Prethermal ripplons in quenched binary Bose-Einstein condensates

In the quiet world of quantum physics, where atoms behave less like solid marbles and more like overlapping waves, scientists have long relied on a simple rule: given enough time, a chaotic system will eventually settle down into a calm, predictable state called thermal equilibrium. This is the state where energy is shared equally among all parts of a system, like a cup of coffee cooling until it matches the temperature of the room. However, nature sometimes takes a detour. Before reaching that final calm, many systems get stuck in a long-lasting, semi-stable condition known as a prethermal state. In this phase, the system appears to have settled, yet it holds onto a memory of its initial chaos, refusing to share its energy fairly. Understanding why and how these systems get stuck is a fundamental challenge, offering clues to everything from the early moments of the universe to the behavior of complex materials.

A team of researchers at the Joint Quantum Institute and the National Institute of Standards and Technology has now captured this phenomenon in action, observing it within a cloud of ultra-cold atoms. They created a scenario where two distinct types of atoms, which naturally repel each other, were forced to share a space. When the conditions were suddenly changed, these atoms did not simply mix or separate instantly. Instead, they formed a sharp boundary, a one-dimensional interface, between two large domains. This boundary was not a static wall; it rippled and wavered with waves known as ripplons. By watching these waves evolve over time, the scientists discovered that the interface entered a prethermal state that defied the usual rules of energy sharing.

The experiment began with a cloud of about 1.6 million sodium atoms, cooled to temperatures near absolute zero and trapped in a flat, square-shaped box. Initially, all the atoms were in the same quantum state. The researchers then used a microwave pulse to split the cloud into two equal groups of atoms that were mutually incompatible, like oil and water. These two groups immediately began to separate, forming random droplets that merged and grew until two large, distinct domains emerged on opposite sides of the box. The boundary between them was the focus of the study. As the atoms settled, the interface between the two domains began to fluctuate, creating waves of different sizes. The researchers measured the height of this boundary with extreme precision, tracking how these waves changed over a period of up to four seconds.

What they found was a striking split in behavior. The waves on the interface came in many sizes, from very short, tight ripples to long, sweeping undulations. The short, high-frequency ripples quickly lost their energy to the surrounding cloud of atoms, settling into a temperature that matched the bulk of the gas. However, the long, low-frequency waves behaved differently. These large ripples remained hot, holding onto significantly more energy than the rest of the system, even after the researchers waited for a long time. The system had reached a state where the small waves were calm, but the large waves were still agitated, creating a long-lived prethermal configuration.

To understand this, the scientists had to look at how energy moves between these waves and the surrounding atoms. In a typical system, energy flows freely until everything is the same temperature. Here, the rules of motion prevented that flow for the large waves. The researchers found that the large ripples were kinematically isolated. This means that the laws of physics governing their movement made it impossible for them to easily transfer their energy to the surrounding atoms through the usual collision-like processes. The energy required to make a large ripple give up its heat did not match the energy available in the surrounding atoms, creating a mismatch that blocked the transfer. It is similar to trying to push a heavy boulder with a gentle breeze; the breeze simply cannot move the stone, no matter how long it blows.

The team confirmed this isolation by measuring the temperature of the waves directly. They found that the temperature of the large ripples was much higher than the temperature of the surrounding gas, while the small ripples had cooled down to match the gas. They also ruled out other possibilities, such as the waves forming a special, coherent state like a laser beam, by showing that the waves followed a standard statistical pattern, just with the wrong temperature. The data showed that the large waves decayed incredibly slowly, with a measured time of about five seconds to relax, which is vastly longer than the time it took for the small waves to settle.

This discovery provides a clear, experimental example of how a system can get stuck in a prethermal state not because it is perfectly ordered, but because the specific ways energy can move are blocked by the geometry of the system itself. The researchers observed that the interface between the two atomic domains acted as a subsystem that was effectively cut off from the rest of the world for a significant period. While the small waves found a path to equilibrium, the large waves remained trapped in a state of elevated energy, waiting for a rare, complex interaction to finally allow them to cool down.

The work highlights a fundamental aspect of quantum mechanics: even in a system that is not perfectly isolated, certain parts can remain out of equilibrium for a long time if the pathways for energy exchange are blocked. The researchers noted that while they have identified the mechanism for this slow relaxation, the exact processes that initially created this prethermal state and the full details of how it eventually decays remain open questions. They suggest that the answer may lie in how individual waves lose their phase coherence or mix with one another within the prethermal group. By providing a clean, controllable platform to study these dynamics, this experiment opens a new window into understanding how complex quantum systems approach equilibrium, a process that is central to the behavior of matter at the smallest scales.