Imaginary Barrier, Real Transfer: Non-Hermitian Dynamical Tunnelling

In the quantum world, particles do not behave like billiard balls rolling to a stop; they behave like waves that can slip through walls they should not be able to cross. This strange ability, known as tunneling, is a fundamental feature of nature. Imagine a ball trapped in a valley. In our everyday experience, if the ball does not have enough energy to roll over the hill separating it from a neighboring valley, it stays put. In the quantum realm, however, there is a chance the particle will simply appear on the other side, having passed through the barrier without ever climbing it. This usually happens when a barrier is solid and real, like a wall of rock. But what happens if the barrier is not solid at all, but instead acts like a sponge that swallows anything that touches it? This is the question researchers at Imperial College London set out to answer, exploring a version of quantum mechanics where energy can be lost, or absorbed, rather than just conserved.

The study focuses on a specific setup: a particle trapped in a symmetric container, like a valley with two sides, but with a twist. In the center, instead of a solid wall, there is a region designed to absorb the particle. In the language of physics, this is an "imaginary" barrier, a mathematical description of a place where the particle disappears if it gets too close. The researchers wanted to know if a particle starting on one side of this absorbing zone could still make its way to the other side, and if so, how it would behave differently from the standard tunneling we already know. They found that the answer is yes, but the journey is not the familiar back-and-forth oscillation seen in standard quantum systems. Instead, the particle undergoes a slow, one-way drift toward a state of balance, moving from one side to the other while carefully avoiding the middle.

To understand this, the team first looked at a particle trapped in a smooth, bowl-shaped potential, similar to a marble rolling in a curved dish, but with a Gaussian-shaped absorption zone in the very center. They simulated the behavior of this system using a computer, increasing the strength of the absorption to see how the particle reacted. As the absorbing region became stronger, it effectively acted like a wall, splitting the single bowl into two separate valleys. In this split state, the particle could exist in two special forms: one where it is symmetrically balanced, and one where it is antisymmetric, with a slight difference in how long each form lasts before being absorbed. When the researchers started with a particle on just one side, they observed a fascinating dynamic. The particle did not simply bounce back and forth between the two sides as it would with a solid wall. Instead, it slowly relaxed into a state where it was equally likely to be found on either side. Throughout this process, the particle spent very little time in the dangerous, absorbing middle. It moved from one side to the other not by crashing through the center, but by evolving into a stable configuration that naturally distributed its presence across both sides.

The researchers confirmed that this behavior was not unique to the smooth bowl shape. They repeated the experiment with a different setup: a particle in a box with a rectangular absorbing region in the middle. The results were the same. The particle started on one side, avoided the center, and eventually settled into an equal distribution across the two outer sections. To explain why this happens so clearly, the team built a simplified model using a grid of just three points: a left spot, a middle spot, and a right spot. In this model, the middle spot was the absorber. By solving the equations for this tiny system, they showed that the initial state, which is entirely on the left, naturally transforms over time. The part of the particle that would have been absorbed dies away quickly, while the remaining part slowly shifts until it is shared equally between the left and right spots. This minimal model captured the essence of the phenomenon, proving that the effect is a fundamental consequence of having a lossy barrier in a symmetric trap.

Finally, the team proposed a way to see this effect in the real world using light. They suggested an experiment using a special glass structure called a waveguide, which channels light much like a pipe channels water. By designing a waveguide with a central strip made of metal, they could create a region that absorbs light, mimicking the imaginary barrier. In their calculations, they showed that if they sent a beam of light into the left side of this waveguide, the light would not just get stuck or vanish immediately. Instead, as it traveled down the waveguide, the light would gradually spread out, eventually appearing with equal intensity on both the left and right sides of the absorbing strip, while the strip itself remained relatively dim. They calculated that this transition would happen over a distance of about one hundred micrometers to one centimeter, a scale that is easily achievable in a laboratory. This proposal turns a theoretical curiosity into a tangible experiment, suggesting that we can watch light perform this non-standard tunneling dance right before our eyes.

The significance of this work lies in how it changes our understanding of barriers. In the standard quantum world, a barrier causes a particle to oscillate, moving back and forth between two sides. In this non-standard world, where the barrier absorbs energy, the oscillation stops, and the system settles into a calm, balanced state. The particle does not fight the barrier; it adapts to it, finding a way to exist on both sides without ever truly occupying the dangerous middle. This discovery reveals a new kind of stability in systems that lose energy, showing that even in the presence of a sink that eats away at existence, order and balance can emerge. It suggests that in the right conditions, loss can act as a guide, steering a system toward a specific, shared state rather than destroying it entirely. The researchers have not just found a new equation; they have identified a new way for nature to behave when the rules of conservation are relaxed, opening the door to observing these subtle shifts in the behavior of light and matter.