# Dynamical stabilization of two-dimensional trapless Bose-Einstein condensates by three-body interaction and quantum fluctuations

## TL;DR

This paper investigates how three-body interactions and quantum fluctuations can stabilize two-dimensional trapless Bose-Einstein condensates, combining analytical variational methods with numerical simulations to identify conditions for stability.

## Contribution

It introduces a combined analytical and numerical study showing stabilization of 2D trapless BECs via three-body interactions and quantum fluctuations, including effects of rapid temporal modulation.

## Key findings

- Quantum fluctuations enable stabilization without oscillatory nonlinearities.
- Three-body interactions enhance the stability of 2D trapless BECs.
- Numerical simulations confirm analytical stability predictions.

## Abstract

Analyzing a Gross-Pitaevskii equation with cubic, quartic, and quintic nonlinearities through analytical and numerical methods, we examine the stability of two-dimensional (2D) trapless Bose-Einstein condensates (BECs) with two-, three-body interactions and quantum fluctuations. Applying a variational approach, we derive the equation of motion and effective potential to discuss in detail the stability of the BECs in 2D free space. We show that with the aid of quantum fluctuations it is possible to stabilize 2D trapless BEC without any oscillatory nonlinearities. Also, there is an enhancement of the stability of the system, due to the inclusion of the three-body interaction and quantum fluctuations in addition to the two-body interaction. We further study the stability of 2D trapless BECs with rapid periodic temporal modulation of scattering length by using a Feshbach resonance. We discuss all possible ways of stabilization of trapless BECs in 2D by three-body interaction and quantum fluctuations. Finally, we verify our analytical results with numerical simulation using split-step Crank-Nicholson method. These match well with the analytical predictions.