Bound-state spectrum of an impurity in a quantum vortex

TL;DR

This paper investigates the bound-state energy spectrum of an impurity in a 2D Bose-Einstein condensate with a vortex, highlighting finite bound states and potential applications in quantum computing and turbulence studies.

Contribution

It provides approximate energy level expressions for impurities in vortex-supporting condensates, linking topological features to bound-state accessibility and quantum information applications.

Findings

Finite number of bound states due to condensate size

Impurity states influenced by vortex topological quantization

Potential platform for qubits and turbulence studies

Abstract

We consider the problem of finding the bound-state spectrum of an impurity immersed in a weakly interacting two-dimensional Bose-Einstein condensate supporting a single vortex. We obtain approximate expressions for the energy levels and show that, due to the finite size of the condensate, the impurity can access only a finite number of physical bound states. By virtue of the topological quantization of the vorticity and of the emergence of the Tkachenko lattice, this system is promising as a robust and scalable platform for the realization of qubits. Moreover, it provides a potentially new paradigm for polaron physics in Bose-Einstein condensates and a glimpse towards the study of quantum turbulence in low-dimensionality systems.