Spatial delocalization of cold oscillators in hollow-core fibers

In the quiet world of quantum physics, scientists often try to make things as still as possible. By cooling tiny objects to temperatures near absolute zero, they can freeze out the random jiggling caused by heat, allowing the object to behave more like a wave than a particle. This state of extreme stillness is the starting point for some of the most sensitive measurements ever conceived, capable of detecting forces as faint as a single atom's touch. However, to measure these tiny forces even better, researchers sometimes need to do the opposite: they must deliberately make the object's position uncertain. By spreading the object's location out over a wider area, they can amplify its response to external pushes, effectively turning up the volume on the signal they are trying to hear. This counterintuitive strategy, known as delocalization, is a powerful tool for pushing the limits of what can be measured, but it is notoriously difficult to control without losing the object entirely.

A team of researchers at the Max Planck Institute for the Science of Light and TU Darmstadt has now demonstrated a way to master this delicate balance using a suspended glass bead inside a hollow fiber. Their work, published in a recent study, shows how to take a nanoparticle that has been cooled to a near-motionless state and stretch its position uncertainty by a factor of more than twenty, all while keeping it trapped and stable. The experiment centers on a tiny silica sphere, just 234 nanometers across, which is levitated inside a hollow-core photonic crystal fiber. This fiber acts as a microscopic tunnel that guides laser light, creating a pattern of bright and dark stripes, or fringes, along its length. The particle gets trapped in the bright stripes, held in place by the gentle push of the light.

The researchers began by cooling the particle's movement in two directions at once: along the length of the fiber and side-to-side across it. They achieved this by using feedback loops that sensed the particle's motion and adjusted the laser light to act like a brake, slowing the particle down until its temperature dropped to just a few degrees above absolute zero. Once the particle was this cold, the team set out to stretch its position. They tried two different methods to achieve this, both of which relied on manipulating the light pattern without changing the overall power of the laser.

In the first approach, the team quickly rotated the polarization of the laser beams, which effectively weakened the grip of the trap along the fiber's length for a brief moment. This sudden change caused the particle's position to spread out, much like a spring that is suddenly allowed to expand. The particle's position variance increased by 11.83 decibels relative to its initial cold state. Crucially, the particle remained in a predictable, bell-curve distribution, meaning its motion was still Gaussian and could be described by standard statistics. This state lasted only a short time before the particle settled back down, but the measurement confirmed that the stretching was real and controllable.

The second method proved even more effective. Instead of weakening the trap, the researchers used rapid phase control to move the particle from a bright stripe of light to a dark one. In the dark fringe, the light intensity is nearly zero, and the optical forces create an inverted potential, meaning the particle is pushed away from the center rather than pulled toward it. This inverted landscape causes the particle to accelerate away from its starting point exponentially. The team moved the particle into this dark zone for a tiny fraction of a microsecond, then quickly moved it back to a bright zone before it could escape. By repeating this cycle of moving the particle into the dark and back to the bright, they accumulated the stretching effect. This technique increased the position variance by 13.23 decibels, a significant improvement over the first method.

The researchers found that if they pushed this process even further, the particle began to explore the edges of the light trap where the forces are no longer perfectly linear. This led to a third outcome: the creation of a non-Gaussian state. In this regime, the particle's position distribution developed curved, fanning tails, indicating that the simple rules of a harmonic oscillator no longer applied. The team confirmed this behavior by comparing their experimental data with complex simulations of the nonlinear forces at play, finding a precise match between the two.

This work is significant because it demonstrates a new level of control over levitated particles without needing complex auxiliary traps or electrically charged particles, which are often sensitive to stray electric fields. The ability to rapidly switch between a tightly held state and a widely delocalized state inside a fiber opens the door to more sensitive force detectors. For instance, the 13-decibel increase in position variance corresponds to a nearly fivefold improvement in the ability to detect tiny forces. Furthermore, the dark fringe technique offers a unique way to measure position without disturbing the particle's momentum, a feature that could be vital for future experiments aiming to create large-scale quantum superpositions. The study establishes hollow-core fibers as a versatile platform for these advanced optomechanical experiments, proving that the delicate art of stretching a quantum state can be performed with high precision and reliability.