Inferring rotations using a bosonic Josephson junction

In the quiet, frigid realm of ultracold atoms, where matter behaves less like a solid and more like a single, giant wave, rotation is a powerful force that reshapes reality. When scientists spin these clouds of atoms, they do not just create a whirlwind; they alter the fundamental rules of how the particles move and interact. This phenomenon allows researchers to create exotic states of matter, such as tiny tornadoes of atoms called quantized vortices, and to simulate complex cosmic events in a laboratory setting. Beyond these exotic states, the ability to measure rotation with extreme precision is a practical necessity for navigation, guiding everything from spacecraft to consumer electronics. For decades, the most accurate sensors have relied on light traveling in loops, but these devices are often large and limited by their physical size. This has driven physicists to look toward quantum systems, where the sensitivity of individual atoms might offer a path to smaller, more precise instruments that can detect even the slightest turn.

A new theoretical study explores how a specific quantum setup, known as a bosonic Josephson junction, can serve as such a sensor. Imagine a container holding a cloud of ultra-cold atoms, shaped into two distinct valleys or "wells" separated by a small hill. In a stationary world, atoms can quantum mechanically tunnel through this hill, moving back and forth between the two valleys in a rhythmic, predictable pattern. The researchers investigated what happens when this entire system is placed on a rotating platform. They found that the act of rotation fundamentally changes the rhythm of this tunneling, creating a unique signature that reveals exactly how fast the system is spinning. By analyzing the motion of the atoms, the team demonstrated that one could deduce the rotation speed, the distance of the setup from the center of rotation, and even the orientation of the setup, simply by watching how the atoms tunnel.

The study began with the simplest scenario: a double-well container perfectly centered on the axis of rotation. In this balanced state, the rotation acts like a centrifugal force, effectively pushing the atoms away from the center and raising the hill between the two valleys. As the rotation speed increases, this hill becomes higher, making it harder for the atoms to cross over. The researchers observed that the time it takes for the atoms to complete a full cycle of tunneling increases dramatically as the spin speeds up. Specifically, the duration of this cycle grows exponentially with the rotation frequency. At the same time, the atoms begin to acquire a sideways momentum and a spinning motion, or angular momentum, that also increases with the rotation. By measuring how long the tunneling cycle takes or how much angular momentum the atoms possess, a scientist could calculate the rotation speed directly. The study showed that this method is particularly effective at higher rotation speeds, where even a tiny change in spin causes a noticeable shift in the tunneling rhythm.

The researchers then moved to a more complex situation where the double-well container was shifted away from the center of rotation. In this off-center position, the two valleys are no longer equidistant from the spinning axis. One valley is closer to the center, and the other is farther away, causing the centrifugal force to push harder on the farther side. This creates an effective tilt, making one valley deeper than the other. This asymmetry changes the tunneling behavior significantly. Instead of a clean back-and-forth rhythm, the atoms tend to get stuck, or "self-trapped," in the deeper valley. The study found that the amount of time the atoms spend stuck in one valley increases exponentially with both the rotation speed and the distance of the container from the center. Furthermore, the average spinning motion of the atoms changes in a predictable way: it grows linearly with the rotation speed but increases with the square of the distance from the center. These distinct patterns allow an observer to determine not just how fast the system is spinning, but also exactly how far the container is displaced from the rotation axis.

The final layer of complexity involved the orientation of the off-center container. If the container is shifted but rotated at an angle relative to the direction of the spin, the effect of the centrifugal force changes. When the tunneling path is aligned with the direction of the spin, the tilt is strongest, and the atoms get trapped easily. When the tunneling path is perpendicular to the spin, the tilt has no effect on the tunneling direction, and the atoms move freely as if they were centered. The researchers discovered that the degree of trapping follows a smooth, bell-shaped curve as the angle changes. By measuring how much the atoms are trapped or how their angular momentum behaves at different angles, one can infer the precise orientation of the container. This sensitivity to direction adds another dimension to the sensor's capabilities, allowing it to map out the geometry of the rotation relative to the trap.

To ensure these findings were robust, the team performed calculations using two different levels of theory. The first approach treated the atoms as a single, smooth fluid, which is a standard approximation for large groups of atoms. The second approach treated each atom individually, accounting for the complex interactions and correlations between them. Both methods agreed on the main results: rotation strongly modifies the tunneling dynamics, and these modifications provide a clear window into the rotation's properties. The many-body analysis revealed that the way the atoms spread out or "deplete" from their initial state also depends heavily on the rotation and the orientation of the trap, offering yet another way to measure the spin. The study also considered a realistic scenario where the rotation is turned on gradually rather than instantly. They found that the way the system responds during this transition depends sensitively on how quickly the spin is applied, providing additional dynamic signatures that can be used to assess the rotation frequency.

Ultimately, this work establishes a comprehensive framework for using the tunneling dynamics of ultracold atoms as a precise rotation sensor. It shows that by observing simple, measurable quantities like the time it takes for atoms to tunnel, their sideways momentum, and their average spin, one can extract detailed information about the rotation frequency, the displacement of the sensor, and its orientation. The findings suggest that bosonic Josephson junctions could offer a viable route toward compact, high-precision rotation sensors that operate on quantum principles. While these results are currently theoretical, derived from detailed simulations rather than physical experiments, they provide a clear roadmap for future work. The study confirms that the interplay between quantum tunneling and rotation creates a rich set of dynamical responses, turning a simple double-well trap into a sophisticated instrument capable of sensing the invisible forces of a rotating world.