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Total Ellipse of the SU(N)

SU(N) fermions display unique properties.

SU(N) fermion systems' unique interactions allow them to be quickly cooled and prepared for use in quantum-matter based atomic clocks.

Image Credit
Steven Burrows/Ye Group

There was something odd going on with the SU(N) fermions in the Ye Lab.

Normally, when a noninteracting Fermi gas of atoms is released from a trap, it expands isotropically. The atoms' pent-up kinetic energy sends them shooting away from each other in a ballistic expansion, forming a round, spherical pattern—that shape reflects the isotropic momentum distribution of the trapped gas. But with the SU(N) fermions, the Ye Group saw an anisotropic cloud—an ellipse, not a sphere.

"We were like, 'what is going on?'" said Lindsay Sonderhouse, a graduate student in the Ye Group. "This is like a smoking gun signature of interactions in the gas. And we saw this, despite the fact that we have such a negligibly small scattering length."

In other words, the atoms had pronounced interactions, even though they could barely "see" each other.

To understand this strange shape, Sonderhouse and the Ye Group studied the interactions and thermodynamics of SU(N) fermion systems. They collaborated with Ana Maria Rey's group, who provided detailed modeling for the SU(N)-symmetric interacting system. They discovered an unexpected relationship between the gas's interactions and its thermodynamics, and that these fermion systems are an untapped resource for atomic cooling-reducing cooling time to a mere 600 milliseconds. Their results were recently published in Nature Physics.

"That is the fastest evaporation time that has been seen for fermions," Sonderhouse said. "It's a very interesting, unique form of quantum matter to study. Practically, it is also a useful experimental tool that we can add to our toolbox in cold atom systems."

Causing the ellipse

SU(N) systems are pretty unusual in the atomic world. For a single component system, fermions all shy away from each other; two identical spin-state fermions can't occupy the same energy level. In those systems, fermions fill in each available energy level from ground up, forming a "Fermi sea." But SU(N) fermion systems have multiple spin components. A single non-interacting Fermi sea turns into multiple Fermi seas that are interacting with each other, giving rise to interesting dynamics.

And, unlike other fermionic systems, the spins in SU(N) fermions all look the same. Sonderhouse worked with strontium-87 atoms, where the large number of nuclear spin states under SU(N) symmetry is unprecedented - these atoms can have up to ten spin states per energy level. This is distinct from the two-component Fermi gases that are more commonly studied.

In single component systems, the fermions don't interact with each other at ultralow temperatures. Multiple components are required to make the atoms interact. And in SU(N) fermions, these atoms' scattering lengths are all equal-meaning if two of these fermions collide, they will scatter the same way regardless of their individual spin properties. This gives SU(N) systems an astonishing symmetry.

"Their collisional properties are independent of the spin, and that is unique in SU(N) atoms. That is not normally true," she said.

As the team studied the elliptical cloud, they learned that these characteristics explained what they were seeing.

"Those multiple components turned out to be the reason why the gas could experience so many interactions, causing that anisotropic cloud," Sonderhouse said. "Since we have ten components, there are a lot of different particles that the fermions can interact with at low temperatures. We are effectively increasing our interaction parameter very efficiently by increasing the number of spin components."

Seeing that elliptical cloud then led the group to ask: how does the strong interaction in this gas modify its thermodynamics?

A quick chill

To understand its thermodynamics, the Ye Group tried to compress the SU(N) cloud. But as the atoms were forced closer to each other, they repelled each other.

"If [the atoms] are repulsively interacting with one another, they don't want to be close to one another...As you compress them, they resist that compression," Sonderhouse said. In that way, they mimicked colder, non-interacting Fermi systems.

"You can basically have a noninteracting Fermi system that is really cold (where it has a Fermi pressure to stop the system from collapsing onto itself), and that will give you the same low compressibility as if you had an interacting system that is kind of hot," she added.

This indistinguishability made it hard for the group to disentangle the two effects by looking at the compressibility alone. However, together with theory colleagues, they found hidden anisotropies in the shape of the cloud that provided more insight-something that hadn't been seen before.

Now Sonderhouse and her colleagues could figure out how the system's thermodynamics and its multiple, symmetrical, interacting components worked. And they realized that by using evaporative cooling techniques, these atoms could be chilled to ultralow temperatures in only 600 milliseconds—much faster than what has been seen previously.

As a result of the rapid evaporation, the total preparation time of the Fermi gas was under three seconds.

That means less downtime to prepare atoms for metrology tools like optical atomic clocks-something the physics community has been looking for, Sonderhouse added. Shorter preparation times for the atoms means that the clocks can run more often and take more measurements.

"It used to take us 15 seconds in preparation time before we measured [the atoms], and with these new techniques, we can do it in under three seconds. So, that is a very big improvement," she said.

This research was published in Nature Physics on August 31, 2020, and was supported by the National Science Foundation Physics Frontier Center grant, NIST, DARPA, and Air Force Office of Scientific Research grants.


SU(N) fermion systems are multi-component, spin-symmetrical collections of atoms—which are unique among degenerate gases. The Ye Group found that SU(N) fermion systems display special properties that allow them to be quickly cooled and prepared for use in quantum-matter based atomic clocks.

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