Of all the atoms that quantum physicists study, alkaline atoms hold a special place due to their unique structure. Found in the second column of the periodic table, these atoms have two outer electrons, allowing the atoms to interact with one another in intriguing ways. “They have received a lot of attention in recent years among the physics community because of two reasons,” explained JILA and NIST Fellow Ana Maria Rey. “One is that they have a unique atomic structure, which makes them ideal for atomic clocks. This is because they have a long-lived electronic excited state that can live longer than 100 seconds. The second is that their electronic and nuclear spin degrees of freedom are highly decoupled and therefore the nuclear spins do not participate in the atomic collisions.”
Like planets orbiting the sun while rotating, an atom's electrons orbit the nucleus while spinning. The nucleus itself also spins, and this spin can be linked, or “coupled” to the electrons' spins. If the nuclear spin is coupled, it (indirectly) participates in collisions with other atoms. If it is not coupled (decoupled), the nuclear spin is uninvolved in these collisions. For decoupled nuclei, their properties give rise to a unique symmetry called SU(n) symmetry, where the strength of the interactions between the atoms is uninfluenced by what nuclear spins are involved in the collisions. “Here n corresponds to the number of nuclear spin states,” Rey added. “In an alkaline earth atom like strontium, it can be up to 10.” In a new paper published in PRX Quantum, Rey and her team of researchers proposed a new method for seeing the quantum effects enabled by SU(n) symmetry in current experimental conditions, something that has been historically challenging for physicists.
The Struggles of Observing SU(n) Symmetric Phases
“The SU(n) symmetry is really quite a unique property which can have tremendous consequences in the quantum world,” Rey said. “Theorists have predicted unique equilibrium states emerging from SU(n) symmetry including what are called quantum spin liquids. Nevertheless, the issue is that the observation of such phases is extraordinarily challenging for experiments because they require extremely low temperatures which at the moment are not attainable [or] accessible.” To work around this challenge, the team proposed to study the quantum dynamics that SU(n) symmetry enables in an out-of-equilibrium setting, with a proposed system havinga very strong synthetic magnetic field, which would affect how the atoms behaved, allowing for more fine tuning.
A Quantum Traffic Jam
Imagine the quantum world as a road, where each atom is a car taking up space. Rey and her team considered a lattice filled with many atoms, meaning that the road was full of cars. Normally they can’t get past each other because their interactions are too strong—almost like a traffic jam. But the nuclear spin can help. Rey elaborated: “Because we have at hand up to n=10 nuclear spin levels for these atoms, we decided to look at them as an additional dimension, i.e., a synthetic dimension. More specifically, if we imagine the atoms are confined to move along a one-dimensional array of wells, then the combination of the spatial 1-D array and then-internal [nuclear spin states] levels can be visualized as a synthetic n-leg ladder.” So, the nuclear spin states can be thought of as additional lanes on the road, which can help clear the jam. Under the right conditions (resonances of the magnetic field) the interactions, or “collisions”, can even make it easier for the atoms to get past each other.
The team proposed using laser beams to couple the nuclear spins in such a way that they act as if they were charged particles in a magnetic field—the field enables the atoms to change their spin when they move, allowing them to “change lanes”. “Using lasers, we could emulate a magnetic field that pierces through this ladder,” said Mikhail Mamaev, first author and graduate student in Rey's group. “So, when you've got a synthetically 2-D system with magnetic fields, the typical signature is that of chiral flow. If I have this ladder, stuff on top of the ladder will flow one way, and stuff on the bottom of the ladder will flow in the equal and opposite way.” This means that the researchers can predict the particles’ movements. Mamaev continued: “Near the resonances enabled by interactions, which happen when atoms are driven at the right conditions, they can move past each other by trading the driving energy for interaction energy, and feature such asymmetric flow patterns in response to the magnetic field.” Looking at the interactions in the quantum traffic jam, the researchers found that the particles could move around each other by switching energies. With their proposed new method, Rey and her team offered a new way to study the role played by SU(n) symmetry interactions that allow atoms to pick any lane they want.
Digging Into the Quantum Hall Effect
For decades, physicists have been interested in a process called the quantum Hall effect. “It's a phenomenon where a transverse electric field develops in a solid material when it carries an electric current and is placed in a magnetic field that is perpendicular to the current,” stated Rey. “In the quantum version of the Hall effect, the longitudinal current features a series of spikes, or resonances at certain values of magnetic field. That means at specific values of the magnetic field, electrons become mobile and generate a special current of their own.” The researchers found a similar process within their simulations when considering SU(n) symmetric interacting cold atoms in synthetic magnetic fields. “We found that at specific values of the laser intensity used to engineer the effective magnetic field, atoms become free to move. These ‘resonances’ resemble the ones found not only in the quantum Hall effect but also in what is called the fractional quantum Hall effect that emerges when electrons are strongly interacting,” Rey said.
Thanks to this new method, the researchers have proposed a work-around for the required cold temperatures needed in these types of experiments, making the study of SU(n) quantum interactions more accessible. As Mamaev added: “We did a lot of work in trying to translate how our theoretical predictions could be implemented in the state-of-the-art experiments that we have here at JILA and elsewhere.”
Written by Kenna Castleberry, JILA Science Communicator