A new form of liquid matter: quantum droplets

Abstract: This brief review summarizes recent theoretical and experimental results which predict and establish the existence of quantum droplets (QDs), i.e., robust two- and three-dimensional (2D and 3D) self-trapped states in Bose-Einstein condensates (BECs), which are stabilized by effective selffirepulsion induced by quantum fluctuations around the mean-field (MF) states [alias the Lee-Huang--Yang (LHY) effect]. The basic models are presented, taking special care of the dimension crossover, 2D -> 3D. Recently reported experimental results, which exhibit stable 3D and quasi-2D QDs in binary BECs, with the inter-component attraction slightly exceeding the MF self-repulsion in each component, and in single-component condensates of atoms carrying permanent magnetic moments, are presented in some detail. The summary of theoretical results is focused, chiefly, on 3D and quasi-2D QDs with embedded vorticity, as the possibility to stabilize such states is a remarkable prediction. Stable vortex states are presented both for QDs in free space, and for singular but physically relevant 2D modes pulled to the center by the inverse-square potential, with the quantum collapse suppressed by the LHY effect.

• The paper demonstrates that quantum droplets emerge in Bose-Einstein condensates through a balance of mean-field attractions and quantum fluctuating repulsions.
• It employs the Gross-Pitaevskii equation with Lee-Huang-Yang corrections to model multidimensional solitons across 2D and 3D configurations.
• Experimental observations in binary condensates verify that finely tuned inter-species interactions via Feshbach resonances lead to the formation of stable quantum droplets.

Quantum Droplets in Bose-Einstein Condensates

The paper "A new form of liquid matter: quantum droplets" discusses an intriguing class of self-bound states known as quantum droplets (QDs). These droplets are formed in Bose-Einstein condensates (BECs) due to the interplay between competing mean-field interactions and the stabilizing effect of quantum fluctuations, described by the Lee-Huang-Yang (LHY) corrections. The authors provide both theoretical models and experimental observations to substantiate the existence and properties of QDs in two- and three-dimensional settings.

Theoretical Framework

The study primarily focuses on multidimensional solitons in BECs, stabilized by effective self-repulsion induced by quantum fluctuations. The theoretical underpinning is based on the Gross-Pitaevskii equation (GPE) augmented by the LHY correction, which introduces a stabilizing quartic defocusing term. This correction is crucial in preventing collapse that can occur due to attractive mean-field interactions. The models predict the formation of robust QDs in both binary and single-component condensates, with particular attention given to the dimensional crossover from 2D to 3D.

Experimental Observations

The empirical aspect of the study confirms the theoretical predictions through various experiments with binary BECs, particularly using mixtures of different isotopes and states, such as in potassium ($^{39}$K) and erbium ($^{166}$Er) atoms. Notably, the QDs are formed when the inter-species attraction slightly overcomes the intra-species repulsion, a condition finely tuned using Feshbach resonances. These experiments showcase the ability to maintain stable QDs in both oblate and full 3D geometries, substantiating the proposed theoretical models.

Implications and Future Directions

The implications of this research are manifold. The robust nature of QDs as soliton-like structures in multidimensional settings could enable novel applications in precision measurements and quantum simulations, where maintaining coherence and stability is paramount. The study also opens avenues for further exploration into complex structures such as vortical droplets, interactions in mixtures exhibiting supersolidity, and exploring beyond mean-field corrections in more exotic quantum states.

Future research could focus on empirically exploring the theoretically predicted vortical structures and their potential stability domains. Additionally, there is a scope for studying QDs under different boundary conditions and external potentials to better understand their dynamics and potential for use in technological applications. Investigating interactions between QDs, such as collisions and fusion processes, could provide deeper insights into the nonlinear dynamics governing these quantum structures.

In conclusion, the study of quantum droplets presents a vital contribution to the field of quantum fluids, showcasing a synergy between theoretical predictions and experimental verifications. This alignment serves as a promising platform for future breakthroughs in condensed matter physics and its applications in technology.