Researchers from the FAMU-FSU College of Engineering and the National High Magnetic Field Laboratory have discovered new information about the formation of vortices in a type of quantum fluid, which could aid our understanding of the physics mystery of how vortex clusters form and provide insight into the swirling motion of the atmosphere on planets like Earth and Jupiter.
In a two-dimensional superfluid, a sort of quantum fluid that can flow without friction, the researchers discovered an alternate explanation for the production of so-called Onsager vortices. Physical Review Letters reported their findings.
“This finding gives us a new explanation for how these vortices might form and is an important step toward continuing to improve our understanding of quantum physics,” said Wei Guo, associate professor in mechanical engineering and lead investigator of the study.
Lars Onsager, a Nobel Laureate, devised a simple theory in 1949 to explain the swirling motion of turbulent 2D fluids, which are fluids limited to flow in a two-dimensional environment.
Onsager’s theory requires energy to be added to the 2D fluid. However, recent publications revealed that in 2D Bose-Einstein Condensates (BECs), Onsager vortices can appear spontaneously without energy input. We set out to do more investigations into these surprising results.
Wei Guo
According to Onsager’s idea, when energy is continuously injected to a 2D turbulent fluid containing chaotic tiny swirls (officially termed vortices), the swirls moving in the same direction cluster to produce large-scale persistent swirls. “Onsager vortices” are these large-scale swirls or clusters. The Great Red Spot on Jupiter is a nice example.
“Onsager’s theory requires energy to be added to the 2D fluid,” Guo said. “However, recent publications revealed that in 2D Bose-Einstein Condensates (BECs), Onsager vortices can appear spontaneously without energy input. We set out to do more investigations into these surprising results.”
BEC is a state of matter in which identical atoms or molecules are contained and chilled to near absolute zero by a laser or magnetic trap. The particles in the BEC state share the same quantum mechanical energy level and can show superfluid behaviors including flowing without apparent kinetic energy loss and whirling around small hollow tubes known as vortex tubes.
A BEC may be constrained to have a quasi-2D disk form, that is, a shape with a tiny thickness but a big radius, using the right trap. A 2D BEC’s vortex tubes resemble small point swirls, making it a suitable testbed for Onsager’s hypothesis.
“A well-accepted explanation of the spontaneous appearance of Onsager vortices in 2D disk BECs is the evaporative heating mechanism,” Guo said. “This mechanism refers to what physicists call vortex annihilation, which is when a pair of vortices with opposite rotations merge and disappear, just like a positive charge neutralizes with a negative charge.”
“As the vortices annihilate, the energy per vortex increases, which leads to the formation of Onsager vortices,” said Toshiaki Kanai, a graduate research student working with Guo at the National High Magnetic Field Laboratory.
However, despite the annihilation of the vortex pairs, Kanai and Guo discovered that Onsager vortices never formed in a computational simulation of turbulent swirling motion in 2D with BECs restricted on the surface of a sphere. After that, the researchers compared the vortex dynamics in disk and spherical shell BECs.
“We finally figured out that the spontaneous formation of Onsager vortices is not due to the well-accepted evaporative heating mechanism,” Guo said. “The true mechanism is the exiting of the vortices from the 2D BEC boundary.”
The vortices can depart the disk BEC throughout its perimeter, but the spherical shell BEC has no restrictions. According to the researchers, Onsager vortices can only be seen in disk BEC shells and not in spherical BEC shells.
“Identifying the true mechanism for the spontaneous formation of Onsager vortices in 2D BECs represents a major progress in our understanding of 2D superfluid turbulence,” Guo said. “Our findings about the point vortices on a sphere may represent a conceptually interesting model of a planetary atmosphere, and these findings can be tested experimentally at NASA’s space laboratory.”
NASA has established a cold atom laboratory on the International Space Station, allowing for the production of BECs with spherical shell shape. Future zero-gravity experiments may aid in the advancement of knowledge in this subject.
This research was funded by a three-year National Science Foundation grant (Grant # DMR-2100790).
