Rotation-mediated bosonic Josephson junctions in position and momentum spaces

Imagine a world where atoms, cooled to temperatures near absolute zero, behave not as individual particles but as a single, unified wave of matter. In this state, known as a Bose-Einstein condensate, these atoms can flow without friction, much like a superfluid. Scientists have long been fascinated by how these waves move when they encounter a barrier, specifically when they are trapped in a landscape with two distinct valleys, or "wells." If the barrier between the wells is low enough, the atoms can tunnel through it, moving back and forth in a rhythmic exchange. This phenomenon, called the Josephson effect, is a cornerstone of quantum physics and is already used in highly sensitive devices and quantum computers. For decades, researchers have studied this effect in the physical space where the atoms sit, watching them jump from one side of a trap to the other. However, a newer frontier has emerged: what if the tunneling happens not in physical space, but in the space of momentum, which describes how fast and in what direction the atoms are moving? Until now, creating this kind of momentum-based tunneling required complex setups involving atoms with specific internal magnetic properties.

A team of researchers at the University of Haifa has now discovered a way to create this elusive momentum-space tunneling using a much simpler system: a single type of atom with no special magnetic properties, simply by spinning the entire trap. In their study, they simulated a cloud of ten interacting atoms confined in a double-well trap and set the entire system rotating. They found that while spinning the trap too fast usually stops the atoms from moving between the physical wells, trapping them in place, a clever adjustment to the shape of the trap could overcome this. By slightly modifying the geometry of the trap to counteract the forces created by the spin, they were able to restore the flow of atoms between the physical wells. More surprisingly, this same rotation created a second, invisible tunneling channel. As the system spun, the atoms began to oscillate not just between the left and right physical locations, but also between two distinct states of motion in the sideways direction. The rotation effectively split the atoms' momentum into two separate "wells," creating a Josephson junction in the realm of motion itself.

The researchers began by observing what happens when a double-well trap is simply spun without any special adjustments. They found that as the rotation speed increased, the atoms found it harder and harder to tunnel from one side of the trap to the other. At a specific critical speed, the tunneling stopped completely, and the atoms became stuck in the left well, a state known as self-trapping. This happened because the spinning created a centrifugal force that acted like an additional, impenetrable wall, blocking the path between the two physical valleys. In this scenario, the atoms were frozen in place, and no new momentum-based effects appeared. The team realized that to unlock the potential for momentum tunneling, they needed to neutralize this blocking effect. They devised a protocol where they added a gentle, extra push to the trap's shape, effectively canceling out the extra barrier created by the spin. This adjustment allowed the atoms to resume their physical tunneling, but with a twist: the rotation imprinted a new structure onto their motion.

When the researchers turned on this adjusted protocol and increased the rotation speed, they observed something remarkable. The atoms continued to flow between the left and right physical wells, but simultaneously, they began to oscillate between two different momentum states in the direction perpendicular to the flow. In the language of physics, the rotation had created an effective double-well potential in momentum space. The atoms were no longer just moving back and forth in space; they were also swapping between moving slightly to the left and slightly to the right in their momentum. This dual behavior was confirmed by tracking the average momentum of the atoms. Without rotation, the average sideways momentum was zero. As the rotation speed increased, this average momentum began to oscillate between positive and negative values, indicating that the atoms were tunneling between two distinct states of motion. This effect was visible even when the researchers accounted for the complex interactions between the atoms, showing that the phenomenon was robust and not just a simple average behavior.

The study also explored what would happen if the physical barrier between the two wells were removed entirely, leaving a single, wide valley. Even in this barrier-free environment, the rotation alone was sufficient to generate the momentum-space tunneling. When the system was spun at the right speed, the atoms again split their motion into two distinct momentum states, oscillating back and forth. This finding is significant because it demonstrates that the momentum-space junction is a fundamental consequence of the rotation and the trap's geometry, rather than a result of the physical barrier itself. The researchers noted that this behavior was observed in their computer simulations, which modeled the quantum mechanics of the system with high precision. They compared their results with simpler models that ignore the complex interactions between atoms and found that while the basic pattern held, the full interaction between the atoms caused the tunneling to be slightly less perfect, a detail that highlights the importance of studying these systems with advanced methods.

This work opens a new door for understanding and controlling quantum matter. By showing that a simple rotation can create a Josephson junction in momentum space for a single type of atom, the researchers have provided a new tool for scientists. Previously, such momentum-based junctions were only known to exist in systems with more complex internal structures. Now, it appears that the rotation of the trap itself is enough to engineer these states. This discovery suggests that future quantum devices could be built using these rotating traps to create stable, tunable junctions that operate in both physical space and momentum space. The ability to control the flow of atoms in these two different realms simultaneously could lead to more sensitive quantum sensors and new types of quantum mechanical devices. The researchers emphasize that while their findings are currently based on simulations, they offer a clear blueprint for experimentalists to try this in the lab, potentially bringing these momentum-space effects into the realm of observable reality.