanism. Their future efforts could lead to other valuable observations, further improving the understanding of the dynamics of non-equilibrium phase transitions in Fermi superfluids.
“For fast quenches, we observed a deviation from the KZ scaling behavior for temperature and interaction quenches,” Lee explained. “One possible scenario to explain this is what is called early coarsening.”
“Simply put, early coarsening suggests that the initial (or early) superfluid growth dynamics suppress quantum vortex formation for rapid quenching. Using interferometric methods to measure phase coherence, it would now be interesting to study how coarsening dynamics fit into the picture.”
More information:
Kyuhwan Lee et al., Universal Kibble–Zurek scaling in an atomic Fermi superfluid, Physics of nature (2024). DOI: 10.1038/s41567-024-02592-z
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