Quantum droplets in one-dimensional mixtures of quasi–Bose-Einstein condensates and Tonks-Girardeau gases

While binary atomic Bose-Einstein condensates (BECs) are typically prone to collapse under strong interspecies attraction, it has been shown that higher-order fluctuation corrections, known as Lee-Huang-Yang corrections, can stabilize the mixture. In this work we demonstrate an alternative stabilization mechanism based on kinetic energy. Specifically, we consider a one-dimensional mixture of a quasi-BEC and a Tonks-Girardeau (TG) gas and show that the kinetic energy of the TG component can counteract the interspecies attraction, thereby preventing collapse. This balance leads to the formation of a self-bound quantum droplet, which exhibits two distinct regimes: a low-density droplet and a high-density droplet. We argue that these regimes are smoothly connected by a crossover. Furthermore, an analysis of the derivatives of the ground-state energy and bulk modulus reveals that the transition from a miscible mixture to the droplet phase is of third order. Our findings extend the theoretical understanding of quantum droplets in low-dimensional quantum gases, and the proposed system may be experimentally accessible within current ultracold-atom platforms.