Dipolar Droplets at 3D-1D Crossover

TL;DR

This paper studies how beyond-mean-field effects stabilize dipolar Bose gases in elongated traps, leading to the formation of quantum droplets through an effective three-body repulsion.

Contribution

It demonstrates that beyond-mean-field corrections in quasi-1D dipolar gases create a stabilizing energy term proportional to density cubed, crucial for droplet formation.

Findings

Beyond-mean-field effects significantly alter the ground state.

Effective three-body repulsion stabilizes the gas.

Quantum droplets form in elongated dipolar gases.

Abstract

We investigate beyond-mean-field corrections to the energy of an elongated homogeneous Bose gas strongly confined in two directions, with dipoles aligned along the long axis of the system. When the dipolar interaction reaches its critical strength, the mean-field approach predicts instability. However, similar to the free-space case, beyond-mean-field effects significantly alter the ground state of the system, leading to the formation of a self-bound atomic cloud known as a quantum droplet. Our analysis demonstrates that the beyond-mean-field contribution to the energy in the quasi-1D region, in addition to the confinement induced shift of the mean field energy, is proportional to the third power of the density $\sim n^3$. Therefore, it can be interpreted as an effective three-body repulsion that stabilizes the gas, preventing collapse and leading to a finite-density solution. We also show that the same effect plays a crucial role in the binding of strongly elongated dipolar droplets under harmonic confinement.