Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Bistable multipole quantum droplets in binary Bose-Einstein condensates

Liangwei Dong, Dongshuai Liu, Zhijing Du, Kai Shi, Wei Qi

Published Mar 28, 2022• 30 citations
Publisher

Abstract

We address the existence and stability of multipole quantum droplets in symmetric binary Bose-Einstein condensates described by the amended Gross-Pitaevskii equation with Lee-Huang-Yang quantum corrections. Quantum droplets trapped in a weakly anharmonic potential can be composed of different numbers of globally linked poles with an azimuthally periodic distribution. Due to the competing Lee-Huang-Yang-augmented nonlinearity, the norm of two branches of droplets with slopes of opposite sign merges together at a lower cutoff of chemical potential. The lower and upper branches of droplets at the same chemical potential, but with a different norm, can evolve stably in certain parameter regions simultaneously. The stability domain of droplets shrinks with the growth of the number of poles. Even unstable necklacelike droplets can survive for a very long time.

DOI
10.1103/physreva.105.033321

Related papers

Rotating dipole and quadrupole quantum droplets in binary Bose-Einstein condensates

Dongshuai Liu, Yanxia Gao, Dianyuan Fan +2 more

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 vortex QDs with vorticity S = 1 (DQDs and VQDs, respectively) are numerically studied in the framework of the accordingly modified two-component system. The rotating DQDs trapped in an annular potential are built of two crescentlike components, stretching along the azimuthal direction with the increase of the rotation frequency. Rotating quadrupole QDs (QQDs) bifurcate from the VQDs with S = 2 . Above a certain rotation frequency, they transform back into VQDs with a flat-top shape. Rotating DQDs and QQDs are stable in a broad interval of values of the chemical potential. The results provide the first example of stable modes which are intermediate states between the rotating DQDs and QQDs on the one hand and VQDs on the other. Published by the American Physical Society 2024

arXiv:2407.09129•Physical Review Research•Aug 19, 2024•3 citations

Toroidal Confinement and Beyond: Vorticity-Defined Morphologies of Dipolar $^{164}$Dy Quantum Droplets

S. Sanjay, S. Saravana Veni, 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 in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDI) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity $S$) are shaped as necklace-like modes, with the number of \textquotedblleft beads" (multipole's order) $n=2S$, up to $S=6$. The stability area of the multipoles shrinks with the increase of $S$. For higher values of $S$ the centrifugal effect associated with the phase winding destabilizes the annular density and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy and peak density on the norm (number of particles) and $S$ is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the non-rotating configurations.

arXiv:2602.09683•Feb 10, 2026•0 citations

Toroidal confinement and beyond: Vorticity-defined morphologies of dipolar Dy 164 quantum droplets

S. Sanjay, S. Saravana Veni, Boris A. Malomed

We investigate the formation, stability, and dynamics of three-dimensional ring-shaped and multipole vortical quantum droplets (QDs) in nonrotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDIs) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity S) are shaped as necklacelike modes, with the number of "beads" (multipole order) n=2S, up to S=6. The stability area of the multipoles shrinks with the increase of S. For higher values of S the centrifugal effect associated with the phase winding destabilizes the ring-shaped QDs and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy, and peak density on the norm (number of particles) and S is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the nonrotating configurations.

Physical review. E•Feb 9, 2026•2 citations

Vortex-ring quantum droplets in a radially-periodic potential

Bin Liu, Yi Xi Chen, Ao wei Yang +7 more

Abstract We establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose–Einstein condensates. The system is modeled by the Gross–Pitaevskii (GP) equation with the cubic term multiplied by a logarithmic factor (as produced by the Lee-Huang-Yang correction to the mean-field theory) and a potential which is a periodic function of the radial coordinate. Narrow vortex rings with high values of the topological charge, trapped in particular circular troughs of the radial potential, are produced. These results suggest an experimentally relevant method for the creation of vortical QDs (thus far, only zero-vorticity ones have been reported). The 2D GP equation for the narrow rings is approximately reduced to the one-dimensional form, which makes it possible to study the modulational stability of the rings against azimuthal perturbations. Full stability areas are delineated for these modes. The trapping capacity of the circular troughs is identified for the vortex rings with different winding numbers (WNs). Stable compound states in the form of mutually nested concentric multiple rings are constructed too, including ones with opposite signs of the WNs. Other robust compound states combine a modulationally stable narrow ring in one circular potential trough and an azimuthal soliton performing orbital motion in an adjacent one. The results may be used to design a device employing coexisting ring-shaped modes with different WNs for data storage.

arXiv:2212.05838•New Journal of Physics•Dec 1, 2022•23 citations

Dynamics of dipolar quantum droplets in an extended Gross–Pitaevskii equation in the presence of time-dependent harmonic trapping potential and a damping term

Brahim Alouini, Hichem Hajaiej

The purpose of this paper is to study the dynamics of solutions to an extended Gross–Pitaevskii equation that models the formation of droplets in a dipolar Bose–Einstein condensate (BEC). The formation of these droplets has been recently discovered by driving the BEC into the strongly dipolar regime. Surprisingly, instead of collapsing, the system formed stable droplets. So far, no rigorous mathematical explanation has been proved. To the best of our knowledge, only experimental results have been obtained. The goal of this paper is to validate this breakthrough discovery. Many predictions/ conjectures properties of these droplets have been stated by some research groups in physics and engineering. In particular, it has been claimed that the stability of these droplets is a consequence of the presence of the damping term in the extended Gross–Pitaevskii equation under study. This term describes the three-body loss process. To accurately model the dynamics of formation of these droplets, it is necessary to consider a time-dependent harmonic trapping potential as well as other terms with different types of nonlinearity among them that describe the Lee–Huang–Yang (LHY). This presents some challenges that will be solved in this paper.

Analysis and Applications•Jun 23, 2022•0 citations

Rotating Multidimensional Quantum Droplets

Liangwei Dong, Yaroslav V. Kartashov

We predict a new type of two- and three-dimensional stable quantum droplets persistently rotating in broad external two-dimensional and weakly anharmonic potential. Their evolution is described by the system of the Gross-Pitaevskii equations with Lee-Huang-Yang quantum corrections. Such droplets resemble whispering-gallery modes localized in the polar direction due to nonlinear interactions and, depending on their chemical potential and rotation frequency, they appear in rich variety of shapes, ranging from nearly flat-top or strongly localized rotating wave packets, to crescentlike objects extending nearly over the entire range of polar angles. Above critical rotation frequency quantum droplets transform into vortex droplets (in two dimensions) or vortex tori (in three dimensions), whose topological charge gradually increase with the increase of the modulus of chemical potential, and therefore they belong to the family of nonlinear modes connecting fundamental and vortex quantum droplets. Rotating quantum droplets are exceptionally robust objects, stable practically in the entire range of their existence.

Physical Review Letters•Jun 17, 2021•89 citations
We address the existence and stability of multipole quantum droplets in symmetric binary Bose-Einstein condensates described by the amended Gross-Pitaevskii equation with Lee-Huang-Yang quantum corrections. Quantum droplets trapped in a weakly anharmonic potential can be composed of different numbers of globally linked poles with an azimuthally periodic distribution. Due to the competing Lee-Huang-Yang-augmented nonlinearity, the norm of two branches of droplets with slopes of opposite sign merges together at a lower cutoff of chemical potential. The lower and upper branches of droplets at the same chemical potential, but with a different norm, can evolve stably in certain parameter regions simultaneously. The stability domain of droplets shrinks with the growth of the number of poles. Even unstable necklacelike droplets can survive for a very long time.
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 vortex QDs with vorticity S = 1 (DQDs and VQDs, respectively) are numerically studied in the framework of the accordingly modified two-component system. The rotating DQDs trapped in an annular potential are built of two crescentlike components, stretching along the azimuthal direction with the increase of the rotation frequency. Rotating quadrupole QDs (QQDs) bifurcate from the VQDs with S = 2 . Above a certain rotation frequency, they transform back into VQDs with a flat-top shape. Rotating DQDs and QQDs are stable in a broad interval of values of the chemical potential. The results provide the first example of stable modes which are intermediate states between the rotating DQDs and QQDs on the one hand and VQDs on the other. Published by the American Physical Society 2024
Toroidal Confinement and Beyond: Vorticity-Defined Morphologies of Dipolar 164^{164}164Dy Quantum Droplets
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 in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDI) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity SSS) are shaped as necklace-like modes, with the number of \textquotedblleft beads" (multipole's order) n=2Sn=2Sn=2S, up to S=6S=6S=6. The stability area of the multipoles shrinks with the increase of SSS. For higher values of SSS the centrifugal effect associated with the phase winding destabilizes the annular density and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy and peak density on the norm (number of particles) and SSS is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the non-rotating configurations.
We investigate the formation, stability, and dynamics of three-dimensional ring-shaped and multipole vortical quantum droplets (QDs) in nonrotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDIs) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity S) are shaped as necklacelike modes, with the number of "beads" (multipole order) n=2S, up to S=6. The stability area of the multipoles shrinks with the increase of S. For higher values of S the centrifugal effect associated with the phase winding destabilizes the ring-shaped QDs and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy, and peak density on the norm (number of particles) and S is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the nonrotating configurations.
Abstract We establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose–Einstein condensates. The system is modeled by the Gross–Pitaevskii (GP) equation with the cubic term multiplied by a logarithmic factor (as produced by the Lee-Huang-Yang correction to the mean-field theory) and a potential which is a periodic function of the radial coordinate. Narrow vortex rings with high values of the topological charge, trapped in particular circular troughs of the radial potential, are produced. These results suggest an experimentally relevant method for the creation of vortical QDs (thus far, only zero-vorticity ones have been reported). The 2D GP equation for the narrow rings is approximately reduced to the one-dimensional form, which makes it possible to study the modulational stability of the rings against azimuthal perturbations. Full stability areas are delineated for these modes. The trapping capacity of the circular troughs is identified for the vortex rings with different winding numbers (WNs). Stable compound states in the form of mutually nested concentric multiple rings are constructed too, including ones with opposite signs of the WNs. Other robust compound states combine a modulationally stable narrow ring in one circular potential trough and an azimuthal soliton performing orbital motion in an adjacent one. The results may be used to design a device employing coexisting ring-shaped modes with different WNs for data storage.
The purpose of this paper is to study the dynamics of solutions to an extended Gross–Pitaevskii equation that models the formation of droplets in a dipolar Bose–Einstein condensate (BEC). The formation of these droplets has been recently discovered by driving the BEC into the strongly dipolar regime. Surprisingly, instead of collapsing, the system formed stable droplets. So far, no rigorous mathematical explanation has been proved. To the best of our knowledge, only experimental results have been obtained. The goal of this paper is to validate this breakthrough discovery. Many predictions/ conjectures properties of these droplets have been stated by some research groups in physics and engineering. In particular, it has been claimed that the stability of these droplets is a consequence of the presence of the damping term in the extended Gross–Pitaevskii equation under study. This term describes the three-body loss process. To accurately model the dynamics of formation of these droplets, it is necessary to consider a time-dependent harmonic trapping potential as well as other terms with different types of nonlinearity among them that describe the Lee–Huang–Yang (LHY). This presents some challenges that will be solved in this paper.
We predict a new type of two- and three-dimensional stable quantum droplets persistently rotating in broad external two-dimensional and weakly anharmonic potential. Their evolution is described by the system of the Gross-Pitaevskii equations with Lee-Huang-Yang quantum corrections. Such droplets resemble whispering-gallery modes localized in the polar direction due to nonlinear interactions and, depending on their chemical potential and rotation frequency, they appear in rich variety of shapes, ranging from nearly flat-top or strongly localized rotating wave packets, to crescentlike objects extending nearly over the entire range of polar angles. Above critical rotation frequency quantum droplets transform into vortex droplets (in two dimensions) or vortex tori (in three dimensions), whose topological charge gradually increase with the increase of the modulus of chemical potential, and therefore they belong to the family of nonlinear modes connecting fundamental and vortex quantum droplets. Rotating quantum droplets are exceptionally robust objects, stable practically in the entire range of their existence.