Suppression of quantum-mechanical collapse in bosonic gases with intrinsic repulsion: A brief review

TL;DR

This review summarizes theoretical work on preventing quantum collapse in bosonic gases with attractive potentials by using repulsive interactions, highlighting the creation of stable ground states and metastable modes in various dimensions.

Contribution

It consolidates existing theoretical analyses showing how repulsive interactions suppress collapse and enable stable states in bosonic gases under attractive potentials.

Findings

Collapse can be suppressed in 3D with repulsive contact interactions.

In 2D, quintic or effective quartic repulsion prevents collapse.

Metastable self-trapped states exist in many-body systems despite incomplete suppression.

Abstract

It is well known that attractive potential which is inversely proportional to the squared distance from the origin gives rise to the critical quantum collapse in the framework of the three-dimensional (3D) linear Schroedinger equation. This article summarizes theoretical analysis, chiefly published in several original papers, which demonstrates suppression of the collapse caused by this potential, and the creation of the otherwise missing ground state in a 3D gas of bosonic dipoles pulled by the same potential to the central charge, with repulsive contact interactions between them, represented by the cubic term in the respective Gross-Pitaevskii equation (GPE). In two dimensions (2D), quintic self-repulsion is necessary for the suppression of the collapse; alternatively, this may be provided by the effective quartic repulsion, produced by the Lee-Huang-Yang correction to the GPE. 3D states carrying angular momentum are constructed in the model with the symmetry reduced from spherical to cylindrical by an external polarizing field. Interplay of the collapse suppression and miscibility-immiscibility transition is considered in a binary condensate. The consideration of the 3D setting in the form of the many-body quantum system, with the help of the Monte Carlo method, demonstrates that, although the quantum collapse cannot be fully suppressed, the self-trapped states, predicted by the GPE, exist in the many-body setting as metastable modes protected against the collapse by a tall potential barrier.