Spatial correlations of vortex quantum states

TL;DR

This paper investigates the spatial correlations of vortex quantum states across different quantum statistics, revealing unexpected behaviors such as bimodal distributions and spatial condensation effects in bosons and fermions.

Contribution

It introduces a formalism to analyze spatial correlations of vortices in quantum states, applicable to various platforms like optical vortices and microcavity polaritons, uncovering novel phenomena.

Findings

Bosons can exhibit bimodal distance distributions, placing them farther apart than fermions in over 40% of cases.

Spatial correlations can mimic behaviors of coherent states, concealing quantum statistical differences.

The formalism applies to experimental setups in extreme environments, enhancing understanding of quantum vortex behavior.

Abstract

We study spatial correlations of vortices in different quantum states or with Bose or Fermi statistics. This is relevant for both optical vortices and condensed-matter ones such as microcavity polaritons, or any platform that can prepare and image fields in space at the few-particle level. While we focus on this particular case for illustration of the formalism, we already reveal unexpected features of spatial condensation whereby bosons exhibit a bimodal distribution of their distances which places them farther apart than fermions in over 40% of the cases, or on the opposite conceal spatial correlations to behave like coherent states. Such experiments upgrade in the laboratory successful techniques in uncontrolled extreme environments (stars and nuclei).