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It was recently found that the Lee-Huang-Yang (LHY) correction to the mean-field Hamiltonian suppresses the collapse and creates stable localized modes (two-component "quantum droplets", QDs) in two and three dimensions. We construct…

Quantum Gases · Physics 2018-12-12 Yongyao Li , Zhaopin Chen , Zhihuan Luo , Chunqing Huang , Haishu Tan , Wei Pang , Boris A. Malomed

We address the existence, stability, and evolution of two-dimensional vortex quantum droplets (VQDs) in binary Bose-Einstein condensates trapped in a ring-shaped potential. The interplay of the Lee-Huang-Yang-amended nonlinearity and…

Quantum Gases · Physics 2024-01-17 Liangwei Dong , Mingjing Fan , Boris A. Malomed

We study the stability of zero-vorticity and vortex lattice quantum droplets (LQDs), which are described by a two-dimensional (2D) Gross-Pitaevskii (GP) equation with a periodic potential and Lee-Huang-Yang (LHY) term. The LQDs are divided…

Pattern Formation and Solitons · Physics 2020-09-24 Yiyin Zheng , Shantong Chen , Zhipeng Huang , Shixuan Dai , Bin Liu , Yongyao Li , Shurong Wang

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…

Quantum Gases · Physics 2020-10-21 Zhihuan Luo , Wei Pang , Bin Liu , Yongyao Li , Boris A. Malomed

In this paper, vortex solitons are produced for a variety of 2D spinning quantum droplets (QDs) in a PT-symmetric potential, modeled by the amended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. In particular, exact QD states…

Quantum Physics · Physics 2023-10-02 Jin Song , Zhenya Yan , Boris A. Malomed

We investigate the formation, stability, and dynamics of 3D ring-shaped and multipole vortical quantum droplets (QDs) in non-rotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated…

Quantum Gases · Physics 2026-02-11 S. Sanjay , S. Saravana Veni , Boris A. Malomed

We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional…

Pattern Formation and Solitons · Physics 2019-10-01 Xiliang Zhang , Xiaoxi Xu , Yiyin Zheng , Zhaopin Chen , Bin Liu , Chunqing Huang , Boris A. Malomed , Yongyao Li

We study the stability and characteristics of two-dimensional (2D) circular quantum droplets (QDs) with embedded hidden vorticity (HV), i.e., opposite angular momenta in two components, formed by binary Bose-Einstein condensates (BECs)…

Pattern Formation and Solitons · Physics 2023-09-22 Bin Liu , Xiaoyan Cai , Xizhou Qin , Xunda Jiang , Jianing Xie , Boris A. Malomed , Yongyao Li

We establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose-Einstein condensates (BECs). The system is modeled by the Gross-Pitaevskii (GP) equation with the cubic term…

Pattern Formation and Solitons · Physics 2023-01-04 Bin Liu , Yi xi Chen , Ao wei Yang , Xiao yan Cai , Yan Liu , Zhi huan Luo , Xi zhou Qin , Xun da Jiang , Yong yao Li , Boris A. Malomed

We predict that Lee-Huang-Yang effect makes it possible to create stable quantum droplets (QDs) in binary Bose-Einstein condensates with a hetero-symmetric or hetero-multipole structure, i.e., different vorticities or multipolarities in…

Quantum Gases · Physics 2020-10-07 Yaroslav V. Kartashov , Boris A. Malomed , Lluis Torner

Quantum droplets (QDs) are self-trapped modes stabilized by the Lee-Huang-Yang correction to the mean-field Hamiltonian of binary atomic Bose-Einstein condensates. The existence and stability of quiescent and rotating dipole-shaped and…

Quantum Gases · Physics 2024-07-15 Dongshuai Liu , Yanxia Gao , Dianyuan Fan , Boris A. Malomed , Lifu Zhang

Ultracold dipolar droplets have been realized in a series of ground-breaking experiments, where the stability of the droplet state is attributed to beyond-mean-field effects in the form of the celebrated Lee-Huang-Yang (LHY) correction. We…

Quantum Gases · Physics 2020-12-17 Matthew Edmonds , Thomas Bland , Nick G. Parker

The nucleation and dynamics of vortices in the quasi-two-dimensional rotating dipolar Bose-Einstein condensate are explored by taking into account the Lee-Huang-Yang (LHY) correction to the mean-field (MF) theory. Assuming approximate…

Quantum Gases · Physics 2026-02-16 S. Sabari , R. Radha , Lauro Tomio , B. A. Malomed

Quantum collapse in three and two dimensions (3D and 2D) is induced by attractive potential ~ -1/r^2. It was demonstrated that the mean-field (MF) cubic self-repulsion in the 3D bosonic gas suppresses the collapse and creates the missing…

Quantum Gases · Physics 2020-07-15 Elad Shamriz , Zhaoping Chen , Boris A. Malomed

A new method for the creation of 3D solitary topological modes, corresponding to vortical droplets of a two-component dilute superfluid, is presented. We use the recently introduced system of nonlinearly coupled Gross-Pitaevskii equations,…

Quantum Gases · Physics 2018-07-18 Yaroslav V. Kartashov , Boris A. Malomed , Leticia Tarruell , Lluis Torner

A review is given of some well-known and some recent results for two- and three-dimensional (2D and 3D) solitons, with emphasis on states carrying embedded vorticity. Unlike typically stable 1D solitons, 2D and 3D ones are vulnerable to…

Optics · Physics 2019-09-04 Boris A. Malomed

We address static and dynamical properties of one-dimensional (1D) quantum droplets (QDs) under the action of local potentials in the form of narrow wells and barriers. The QDs are governed by the 1D Gross-Pitaevskii equation including the…

Quantum Gases · Physics 2023-08-07 Argha Debnath , Ayan Khan , Boris Malomed

We exemplify the impact of beyond Lee-Huang-Yang (LHY) physics, especially due to intercomponent correlations, in the ground state and the quench dynamics of one-dimensional so-called quantum droplets using an ab-initio nonperturbative…

Quantum Gases · Physics 2021-11-23 S. I. Mistakidis , T. Mithun , P. G. Kevrekidis , H. R. Sadeghpour , P. Schmelcher

Quantum droplets (QDs), formed by ultradilute quantum fluids under the action of the Lee-Huang-Yang (LHY) effect, provide a unique platform for investigating a wide range of macroscopic quantum effects. Recent studies of QDs' breathing…

Quantum Gases · Physics 2026-04-23 Zibin Zhao , Guilong Li , Zhaopin Chen , Huan-Bo Luo , Bin Liu , Boris A. Malomed , Yongyao Li

Quantum droplets, stabilized by beyond-mean-field effects, represent a novel state of matter in quantum many-body systems. While previous studies have focused primarily on dipolar and contact-interacting systems, quadrupolar condensates…

Quantum Gases · Physics 2025-10-16 Wei-qi Xia , Xiao-ting Zheng , Xiao-wei Chen , Gui-hua Chen
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