Quantum Dynamics of a Single Vortex

An explanation of the basic ideas and our experimental findings

written by Andreas Wallraff

Vortices ...
... macroscopic objects in a quantum world

Vortices do appear naturally in a wide range of gases and fluids. One can observe a vortex for example when water funnels in a circular motion into the drain of a filled bath tub after pulling the plug. Or, for example, during storms when tornados, which are extremely large vortices, do form. But vortices also exist on very small scales, e.g. in quantum liquids such as superfluid Helium, ultra-cold atomic gases or in superconductors in which vortices have properties governed by the laws of quantum physics, which sometimes has bizarre and non-intuitive implications.

The size of a vortex is characterized by the total current of particles circulating around the center of the vortex, its core. In quantum liquids vortices do not come in arbitrary sizes but do only exist in a quantized set of sizes. The smallest vortex has a single quantum. No smaller vortex can exist in a homogeneous quantum liquid. All bigger vortices have integer multiples of the size of the smallest vortex. Quantization of the vortex size occurs because the liquid is forced by the laws of quantum mechanics into a circulating lock-step motion around the vortex core.

In our experiment we have generated a single quantum vortex in a small doughnut-shaped sandwich made from two ring-shaped superconducting electrodes of 100 micron diameter which are separated by a very thin dielectric film. In this system we were able to confine the vortex into a potential well using a small magnetic field. The vortex in the potential well behaves essentially like a marble in a bowl. If one displaces the marble from the center of the bowl it will roll back to its center in an oscillatory motion.

We have then very carefully experimentally investigated the dynamics of such a vortex trapped in a potential well at very low temperatures. We have observed that, when the vortex oscillates at the bottom of the well, it will do so only with a discrete set of amplitudes allowed by the laws of quantum mechanics. Similarly to the fact that vortices themselves exist only in a quantized set of sizes, at low temperatures they can also only oscillate with a certain discrete set of amplitudes in the potential. We have observed this property of the vortex by kicking it with microwave radiation from one of its oscillatory states to the other.

Also, as we have lowered one of the edges of the potential well (corresponding to a tilt of the bowl), we have been able to watch the vortex escaping from the well by tunnelling through the side-wall of the well. I.e. the vortex can escape from the well even though the amplitude of its oscillations are to small to overcome the top of the barrier. This process is allowed for our tiny vortices by the rules of quantum mechanics.

These genuinely quantum mechanical properties in the dynamics of a single isolated vortex have been observed for the first time in our experiments. Our experiments will help scientist to better understand the low temperature properties of vortices and materials containing vortices. On the one hand, vortices frequently limit the performance of superconducting materials or devices such as superconducting films used for current transport, sensitive magnetic field sensors (SQUIDs) or other superconducting electronics. On the other hand, the controlled quantum dynamics of vortices may also open a feasible path towards building elements for a quantum computer based on the observed phenomena.