Consistent theory of self-bound quantum droplets with bosonic pairing

TL;DR

This paper refines the theoretical understanding of quantum droplets in ultracold Bose-Bose mixtures by incorporating bosonic pairing into Bogoliubov theory, resolving previous inconsistencies and aligning predictions with recent experimental and simulation results.

Contribution

It introduces bosonic pairing into Bogoliubov theory for quantum droplets, providing a more consistent framework that explains observed properties and resolves prior theoretical loopholes.

Findings

Equilibrium density of droplets decreases with bosonic pairing.

The theory aligns with diffusion Monte Carlo simulation results.

Provides insights into the low critical number of small quantum droplets.

Abstract

We revisit the Bogoliubov theory of quantum droplets proposed by Petrov {[}Phys. Rev. Lett. \textbf{115}, 155302 (2015){]} for an ultracold Bose-Bose mixture, where the mean-field collapse is stabilized by the Lee-Huang-Yang quantum fluctuations. We show that a loophole in Petrov's theory, i.e., the ignorance of the softening complex Bogoliubov spectrum, can be naturally removed by the introduction of bosonic pairing. The pairing leads to weaker mean-field attractions, and also stronger Lee-Huang-Yang term in the case of unequal intraspecies interactions. As a result, the equilibrium density for the formation of self-bound droplets significantly decrease in the deep droplet regime, in agreement with a recent observation from diffusion Monte Carlo simulations. Our construction of a consistent Bogoliubov theory paves the way to understand the puzzling low critical number of small quantum droplets observed in the experiment {[}Science \textbf{359}, 301 (2018){]}.