The gauge coupled two-body problem in a ring

TL;DR

This paper investigates a two-particle quantum system on a ring with gauge-mediated long-range interactions, revealing ground states with non-zero angular momentum and position-dependent correlations, and explores measurement effects on the system.

Contribution

It introduces a model of two particles with gauge interactions on a ring, analyzing their ground states, correlations, and measurement-induced state preparation, which is novel in this context.

Findings

Ground state can have non-zero angular momentum under strong interactions.

Particles exhibit position-dependent correlations, favoring proximity or separation.

Measurement of one particle can prepare the other in a non-dispersive state.

Abstract

We study the properties of two quantum particles which are confined in a ring. The particles interact via a long-range gauge potential proportional to the distance between the particles. It is found that the two-body ground state corresponds to a state with non-zero angular momentum provided that the interaction between the particles is strong enough. In addition, the particles are correlated in the sense that depending on the interaction strength there is a propensity to be found close together or separated in the ring. We discuss the effect of measuring the position of one of the particles and thereby removing the particle from the ring, where we show that the remaining particle can be prepared in a non-dispersive state with non-zero angular momentum.