Breakdown of the single-mode description of ultradilute quantum droplets in binary Bose mixtures: A perspective from a microscopic bosonic pairing theory

TL;DR

This paper challenges the single-mode approximation for ultradilute quantum droplets in binary Bose mixtures, showing that the density ratio can fluctuate significantly and differ from previous predictions, especially in the deep quantum regime.

Contribution

It introduces a bosonic pairing theory revealing the breakdown of the single-mode description and provides a new microscopic perspective on quantum droplet properties.

Findings

Density ratio fluctuates in the deep quantum regime.

Optimal density ratio differs from the traditional square root of scattering length ratio.

Predicted density ratio interval can be tested experimentally.

Abstract

In his seminal proposal of quantum droplets in binary Bose mixtures {[}Phys. Rev. Lett. \textbf{115}, 155302 (2015){]}, Dmitry Petrov suggested that the density ratio $n_{2}/n_{1}$ of the two bosonic components are locked to an optimal value, which is given by the square root of the ratio of the two intra-species scattering lengths, i.e., $\sqrt{a_{11}/a_{22}}$. Due to such a density locking, quantum droplets can be efficiently described by using an extended Gross--Pitaevskii equation within the single-mode approximation. Here, we find that this single-mode description necessarily breaks down in the deep quantum droplet regime, when the attractive inter-species scattering length $a_{12}$ significantly deviates away from the threshold of mean-field collapse (i.e., $-\sqrt{a_{11}a_{22}}$). By applying a bosonic pairing theory, we show that the density ratio is allowed to fluctuate in a sizable interval. Most importantly, the optimal density ratio would be very different from $\sqrt{a_{11}/a_{22}}$, in the case of unequal intra-species scattering lengths ($a_{11}\neq a_{22}$). Our finding might provide a plausible microscopic explanation of the puzzling low critical particle number of quantum droplets, as experimentally observed. Our predicted interval of the density ratio, as a function of the inter-species scattering length, could also be experimentally examined in cold-atom laboratories in the near future.