Tunable Mpemba Effect in a Prethermal Many-Body Spin Network

Imagine a world where the rules of "getting back to normal" are flipped on their head. In physics, this is the realm of nonequilibrium dynamics, a field that studies how messy, energetic systems settle down into a calm, balanced state. Usually, we assume that if you start closer to the finish line, you'll get there first. But nature loves a plot twist. Enter the Mpemba effect, a counterintuitive phenomenon where a system that starts further away from equilibrium can actually race past one that started closer to it. Think of it like two runners: one starts just a few steps from the finish line but is wearing heavy, dragging boots, while the other starts miles away but is sprinting with perfect form. Surprisingly, the sprinter from far away might cross the finish line first. Scientists have seen this in things like freezing water, but they've been hunting for it in the complex, crowded world of interacting particles, where the "runners" are constantly bumping into each other and changing the rules of the race. Understanding this isn't just a party trick; it's key to figuring out how to control quantum systems, speed up computer resets, and keep delicate quantum sensors stable.

Now, let's dive into a new experiment where researchers at UC Berkeley and Lawrence Berkeley National Laboratory decided to play this race with a network of tiny atomic magnets inside a diamond. They didn't use water or ice; they used a 13C nuclear-spin network—a vast, disordered crowd of carbon-13 atoms acting like tiny spinning tops, all jostling together inside a diamond crystal. The team discovered that they could make these atomic tops behave like the Mpemba runners, and they could even tune exactly when the "slow" runner would overtake the "fast" one.

Here's how they set the stage. Inside the diamond, there are two types of "troublemakers": Nitrogen-Vacancy (NV) centers and P1 centers. These are defects in the crystal that act like magnets, creating a chaotic landscape. Some spots in the diamond are packed with these defects, making them "hot zones" where the spinning atoms relax (lose their energy) very quickly. Other spots are far away from the defects, acting as "safe zones" where the atoms can spin for a long time without getting tired.

The researchers used a clever two-step preparation game to set up their runners. First, they used light to "hyperpolarize" the atoms near the defects, giving them a huge burst of energy. This is like loading the runner near the finish line with heavy, dragging boots (a lot of energy, but in a bad spot). Then, they had two choices:

1. The "Wait" Game: They could let the system sit for a while. During this wait, the atoms near the defects would quickly lose their energy (relax), while the atoms in the safe zones would keep their energy. This effectively moved the "energy" away from the troublemakers and into the safe zones.
2. The "No Wait" Game: They could skip the wait and immediately start the race. In this case, the energy stayed concentrated near the defects, where it was destined to vanish quickly.

The experiment involved shuttling the diamond to a high magnetic field and watching how the atoms relaxed using a special "Floquet driving" technique (a rhythmic pulse sequence) that kept the system in a prethermal regime. This is a special state where the system stays "warm" and active for a long time before finally cooling down to total equilibrium.

The results were a clear victory for the Mpemba effect. When they compared a state prepared with a long "hyperpolarization" time but no "wait" (lots of energy stuck near the fast-relaxing defects) against a state prepared with a long "wait" time (less total energy, but safely tucked away in the slow-relaxing zones), something amazing happened. The state with more energy started far from equilibrium, but because it was stuck in the "hot zones," it lost its energy rapidly. The state with less energy started closer to equilibrium, but because it was hiding in the "safe zones," it held on to its energy much longer.

The "farther" runner overtook the "closer" runner! The researchers observed these Mpemba crossings happening reproducibly. Even cooler, they could tune the exact moment this crossover happened. By adjusting the preparation times, they could shift the crossing point from a few seconds into the long, stable prethermal plateau, tuning the time over several orders of magnitude.

To understand why this happened, the team ran semiclassical simulations. They found that the system has specific "modes" or patterns of relaxation. There is a "slowest mode" that lives in the defect-poor regions of the diamond. If your initial state (your runner) has a lot of overlap with this slow mode, it will last a long time. If your initial state is mostly in the defect-rich regions, it will vanish quickly, regardless of how much total energy it started with. The paper shows that the crossing time is determined by how much your starting state overlaps with this slow, safe mode.

The authors confirm that this isn't just a fluke of how they measured the data. They checked their results using a rigorous mathematical metric called Kullback–Leibler (KL) divergence, and the crossings happened at the same time, proving the effect is real and not an artifact of their measurement method.

In short, this paper demonstrates that in a disordered, interacting network of spins, disorder is a resource. By understanding where the "safe zones" and "danger zones" are, and by carefully preparing the initial state, scientists can control how fast a system relaxes. They showed that you can engineer a situation where a system that looks like it's losing the race actually wins it, and they can dial that victory time up or down at will. This work marks the first observation of the Mpemba effect in an extended many-body spin network and the first experimental demonstration of these dynamics in a prethermal state, offering a new toolkit for controlling relaxation in complex quantum materials.