Squeezing the Efimov effect

TL;DR

This paper develops a framework to study the Efimov effect in three-body quantum systems as the spatial dimensionality is continuously varied from three to one, using mass imbalance and harmonic confinement.

Contribution

It introduces a novel approach to analyze the Efimov effect across different dimensions by continuously tuning the system's geometry with experimental relevance.

Findings

Efimov states can be studied as a function of dimensionality

The framework applies to mass-imbalanced systems in harmonic traps

Dimensional crossover impacts the existence of Efimov states

Abstract

The quantum mechanical three-body problem is a source of continuing interest due to its complexity and not least due to the presence of fascinating solvable cases. The prime example is the Efimov effect where infinitely many bound states of identical bosons can arise at the threshold where the two-body problem has zero binding energy. An important aspect of the Efimov effect is the effect of spatial dimensionality; it has been observed in three dimensional systems, yet it is believed to be impossible in two dimensions. Using modern experimental techniques, it is possible to engineer trap geometry and thus address the intricate nature of quantum few-body physics as function of dimensionality. Here we present a framework for studying the three-body problem as one (continuously) changes the dimensionality of the system all the way from three, through two, and down to a single dimension. This is done by considering the Efimov favorable case of a mass-imbalanced system and with an external confinement provided by a typical experimental case with a (deformed) harmonic trap.