���Ҵ�ý�ƽ������

Dipolar BEC Gas. Image credit: Steven Burrows / JILA

Dipolar gases have become an increasingly important topic in the field of quantum physics in recent years. These gases consist of atoms or molecules that possess a non-zero electric dipole moment, which gives rise to long-range dipole-dipole interactions between particles. These interactions can lead to a variety of interesting and exotic quantum phenomena that are not observed in conventional gases.

One important area of research involving dipolar gases is the study of quantum phases of matter. In particular, dipolar gases have been used to explore the behavior of so-called “quantum droplets”, which are self-adhering quantum states of atoms or molecules that arise due to the interplay between the molecule’s dipole-dipole interactions and quantum fluctuations. These droplets are stable and have been observed experimentally in a variation of two different systems. In a new paper published in JILA Fellow John Bohn and graduate student Eli Halperin looked into the different patterns these droplets made, specifically within a Bose-Einstein Condensate (BEC) dipolar gas. “We’re looking at these arrays of droplets, which have different symmetries,” Halperin explained. “But the most common one, or the one that’s been reproduced in the lab, is this six-fold, hexagonal array of droplets.” From their work, Halperin and Bohn found that the dipolar BEC gas droplets could be disturbed enough to form intermediate patterns and symmetries, thereby creating a method for fine-tuning these interactions.

A Square Lattice and A Frustrated Gas

To look at how these symmetries formed within the BEC droplets, Halperin and Bohn used a method appropriately called “geometric frustration,” or simply, “frustration.” As Bohn elaborated: “This idea of frustration is very important. The atoms in these experiments are left to themselves and may want to do six-fold symmetry. But instead, you might try to force four-fold symmetry on them. And now the atoms are under stress, so they’re going to make a compromise. The frustration here is that compromise.” To apply frustration to the gaseous system, Halperin and Bohn posited using a square optical lattice, a type of web using different lasers, as a weak constraining force on the BEC droplets. “If the square lattice is really strong, you don’t just get the BEC sitting in the lattice,” Halperin added, alluding to the strength of the lattice depending on the laser frequency. However, a weak square lattice creates a weak force on the BEC system, which keeps the BEC in the lattice, and the gaseous droplets begin to struggle with each other to balance out their energy levels in order to reach the lowest energy states.

A Tale of Two Patterns

For Bohn and Halperin, this frustration caused some interesting effects. “We found this intermediate regime where it doesn’t always have six-fold symmetry or four-fold symmetry, it can have neither type of symmetry,” Halperin stated. This created different pattern regimes within the droplets, which the researchers mapped out, showing the different ground state of each regime. “It can have different regions where one section arranges in one pattern and a different section arranges in a different pattern,” Halperin added. “This half and half system ends up being an overall lower energy than when one pattern dominates the whole gas.” Because the dipolar BEC droplets acted as a superfluid system, (where the system has no viscosity and can flow without losing kinetic energy) instead of having more distinct particles such as in other gases, this half and half pattern of droplet frustration suggested something new for further exploration of the dipolar BEC gas. “This frustration gives another kind of knob to turn when you’re looking at patterns that change in the BEC,” Halperin stated.

Besides being a fine-tuning knob, this process of frustration has bigger implications for the field of quantum physics. As Bohn added: “You see frustration all over physics. The interesting stuff happens when there’s two competing things going on and the system has to find its way in-between.” Dipolar interactions can lead to the formation of complex patterns and structures in the gas, such as long-range order or the formation of exotic phases such as super solids. These systems are of great interest to researchers studying condensed matter physics and are being explored in a variety of different experimental systems. Both Bohn and Halperin are hopeful that other researchers could use their theory to further study this unique system.

Directing Sound at Dipoles

Another way to perturb a dipolar gas is to push different types of waves through it. In the research done by Bohn and graduate student Reuben Wang, also reported in the waves being utilized were sound waves. Instead of utilizing the dipolar BEC gas that Halperin used, Wang and Bohn instead studied the interactions of sound waves on a dipolar fermionic system. Fermionic gases are unique in that fermions are difficult to condense, due to the Pauli Exclusion principle which asserts that two particles cannot share identical quantum states. However, by cooling these fermionic gases to ultracold temperatures, researchers can coax the gas to condense into a BEC-type formation and study the gas as one cohesive unit. Above certain temperatures, the fermions are studied as separate units. As Wang explained: “We look at the dipolar gas molecules as distinct things that whiz around and are thermally distributed, but also collide with each other and interact in quantum ways, where the quantum ways are scattering between particles.” ��Besides the scattering interactions, Wang and Bohn also studied the dipolar interactions between polar gases, also known as the mean-field. By taking the gases out of equilibrium, using sound waves, Wang and Bohn hoped to understand how these gases responded to the perturbation.

To disturb the system, the researchers decided to use sound waves, which are a type of compression wave. “Sound is a rather simple probe for this system,” Wang added. “We say: ‘Well, if I weakly poke it, there’s these linear excitations that go on top of the gas.’ So, we want to understand how this evolves with molecular collisions in the gas.” Looking at what would happen when sound waves penetrated the polar gas like ripples in a pond, Wang and Bohn were excited to see that the ripples were unequal. Instead of being symmetric in all directions, they found that the sound deformed the gas based on the directions of the dipole interactions. “The sound moves relatively faster to the direction in which the dipoles were aligned, and only slowly propagates in another direction, creating more oval-shaped ripples,” said Wang. “We’ve seen a somewhat similar thing in other literature on condensates.”

Studying Gaseous Viscosity

Understanding how sound waves move though the dipolar fermionic gas suggested other implications for studying these gaseous systems. As Wang explained, part of understanding dipolar gas dynamics was to look at their viscosity, which he described as a “…form of friction of the gas. “It arises microscopically, from the bumping of all the different molecules and atoms in the system.” Viscosity can tell physicists more about the fluctuations within the system, giving more insight into interactions happening at the quantum level. Like liquids with different viscosities, or runniness, gases with different viscosities behave differently. However, finding viscosity was not a straightforward method. “The method for figuring out the viscosity of a gas is well established and really complicated,” Wang added. “But it’s so much more complicated when the gas is dipolar. Usually, people will just put a number into viscosity, because you need to have some friction coefficient. But in our case, the viscosity becomes this object, which is also characterized by different directions in space.” By using sound waves to disturb the gas, Wang and Bohn found a new method that could yield greater accuracy to calculations of the viscosity of a dipolar gas.

Thanks to the different disturbances they were able to create in dipolar gaseous systems, Bohn, Halperin, and Wang were able to identify new dynamics within these special gases. Because dipolar gases are utilized in many different systems, from creating highly accurate atomic clocks to designing new types of sensors that are capable of detecting tiny variations in electric fields, understanding more about how these gases work can help advance many different subfields within quantum physics. As researchers continue to explore the properties of dipolar gases, we can expect to see many exciting new discoveries in the years to come.