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:2311.06370 · Physical Review A

Spontaneous dipolar Bose-Einstein condensation on the surface of a cylinder

Luis E. Young-S., Sadhan K. Adhikari

Published Nov 27, 2023• 12 citations
arXivHTMLPDF

Abstract

We demonstrate the spontaneous formation of a Bose-Einstein condensate (BEC) of strongly bound harmonically trapped dipolar $^{164}\mathrm{Dy}$ atoms on the outer curved surface of an elliptical or a circular cylinder, with a distinct topology, employing the numerical solution of an improved mean-field model including a Lee-Huang-Yang-type interaction, meant to stop a collapse at high atom density, the axis of the cylindrical-shell-shaped BEC being aligned along the polarization direction of the dipolar atoms. These states are dynamically stable and a Gaussian initial state leads to the cylindrical-shell-shaped state in both imaginary-time and real-time propagation. The formation of the hollow cylindrical BEC by a real-time simulation starting from a solid cylindrical state demonstrate the possibility of the formation of such a condensate experimentally.

DOI
10.1103/physreva.108.053323

Related papers

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

Structure formation during the collapse of a dipolar atomic Bose-Einstein condensate

Nicholas G. Parker, Christopher Ticknor, A. Martin +1 more

We investigate the collapse of a trapped dipolar Bose-Einstein condensate. This is performed by numerical simulations of the Gross-Pitaevskii equation and the novel application of the Thomas-Fermi hydrodynamic equations to collapse. We observe regimes of both global collapse, where the system evolves to a highly elongated or flattened state depending on the sign of the dipolar interaction, and local collapse, which arises due to dynamically unstable phonon modes and leads to a periodic arrangement of density shells, disks, or stripes. In the adiabatic regime, where ground states are followed, collapse can occur globally or locally, while in the nonadiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyze the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.

arXiv:0810.2028•Physical Review A•Jan 21, 2009•79 citations

Dipolar Bose-Einstein condensate in a ring or in a shell

Sadhan K. Adhikari

We study properties of a trapped dipolar Bose-Einstein condensate (BEC) in a circular ring or a spherical shell using the mean-field Gross-Pitaevskii equation. In the case of the ring-shaped trap we consider different orientations of the ring with respect to the polarization direction of the dipoles. In the presence of long-range anisotropic dipolar and short-range contact interactions, the anisotropic density distribution of the dipolar BEC in both traps is discussed in detail. The stability condition of the dipolar BEC in both traps is illustrated in a phase plot of dipolar and contact interactions. We also study and discuss the properties of a vortex dipolar BEC in these traps.

arXiv:1205.2813•Physical Review A•May 22, 2012•38 citations

Stability of trapped degenerate dipolar Bose and Fermi gases

S K Adhikari

Trapped degenerate dipolar Bose and Fermi gases of the cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose–Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using a variational approximation and a numerical solution of a mean-field model. In the disc shape, with the polarization vector perpendicular to the plane of the disc, the atoms experience an overall dipolar repulsion and this fact should contribute to the stability. However, a complete numerical solution of the dynamics leads to the collapse of a strongly disc-shaped dipolar BEC due to the long-range anisotropic dipolar interaction. In the case of fermions, the stability of a trapped single-component degenerate dipolar Fermi gas is studied including the Hartree–Fock exchange and Brueckner–Goldstone correlation energies in the local-density approximation valid for a large number of atoms. Estimates for the maximum allowed number of polar Bose and Fermi molecules in the BEC and degenerate Fermi gas are given.

arXiv:1304.2261•Journal of Physics B Atomic Molecular and Optical Physics•Apr 30, 2013•5 citations

Dipolar droplet bound in a trapped Bose-Einstein condensate

Luis E. Young-S., Sadhan K. Adhikari

We study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by interspecies contact interaction in a trapped nondipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar ${}^{164}$Dy droplet bound in a trapped nondipolar ${}^{87}$Rb BEC with a variable number of ${}^{164}$Dy atoms and interspecies scattering length. A trapped nondipolar BEC of a fixed number of atoms can bind only a dipolar droplet containing fewer atoms than a critical number for the interspecies scattering length between two critical values. The shape and size (statics) as well as the small breathing oscillation (dynamics) of the dipolar BEC droplet are studied using numerical and variational solutions of a mean-field model. We also suggest an experimental procedure for achieving such a ${}^{164}$Dy droplet by relaxing the trap on the ${}^{164}$Dy BEC in a trapped binary ${}^{87}$Rb-${}^{164}$Dy mixture.

arXiv:1212.5004•Physical Review A•Jan 17, 2013•13 citations

Dynamically stable two- and four-droplet solitons in a very strongly dipolar NaCs condensate

Sadhan K. Adhikari

A strongly dipolar Bose-Einstein condensate (BEC) of Dy atoms could sustain different types of states not possible in a nondipolar BECs. Motivated by the observation of a very strongly dipolar condensate of NaCs molecules [N. Bigagli et al., Nature (London) 631, 289 (2024)0028-083610.1038/s41586-024-07492-z], with dipolar interaction stronger by more than an order of magnitude compared with that of Dy atoms, we demonstrate that, in a very strongly dipolar NaCs BEC, it is possible to have a two- and a four-droplet metastable soliton, axially free along the polarization z direction. In this study, we employ imaginary-time propagation of an improved mean-field model, including the Lee-Huang-Yang interaction. The dipolar solitons are subject to an expulsive Gaussian potential at the center and a harmonic potential, both acting in the x-y plane. The phase-coherent solitons, possessing the isolated droplets, are free to move along the z-axis without any relative motion between the droplets. The dynamical stability and mobility of these solitons are demonstrated by real-time propagation employing the converged imaginary-time wave function as the initial state.

arXiv:2501.09903•Physical review. E•May 19, 2025•1 citation
We demonstrate the spontaneous formation of a Bose-Einstein condensate (BEC) of strongly bound harmonically trapped dipolar 164Dy^{164}\mathrm{Dy}164Dy atoms on the outer curved surface of an elliptical or a circular cylinder, with a distinct topology, employing the numerical solution of an improved mean-field model including a Lee-Huang-Yang-type interaction, meant to stop a collapse at high atom density, the axis of the cylindrical-shell-shaped BEC being aligned along the polarization direction of the dipolar atoms. These states are dynamically stable and a Gaussian initial state leads to the cylindrical-shell-shaped state in both imaginary-time and real-time propagation. The formation of the hollow cylindrical BEC by a real-time simulation starting from a solid cylindrical state demonstrate the possibility of the formation of such a condensate experimentally.
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 investigate the collapse of a trapped dipolar Bose-Einstein condensate. This is performed by numerical simulations of the Gross-Pitaevskii equation and the novel application of the Thomas-Fermi hydrodynamic equations to collapse. We observe regimes of both global collapse, where the system evolves to a highly elongated or flattened state depending on the sign of the dipolar interaction, and local collapse, which arises due to dynamically unstable phonon modes and leads to a periodic arrangement of density shells, disks, or stripes. In the adiabatic regime, where ground states are followed, collapse can occur globally or locally, while in the nonadiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyze the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.
We study properties of a trapped dipolar Bose-Einstein condensate (BEC) in a circular ring or a spherical shell using the mean-field Gross-Pitaevskii equation. In the case of the ring-shaped trap we consider different orientations of the ring with respect to the polarization direction of the dipoles. In the presence of long-range anisotropic dipolar and short-range contact interactions, the anisotropic density distribution of the dipolar BEC in both traps is discussed in detail. The stability condition of the dipolar BEC in both traps is illustrated in a phase plot of dipolar and contact interactions. We also study and discuss the properties of a vortex dipolar BEC in these traps.
Trapped degenerate dipolar Bose and Fermi gases of the cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose–Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using a variational approximation and a numerical solution of a mean-field model. In the disc shape, with the polarization vector perpendicular to the plane of the disc, the atoms experience an overall dipolar repulsion and this fact should contribute to the stability. However, a complete numerical solution of the dynamics leads to the collapse of a strongly disc-shaped dipolar BEC due to the long-range anisotropic dipolar interaction. In the case of fermions, the stability of a trapped single-component degenerate dipolar Fermi gas is studied including the Hartree–Fock exchange and Brueckner–Goldstone correlation energies in the local-density approximation valid for a large number of atoms. Estimates for the maximum allowed number of polar Bose and Fermi molecules in the BEC and degenerate Fermi gas are given.
We study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by interspecies contact interaction in a trapped nondipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar 164{}^{164}164Dy droplet bound in a trapped nondipolar 87{}^{87}87Rb BEC with a variable number of 164{}^{164}164Dy atoms and interspecies scattering length. A trapped nondipolar BEC of a fixed number of atoms can bind only a dipolar droplet containing fewer atoms than a critical number for the interspecies scattering length between two critical values. The shape and size (statics) as well as the small breathing oscillation (dynamics) of the dipolar BEC droplet are studied using numerical and variational solutions of a mean-field model. We also suggest an experimental procedure for achieving such a 164{}^{164}164Dy droplet by relaxing the trap on the 164{}^{164}164Dy BEC in a trapped binary 87{}^{87}87Rb-164{}^{164}164Dy mixture.
A strongly dipolar Bose-Einstein condensate (BEC) of Dy atoms could sustain different types of states not possible in a nondipolar BECs. Motivated by the observation of a very strongly dipolar condensate of NaCs molecules [N. Bigagli et al., Nature (London) 631, 289 (2024)0028-083610.1038/s41586-024-07492-z], with dipolar interaction stronger by more than an order of magnitude compared with that of Dy atoms, we demonstrate that, in a very strongly dipolar NaCs BEC, it is possible to have a two- and a four-droplet metastable soliton, axially free along the polarization z direction. In this study, we employ imaginary-time propagation of an improved mean-field model, including the Lee-Huang-Yang interaction. The dipolar solitons are subject to an expulsive Gaussian potential at the center and a harmonic potential, both acting in the x-y plane. The phase-coherent solitons, possessing the isolated droplets, are free to move along the z-axis without any relative motion between the droplets. The dynamical stability and mobility of these solitons are demonstrated by real-time propagation employing the converged imaginary-time wave function as the initial state.