At ultra-cold temperatures, quantum mechanics dictate how particles bump into each other. The collisions depend both on the quantum statistics of the colliding partners (their location within the medium) and on their collisional energy and angular momentum. The angular momentum of the particles creates an energy barrier, a field of energy that prevents two molecules from interacting, and which can also affect particle dynamics in the quantum realm. The two main types of interactions at the quantum level are s-waves and p-waves. S-wave types of collisions happen naturally between fermions when they exist together in two different internal states and happen with zero angular momenta, which creates a low energy barrier. That means that atoms can collide “head-on.” S-wave collisions have been very well studied and characterized. However, quantum statistics prevents identical fermions (those having the same internal state) to collide via s-wave interactions, instead forcing them to interact via the so-called “p-wave” channel.
However, quantum statistics prevents identical fermions (having the same internal state) to collide via s-wave interactions, instead forcing them to interact via the so-called “p-wave” channel. In contrast with s-wave interactions, p-wave interactions are penalized by the aforementioned energy barrier.In order to collide, particles need to carry a non-zero angular momentum in order to overcome that barrier—they need to spin around each other, like a pair of dancers. The net angular momentum of the partners can give rise to rich quantum behaviors and phases of matter that have been intensively sought in real materials and cold atoms, but which have not yet been found. Besides the energy barrier, the dynamics of three-body recombination, which involves interactions when three atoms are present rather than two, can make it complicated to study p-wave interactions in an isolated space. To overcome these problems, and to measure coherent p-wave interactions between two particles for the first time, JILA and NIST Fellow Ana Maria Rey and her group, together with JILA theorist Jose D’Incao, collaborated with the University of Toronto experimentalist team led by Joseph Thywissen. They devised a method to isolate pairs of atoms in an optical lattice, a web of laser light that helps isolate and control particle interactions, then gave the particles the necessary angular momentum, or twist, for the atoms to collide via p-wave using specific laser beam frequencies. This resulted in the first observation of p-wave interactions in an experiment. The researchers have published their findings in the journal Nature.
An Examination of the Three-Body Recombination
Three-body recombination is a process that happens in cold gases and has been a problem for many physicists in designing quantum particle experiments. In the p-wave case, the three-body collisions are so violent that they cause atoms to escape the optical lattice (trap). According to Rey: “When you have a three-atom system, the conditions for energy and momentum conservation allow two of the atoms to group together and release a lot of energy, which the third atom can soak up and use to escape from the trap. So, we can only keep them trapped for very short times in experiments. It's hard to track what is actually happening during these collisions.” To overcome this issue, the researchers managed to isolate pairs of fermions. In an optical lattice, it is possible to prepare conditions at which there are exactly two atoms on a lattice site, but never three. Furthermore, the researchers were able to use a magnetic field to tune the interaction strength and check whether the predicted theoretical values matched the data. As Thywissen added: “The interaction energy cannot exceed a maximum value, which is reached at the so-called unitary point.” This unitary point is a special limiting case where the p-wave interactions are as strong as they can be in the lattice.
Researchers have long sought to generate coherent unitary p-wave interactions because of all the exciting exotic quantum phases of matter that these interactions enable. In the past, three-body recombination stopped them from getting close. Pioneering experiments carried out in a bulk gas by Deborah Jin at JILA were able to actually determine the rate at which particles are lost and provided first insights into the nature of p-wave collisions. However, since particles are lost very fast in a bulk gas it has been hard to make further progress in studying the p-wave processes.
Looking Closer at Atomic Interactions
Besides the three-body recombination, the energy barrier resulting from the mutual angular momentum of the atoms makes it harder to study isolated p-wave interactions. . Vijin Venu, a graduate student in Thywissen’s group said: “This means that the interacting atoms are not colliding head-on but their quantum mechanical collisions are characterized by a circular motion around each other.” This circular motion can create both energy and motional problems in how the atoms collide. Rey added, “This is something that, even though it has been studied for many years, has not been clearly understood, because there have yet to be experiments to validate the various approximations used to characterize the p-wave interactions.” Working to validate these approximations, Rey and her team helped Thywissen and his laboratory develop the right experimental protocols for isolating these interactions.
To quantify the strength of the p-wave collisions, the researchers looked at a value called scattering volume, which describes the intensity or strength of the collision. Systems with strong, naturally-occurring p-wave interactions are rare, as Venu added ,“The only naturally occurring system with well-established p-wave interactions is superfluid 3He.” JILA has had a history of studying p-wave interactions in atoms. “Debbie Jin did a lot of progress studying p-wave interactions,” Rey stated. “Her research accomplished amazing developments but faced challenges. We are now able to control the system in a much better way and we can start to overcome previous issues.”
Making the Atoms Dance to a Faster Beat—with a Magnetic Field
As mentioned previously, the researchers varied the magnetic field to tune the strength of the p-wave interactions. “We control the scattering wave function with our choice of a magnetic field," explained University of Toronto graduate student Peihang Xu, who studied under Thywissen. The magnetic field affects the energy of individual atoms, which in turn adjusts the scattering volume of the collisions. By looking at the scattering volume for different magnetic fields and different lattice depths, the researchers were able to determine a universal curve in the data, suggesting an overall trend that should be followed by any kind of atoms in any lattice potential.
Laser beams were used to excite the atoms and impart the necessary angular momentum on them to twist around each other. To do this, a spectroscopic protocol first prepared atoms that were weakly interacting to increase the strength of their interaction. Twisting then occurred via laser beam stimulation, as the atoms’ angular momenta began to shift. To speed up the twisting rate to the same rate enabled by the imposed magnetic field, atoms were exposed to radio-frequency pulses at a frequency tuned to cause resonance with the atoms—similar to tuning the knob of a radio to find the frequency of the desired radio station. “When the frequency is resonant [with the atoms], we can drive the transition for our pairs of atoms to go from a weakly interacting state to a strongly interacting state,” stated Xu. The experiment was able to not only measure the energy, but the coherence between the atoms and molecules formed during the collision, and in the presence of an external drive,” Rey said. “All the experimental observations agree with a theory description in terms of scattering volume.”
While the experiment resulted in a novel method to study p-wave collisions without the effects of three-body recombination, it also resulted in long-wanted experimental corroboration of physics theory scattering volume predictions. JILA has a reputation for pairings of experimentalists and theorists for research that produce rich scientific results. As Mikhail Mamaev, co-author and graduate student in Rey’s group notes, “The physics that comes out is much more complicated and interesting.”
Written by Kenna Hughes-Castleberry, JILA Science Communicator