The Bose-Einstein Condensate (BEC) has been studied for decades, ever since its prediction by scientists Satyandra Nath Bose and Albert Einstein nearly 100 years ago. The BEC is a gas of atoms cooled to almost absolute zero. At low enough temperatures, quantum mechanics allows the locations of the atoms in the BEC to be uncertain to the extent that they can’t be located individually in the gas. The BEC has a special history with JILA, as it was at JILA that the first gaseous condensate was produced in 1995 by JILA Fellows Eric Cornell (NIST) and Carl Wieman (University of Colorado Boulder). The original BEC was a gas of rubidium atoms, but using other atoms, such as dysprosium, a BEC can also be produced that will have dipolar interactions. Unlike a normal BEC, the atoms in a dipolar BEC have two opposing poles, similar to the two ends of a magnet. This dipolar BEC has been shown to create self-binding droplets, which cohere even in the absence of an electric potential to hold them together. The non-polar BEC does not create these droplets. The droplets are of interest to physicists who have researched ways to describe the droplet’s energetic excitations.
Since 2005, research on dipolar BEC has continued, using different theories to describe the droplet’s interactions. In a paper recently published in Physical Review A, first author, and graduate student, Eli Halperin and JILA fellow John Bohn theorize a way to study the BEC using a hyperspherical approach. While the name may sound intimidating, the hyperspherical approach is simply a systematic way to look at a many-body problem. The many body problem refers to a large category of problems regarding microscopic systems with interacting particles. Bohn and Halperin applied this approach to a dipolar BEC specifically. When speaking of applying this approach, Halperin explained: "Twenty years ago, John wrote this paper applying the hyperspherical approach to a spherically symmetric system... I think the main advantage we get here is this nice linear way of looking at a many-body problem, without too much loss of accuracy." This approach could be used to help researchers describe the energies and wavefunctions of the BEC droplets using relatively straightforward quantum mechanics rather than more sophisticated quantum field theories.
As a theoretical physicist, Bohn was particularly interested in finding ways to describe interactions of the BEC. According to Bohn: "The problem is, whatever one atom is doing affects what all the other atoms are doing. So how do you keep track of them all? The way people normally solve this is to take a representative atom and follow it as it moves around in the background of other atoms that are, basically, exactly like this atom. Our approach with hyperspherical coordinates is to say, ‘There are a lot of atoms there, let's treat them all at once, as opposed to individually.’ So, we have a coordinate, the hyperradius, which is sort of the size of the whole droplet. It accounts for all atoms at the same time, leaves behind this independent particle picture, and tries to look at things in a collective way.” Bohn was not the first to use this approach. "We didn't invent this. Hyperspherical coordinates have been around since the 1930s. They're used all the time in chemistry and nuclear physics," explained Bohn. "And there's a vast literature out there that we basically stole to put to use for this purpose. And even then, it's hard to do." The hyperspherical approach, while effective in making a many-body problem easier to study for the BEC, is difficult to set up, but, as mentioned above, leads to interpretations of the results.
From Liquid to Gas:
While the hyperspherical approach has revealed a new way to look at BEC droplets, both Halperin and Bohn look forward to using it to further study the interactions of the BEC, particularly with its excitations. In clarifying research around the BEC, Bohn stated: "normally in Bose Einstein condensation, you have a trap where you hold the atoms in place with magnetic fields or optical fields. An experiment done in 2016 showed that if you tuned things just right, the dipoles in the gas align head to tail, which makes them attract each other. It turns out, there's a kind of quantum mechanical fluctuation effect that keeps them from crashing in on themselves. Under the right circumstances, you could turn off the trap, and the thing holds together in the middle of the experiment as a self-bound droplet, like a liquid droplet would. There's a transition that happens where this liquid droplet can transform into a gas. And what we're applying this method to is the transition between liquid to gas." Looking at the transition, both Halperin and Bohn hope to find more about the excitations of the BEC as it changes shape when oscillating between a liquid like droplet and gas.
Halperin explained that it was important to look at the energy states for both the droplet and the the BEC as they had similar energies but different excitations. "We think it might be possible to find a regime where you could get the gas to naturally oscillate between the droplet state and the gas state," Halperin said. "We're interested to see if you can first use the hyper-spherical approach and see this oscillation between the liquid and gas states. And then to test this also in a quantum field theory." Being able to describe the oscillation from liquid to gas using this approach would allow a better understanding of the BEC, specifically at a quantum level. According to Bohn: "You think of liquid and gas as an either-or situation. But in quantum mechanics, why can't it be both?" As the work continues, it will be interesting to see how the quantum interactions within the BEC build on the field of quantum physics.
Written by Kenna Castleberry JILA Science Communicator