Ultradilute quantum droplets are intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of ultradilute quantum droplets in three-, one- and two-dimensional two-component Bose-Bose mixtures, by generalizing the conventional Bogoliubov theory to include the bosonic pairing arising from the interspecies attraction. Our pairing theory is fully equivalent to a variational approach and hence gives an upper bound for the energy of quantum droplets. In three dimensions, we predict the existence of a strongly interacting Bose droplet at the crossover from Bose-Einstein condensates (BEC) to Bardeen–Cooper–Schrieffer (BCS) superfluids and map out the bosonic BEC-BCS crossover phase diagram. In one dimension, we find that the energy of the one-dimensional Bose droplet calculated by the pairing theory is in an excellent agreement with the latest diffusion Monte Carlo simulation {[}Phys. Rev. Lett. 122, 105302 (2019){]}, for nearly all the interaction strengths at which quantum droplets exist. In two dimensions, we show that Bose droplets disappear and may turn into a soliton-like many-body bound state, when the interspecies attraction exceeds a critical value. Below the threshold, the pairing theory predicts more or less the same results as the Bogoliubov theory derived by Petrov and Astrakharchik {[}Phys. Rev. Lett. 117, 100401 (2016){]}. The predicted energies from both theories are higher than the diffusion Monte Carlo results, due to the weak interspecies attraction and the increasingly important role played by the beyond-Bogoliubov-approximation effect in two dimensions. Our pairing theory provides an ideal starting point to understand interesting ground-state properties of quantum droplets in various dimensions, including their shape and collective oscillations.

中文翻译：

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具有种间吸引力的二元Bose混合物的微观配对理论：Bosonic BEC-BCS穿越和超稀疏低维量子液滴

超稀疏量子液滴是一种令人着迷的新状态，在这种状态下，有吸引力的平均场力可以与来自量子涨落的排斥力相平衡，从而避免崩溃。在这里，我们通过推广常规的Bogoliubov理论，包括种间吸引所引起的玻色对，提出了在三维，一维和二维二维Bose-Bose混合物中超稀释量子液滴的微观理论。我们的配对理论完全等同于变分方法，因此给出了量子液滴能量的上限。在三个维度上，我们预测在从玻色-爱因斯坦凝聚物（BEC）到Bardeen-Cooper-Schrieffer（BCS）超流体的交汇处会存在强烈相互作用的Bose液滴，并绘制出玻色BEC-BCS交汇相图。在一个维度上 我们发现，通过配对理论计算出的一维Bose液滴的能量与最新的扩散Monte Carlo模拟{[} Phys。莱特牧师 122，105302（2019）{]}，关于存在量子液滴的几乎所有相互作用强度。在二维中，我们显示了当种间吸引力超过临界值时，玻色滴消失并且可能变成孤子状的多体结合状态。在阈值以下，配对理论预测的结果与Petrov和Astrakharchik {[} Phys。]提出的Bogoliubov理论大致相同。莱特牧师 117，100401（2016）{]}。两种理论的预测能量都高于扩散蒙特卡洛法的结果，由于物种间的吸引力较弱，并且超越波哥廖布波夫近似效应在二维中起着越来越重要的作用。我们的配对理论提供了一个理想的起点，以了解各种尺寸的量子液滴的有趣基态特性，包括其形状和集体振荡。