From supersolids to microemulsions: exploring spin-orbit-coupled Bose-Einstein condensates

Spin microemulsion phase found in Rashba spin-orbit coupling, Bose-Einstein condensation simulations. The colored region corresponds to an atomically dense region with the same spin state. Source: Ethan McGarrigle (doi: 10.1103/PhysRevLett.131.173403)

In a new study, researchers from the University of California, Santa Barbara (UCSB) report that they have discovered a spin microemulsion in a two-dimensional system of spin Bose-Einstein condensates, revealing a novel phase transition marked by the loss of superfluidity, complex pseudospin textures, and the emergence of topological defects.

Bose-Einstein (B-E) condensate is a state of matter that occurs at extremely low temperatures, in which bosons, like photons, become indistinguishable and behave as a single quantum entity, forming a superfluid or superconducting state.

B-E condensates can exhibit unique quantum properties, such as spin microemulsions. When the internal spin state of the atoms in the B-E condensate is coupled with its motion, a unique phase called a spin microemulsion emerges.

This stage involves atoms organizing themselves into patterns according to their spin state, similar to the formation of microemulsions in soft matter systems.

Microemulsions are coupled to spin orbits

The concept of microemulsions is not new; They are commonly found in synthetic soft matter systems. These phases occur when two incompatible substances, such as oil and water, form an enriched region, and a third minority component, such as surfactants, stabilizes their interface.

However, the emergence of spin microemulsions in the field of quantum physics has never been seen.

Ethan McGarrigle, lead author of the study and a PhD candidate in the Department of Chemical Engineering at UCSB, told Phys.org: "Quantum microemulsion simulated phases already theoretically exist in two-dimensional electronic systems, where there will be associated charge domains similar to those of microemulsions; However, it has never been observed and has not been confirmed by numerical or experimental evidence. ”

The researchers used advanced field-theory simulations (FTS) to study the transition of low-temperature fringe phases with supersolid characteristics.

As the temperature rises, this streaked phase transforms into what the researchers call a spin microemulsion. The fringe phase is a special configuration of the atoms in the B-E condensate, where they form a stripe pattern.

In the spin emulsion stage, atoms self-organize based on their internal spin state, similar to the formation of emulsions in soft matter systems.

Principal Investigator Dr. Glenn Fredrickson, Distinguished Professor of Chemical Engineering and Materials at UCSB, explained: "This microemulsion phase occurs when the motion of each atom is coupled to its internal spin state, resulting in a spin-orbit coupling effect."

The key to this phenomenon is the isotropic two-dimensional Rashba spin-orbit coupling, i.e., the interaction between atomic spin and motion.

Dr. Frederickson continues, "In B-E condensates, atoms collectively minimize their energy at a specific, preferred momentum. Thus, spin-orbit coupled B-E condensation systems can possess a standing wave fringe superfluid state, which is considered to have supersolid characteristics and is described as a superfluid liquid crystal simulation.

Think of it as a pattern or wave-like arrangement of atoms in a condensate. This state is unique because it combines the characteristics of superfluids and crystals, a phenomenon known as supersolids. It's as if atoms behave like waves, arranged in a structured way.

Kosterlitz-Thouless conversion and future work

In their study, the researchers simulated this striated superfluid state at different temperatures, leading to the discovery of spin microemulsions above critical temperatures.

"McGarrigle applied the FTS method to spin-orbit-coupled Bose-Einstein condensates and computationally found that previously known spin fringes (supersolid) phases melt after being heated into spin microemulsions and then converted into normal fluids," Dr. Fredrickson explained.

"The results of the study show that the spin microemulsion has a qualitative similarity to the double continuous microemulsion in a room-temperature oil/water/surfactant mixture."

In addition, their findings suggest that the thermal phase transition, or melting, of superfluid fringe liquid crystal mimics is similar to the well-established Kosterlitz-Thouless phase transition observed in classical liquid crystal films and planar magnets.

In the Kosterlitz-Thouless transition, the two-dimensional system shifts from one phase to another when the vortex-anti-vortex pair (topological defect) becomes unbound. This will cause a change in the order or behavior of the system.

This analogy provides insight into understanding the behavior of two-dimensional Rashba spin-orbit coupled boson systems.

The discovery of quantum spin microemulsions reveals a new phase transition characterized by the loss of superfluidity, the emergence of complex pseudo-spin textures, and topological defects. The significance of this discovery goes deep into the realm of quantum physics and soft matter systems.

However, many problems remain. The melting mechanism of the fringed superfluid phase in the system, characterized by full vortex, semi-vortex, pseudo-spin domain wall and pseudo-spin canopy, is an important challenge for future research.

Commenting on the Fredrickson group's future research plans, McGarrigle said, "We plan to study the thermodynamic stability of spin microemulsions, involving various system parameters such as spin-orbit coupling anisotropy, miscibility of atoms in different pseudospin states, and pseudospin polarization."

"While our initial work explored non-miscible conditions and isotropic Rashba spin-orbit coupling, we plan to extend our numerical analysis to a wider range of conditions. We will investigate the anisotropy tolerance in the spin-orbit coupling scheme, the presence of spin microemulsions under miscible conditions, and its response to inhomogeneous pseudospin state populations. This study will guide the experimenter to achieve this stage," he concluded.

The results of this study were published in Physical Review Letters.

More information: Ethan C. McGarrigle et al., Emergence of spin microemulsions in spin-orbit coupled Bose-Einstein condensates, Physical Review Letters (2023). DOI: 10.1103 / PhysRevLett.131.173403。

Journal Information: Physical Review Letters