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

arXiv:2012.11103 · Physical Review Research

Numerical calculation of dipolar-quantum-droplet stationary states

Au-Chen Lee, D. Baillie, P. B. Blakie

Published Mar 26, 2021• 29 citations
arXivHTMLPDF

Abstract

We describe and benchmark a method to accurately calculate the quantum droplet states that can be produced from a dipolar Bose-Einstein condensate.Our approach also allows us to consider vortex states, where the atoms circulate around the long-axis of the filament-shaped droplet.We apply our approach to determine a phase diagram showing where self-bound droplets are stable against evaporation, and to quantify the energetics related to the fission of a vortex droplet into two nonvortex droplets.

DOI
10.1103/physrevresearch.3.013283

Related papers

Dipolar Bose-Einstein Condensate with a Vortex

Au-Chen Lee

We theoretically consider the properties of a dipolar Bose-Einstein condensate with a vortex. Our theory includes the influence of the leading order quantum fluctuation corrections which allows the condensate to stabilize into a droplet state in the regime of dominant dipole interactions. We develop numerical techniques to accurately and efficiently calculate the stationary vortex states and the quasi-particle excitations. These methods are carefully benchmarked where possible. We make a brief study of self-bound vortex droplets, considering their basic properties, and presenting a phase diagram for where they exist. We also compare our calculations to results which appeared from another group during our research. We show that their results suffer from serious numerical issues and are unreliable. We focus on studying the properties of a vortex line in an elongated dipolar Bose-Einstein condensate confined by a prolate trap. Increasing the strength of the dipole-dipole interactions relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.

•Jan 1, 2019•0 citations

Two-dimensional anisotropic vortex quantum droplets in dipolar Bose-Einstein condensates

Guilong Li, Xunda Jiang, Bin Liu +3 more

Creation of stable intrinsically anisotropic self-bound states with embedded vorticity is a challenging issue. Previously, no such states in Bose–Einstein condensates (BECs) or other physical settings were known. Dipolar BEC suggests a unique possibility to predict stable two dimensional anisotropic vortex quantum droplets (2D-AVQDs). We demonstrate that they can be created with the vortex axis oriented perpendicular to the polarization of dipoles. The stability area and characteristics of the 2D-AVQDs in the parameter space are revealed by means of analytical and numerical methods. Further, the rotation of the polarizing magnetic field is considered, and the largest angular velocities, up to which spinning 2D-AVQDs can follow the rotation in clockwise and anti-clockwise directions, are found. Collisions between moving 2D-AVQDs are studied too, demonstrating formation of bound states with a vortex-antivortex-vortex structure. A stability domain for such stationary bound states is identified. Unstable dipolar states, that can be readily implemented by means of phase imprinting, quickly transform into robust 2D-AVQDs, which suggests a straightforward possibility for the creation of these states in the experiment.

arXiv:2301.04305•Frontiers of Physics•Dec 7, 2023•64 citations

Variational model for vortex quantum droplets

Ángel Paredes, José R. Salgueiro, Humberto Michinel

Quantum droplets represent a novel state of matter achieved by tailoring a binary Bose–Einstein condensate, where the collapse driven by self-attraction is arrested by quantum effects. This opens the possibility of producing interesting novel physical phenomena, which require accurate mathematical models for its correct description. In this work, we apply variational procedures to the mean field equation governing two-dimensional symmetric quantum droplets, to find simple yet very precise formulae for the droplet profile and the relationships between its main parameters, such as internal and external radii of the bright rings, the chemical potential or the number of atoms of the droplets. The comparison with direct numerical calculations demonstrates that our model provides a highly accurate description of the self-trapped eigenstates with flat-top profiles. These results should aid in the exploration of additional effects in liquid-like solitons and vortex states endowed with angular momentum.

Chaos Solitons & Fractals•Jul 25, 2024•11 citations

Quantum droplets with magnetic vortices in spinor dipolar Bose-Einstein condensates

Shaoxiong Li, Hiroki Saito

Motivated by the recent experimental realization of a Bose-Einstein condensate (BEC) of europium atoms, we investigate the self-bound droplet state for a dipolar BEC with spin degrees of freedom. Under a sufficiently weak magnetic field, the droplet has a torus shape with circulating spin vectors, which is referred to as a magnetic vortex. The ground state transforms from a torus to a cigar shape through bistability with increasing magnetic field. Dynamical change of the magnetic field causes the torus to rotate due to the Einstein–de Haas effect. The magnetic vortices form a supersolid in a confined system. Published by the American Physical Society 2024

arXiv:2402.18885•Physical Review Research•Nov 25, 2024•4 citations

Self-bound dipolar droplets and supersolids in molecular Bose-Einstein condensates

Matthias Schmidt, Lucas Lassablière, Goulven Quéméner +1 more

We numerically study the many-body physics of molecular Bose-Einstein condensates with strong dipole-dipole interactions. We observe the formation of self-bound droplets, and explore phase diagrams that feature a variety of exotic supersolid states. In all of these cases, the large and tunable molecular dipole moments enable the study of unexplored regimes and phenomena, including liquidlike density saturation and universal stability scaling laws for droplets, as well as pattern formation and the limits of droplet supersolidity. We discuss a realistic experimental approach to realize both the required collisional stability of the molecular gases and the independent tunability of their contact and dipolar interaction strengths. Our work provides both a blueprint and a benchmark for near-future experiments with bulk molecular Bose-Einstein condensates.

arXiv:2111.06187•Physical Review Research•Mar 28, 2022•70 citations

Quantum droplets of quasi-one-dimensional dipolar Bose–Einstein condensates

Matthew Edmonds, Thomas Bland, Nick Parker

Abstract 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 scrutinize the dipolar droplet states in a one-dimensional context using a combination of analytical and numerical approaches, and identify experimentally viable parameters for accessing our findings for future experiments. In particular we identify regimes of stability in the restricted geometry, finding multiple roton instabilities as well as regions supporting quasi-one-dimensional droplet states. By applying an interaction quench to the droplet, a modulational instability is induced and multiple droplets are produced, along with bright solitons and atomic radiation. We also assess the droplets robustness to collisions, revealing population transfer and droplet fission.

arXiv:2002.07958•Journal of Physics Communications•Nov 20, 2020•32 citations
We describe and benchmark a method to accurately calculate the quantum droplet states that can be produced from a dipolar Bose-Einstein condensate.Our approach also allows us to consider vortex states, where the atoms circulate around the long-axis of the filament-shaped droplet.We apply our approach to determine a phase diagram showing where self-bound droplets are stable against evaporation, and to quantify the energetics related to the fission of a vortex droplet into two nonvortex droplets.
We theoretically consider the properties of a dipolar Bose-Einstein condensate with a vortex. Our theory includes the influence of the leading order quantum fluctuation corrections which allows the condensate to stabilize into a droplet state in the regime of dominant dipole interactions. We develop numerical techniques to accurately and efficiently calculate the stationary vortex states and the quasi-particle excitations. These methods are carefully benchmarked where possible. We make a brief study of self-bound vortex droplets, considering their basic properties, and presenting a phase diagram for where they exist. We also compare our calculations to results which appeared from another group during our research. We show that their results suffer from serious numerical issues and are unreliable. We focus on studying the properties of a vortex line in an elongated dipolar Bose-Einstein condensate confined by a prolate trap. Increasing the strength of the dipole-dipole interactions relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.
Creation of stable intrinsically anisotropic self-bound states with embedded vorticity is a challenging issue. Previously, no such states in Bose–Einstein condensates (BECs) or other physical settings were known. Dipolar BEC suggests a unique possibility to predict stable two dimensional anisotropic vortex quantum droplets (2D-AVQDs). We demonstrate that they can be created with the vortex axis oriented perpendicular to the polarization of dipoles. The stability area and characteristics of the 2D-AVQDs in the parameter space are revealed by means of analytical and numerical methods. Further, the rotation of the polarizing magnetic field is considered, and the largest angular velocities, up to which spinning 2D-AVQDs can follow the rotation in clockwise and anti-clockwise directions, are found. Collisions between moving 2D-AVQDs are studied too, demonstrating formation of bound states with a vortex-antivortex-vortex structure. A stability domain for such stationary bound states is identified. Unstable dipolar states, that can be readily implemented by means of phase imprinting, quickly transform into robust 2D-AVQDs, which suggests a straightforward possibility for the creation of these states in the experiment.
Quantum droplets represent a novel state of matter achieved by tailoring a binary Bose–Einstein condensate, where the collapse driven by self-attraction is arrested by quantum effects. This opens the possibility of producing interesting novel physical phenomena, which require accurate mathematical models for its correct description. In this work, we apply variational procedures to the mean field equation governing two-dimensional symmetric quantum droplets, to find simple yet very precise formulae for the droplet profile and the relationships between its main parameters, such as internal and external radii of the bright rings, the chemical potential or the number of atoms of the droplets. The comparison with direct numerical calculations demonstrates that our model provides a highly accurate description of the self-trapped eigenstates with flat-top profiles. These results should aid in the exploration of additional effects in liquid-like solitons and vortex states endowed with angular momentum.
Motivated by the recent experimental realization of a Bose-Einstein condensate (BEC) of europium atoms, we investigate the self-bound droplet state for a dipolar BEC with spin degrees of freedom. Under a sufficiently weak magnetic field, the droplet has a torus shape with circulating spin vectors, which is referred to as a magnetic vortex. The ground state transforms from a torus to a cigar shape through bistability with increasing magnetic field. Dynamical change of the magnetic field causes the torus to rotate due to the Einstein–de Haas effect. The magnetic vortices form a supersolid in a confined system. Published by the American Physical Society 2024
We numerically study the many-body physics of molecular Bose-Einstein condensates with strong dipole-dipole interactions. We observe the formation of self-bound droplets, and explore phase diagrams that feature a variety of exotic supersolid states. In all of these cases, the large and tunable molecular dipole moments enable the study of unexplored regimes and phenomena, including liquidlike density saturation and universal stability scaling laws for droplets, as well as pattern formation and the limits of droplet supersolidity. We discuss a realistic experimental approach to realize both the required collisional stability of the molecular gases and the independent tunability of their contact and dipolar interaction strengths. Our work provides both a blueprint and a benchmark for near-future experiments with bulk molecular Bose-Einstein condensates.
Abstract 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 scrutinize the dipolar droplet states in a one-dimensional context using a combination of analytical and numerical approaches, and identify experimentally viable parameters for accessing our findings for future experiments. In particular we identify regimes of stability in the restricted geometry, finding multiple roton instabilities as well as regions supporting quasi-one-dimensional droplet states. By applying an interaction quench to the droplet, a modulational instability is induced and multiple droplets are produced, along with bright solitons and atomic radiation. We also assess the droplets robustness to collisions, revealing population transfer and droplet fission.