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

Atoms

Variational Approaches to Two-Dimensionally Symmetry-Broken Dipolar Bose–Einstein Condensates

Yong-Chang Zhang, Fabian Maucher

Published Jul 6, 2023• 11 citations
Publisher

Abstract

It has been shown that quantum fluctuations in dipolar Bose–Einstein condensates (BECs) lead to a stabilisation against collapse, thereby providing access to a range of states with different symmetries. In this paper, we discuss variational approaches to approximately determine the phase diagrams for dipolar BECs that are trapped along the dipolar orientation and otherwise infinite in the perpendicular direction (thermodynamic limit). The two-dimensional symmetry breaking occurs in the plane perpendicular to the polarisation axis. We show in detail how to derive approximate expressions that are valid in a region where modulations to an otherwise unmodulated perfect superfluid emerge gradually with a small modulation amplitude and compare the results to rigorous numerics.

DOI
10.3390/atoms11070102

Related papers

Supersolidity around a Critical Point in Dipolar Bose-Einstein Condensates

Yong-Chang Zhang, Fabian Maucher, Thomas Pohl

We explore spatial symmetry breaking of a dipolar Bose-Einstein condensate in the thermodynamic limit and reveal a critical point in the phase diagram at which crystallization occurs via a second-order phase transition. This behavior is traced back to the significant effects of quantum fluctuations in dipolar condensates, which moreover stabilize a new supersolid phase, namely a regular honeycomb pattern with high modulational contrast and near-perfect superfluidity.

arXiv:1903.06161•Physical Review Letters•Jul 2, 2019•118 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

Stability of trapped degenerate dipolar Bose and Fermi gases

Sadhan K. Adhikari

Abstract. Trapped degenerate dipolar Bose and Fermi gases of 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 variational approximation and numerical solution of a mean-field model. In the disk shape, with the polarization vector perpendicular to the plane of the disk, 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 disk-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 BEC and degenerate Fermi gas are given. PACS numbers: 03.75.Hh,03.75.Ss,03.75.Kk,05.30.Fk ar

•Aug 18, 2016•4 citations

Supersolidity of a two-dimensional dipolar Bose gas

 Benjamin Ripley

We investigate the crystalline stationary states of a dipolar Bose-Einstein condensate in a planar trapping geometry. Our focus is on the ground state phase diagram in the thermodynamic limit, where triangular, honeycomb and stripe phases occur. We introduce a rigorous method to quantify the superfluidity of these states by analysing their nonclassical translational inertia, which allows us to identify favourable parameter regimes for observing supersolid ground states. The resulting superfluid fraction is a rank-2 tensor which is isotropic for the triangular and honeycomb states but anisotropic for the stripe case. We develop two simplified theories to approximately describe the ground states, and consider the relationship to roton softening in the uniform ground state. This also allows us to extend the phase diagram to the low density regime.

•Jan 1, 2023•0 citations

Accessing elusive two-dimensional phases of dipolar Bose-Einstein condensates by finite temperature

Liang-Jun He, Juan Sánchez-Baena, Fabian Maucher +1 more

It has been shown that dipolar Bose-Einstein condensates that are tightly trapped along the polarization direction can feature a rich phase diagram. In this paper we show that finite temperature can assist in accessing parts of the phase diagram that otherwise appear hard to realize due to excessively large densities and number of atoms being required. These include honeycomb and stripe phases both unconfined and with a finite extent. To map out a phase-diagram, we employ both variational analysis and full numerical calculations solving the finite-temperature extended Gross-Pitaevskii equation (TeGPE). Furthermore, we exhibit real-time evolution simulations leading to such states. We account for the effect of thermal fluctuations by means of Bogoliubov theory, employing the local density approximation. We find that finite temperatures can lead to a significant decrease in the necessary particle number and density that might ultimately pave a route for future experimental realizations.

arXiv:2410.19260•Physical Review Research•Apr 7, 2025•10 citations

Two-dimensional bright solitons in dipolar Bose-Einstein condensates with tilted dipoles

Meghana Raghunandan, Chinmayee Mishra, Kazimierz Łakomy +3 more

The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate plane. The tilting angle constitutes an additional tuning parameter, which helps us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without changing its interaction parameters or trap geometry. The phonon instability in a homogeneous two-dimensional condensate of tilted dipoles always features a transient stripe pattern, which eventually breaks into a metastable soliton gas. Finally, we demonstrate how a dipolar BEC in a shallow trap can eventually be turned into a self-trapped matter wave by an adiabatic approach involving the tuning of the tilting angle.

arXiv:1506.02254•Physical Review A•Jul 31, 2015•41 citations
It has been shown that quantum fluctuations in dipolar Bose–Einstein condensates (BECs) lead to a stabilisation against collapse, thereby providing access to a range of states with different symmetries. In this paper, we discuss variational approaches to approximately determine the phase diagrams for dipolar BECs that are trapped along the dipolar orientation and otherwise infinite in the perpendicular direction (thermodynamic limit). The two-dimensional symmetry breaking occurs in the plane perpendicular to the polarisation axis. We show in detail how to derive approximate expressions that are valid in a region where modulations to an otherwise unmodulated perfect superfluid emerge gradually with a small modulation amplitude and compare the results to rigorous numerics.
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.
Abstract. Trapped degenerate dipolar Bose and Fermi gases of 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 variational approximation and numerical solution of a mean-field model. In the disk shape, with the polarization vector perpendicular to the plane of the disk, 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 disk-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 BEC and degenerate Fermi gas are given. PACS numbers: 03.75.Hh,03.75.Ss,03.75.Kk,05.30.Fk ar
We investigate the crystalline stationary states of a dipolar Bose-Einstein condensate in a planar trapping geometry. Our focus is on the ground state phase diagram in the thermodynamic limit, where triangular, honeycomb and stripe phases occur. We introduce a rigorous method to quantify the superfluidity of these states by analysing their nonclassical translational inertia, which allows us to identify favourable parameter regimes for observing supersolid ground states. The resulting superfluid fraction is a rank-2 tensor which is isotropic for the triangular and honeycomb states but anisotropic for the stripe case. We develop two simplified theories to approximately describe the ground states, and consider the relationship to roton softening in the uniform ground state. This also allows us to extend the phase diagram to the low density regime.
It has been shown that dipolar Bose-Einstein condensates that are tightly trapped along the polarization direction can feature a rich phase diagram. In this paper we show that finite temperature can assist in accessing parts of the phase diagram that otherwise appear hard to realize due to excessively large densities and number of atoms being required. These include honeycomb and stripe phases both unconfined and with a finite extent. To map out a phase-diagram, we employ both variational analysis and full numerical calculations solving the finite-temperature extended Gross-Pitaevskii equation (TeGPE). Furthermore, we exhibit real-time evolution simulations leading to such states. We account for the effect of thermal fluctuations by means of Bogoliubov theory, employing the local density approximation. We find that finite temperatures can lead to a significant decrease in the necessary particle number and density that might ultimately pave a route for future experimental realizations.
The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate plane. The tilting angle constitutes an additional tuning parameter, which helps us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without changing its interaction parameters or trap geometry. The phonon instability in a homogeneous two-dimensional condensate of tilted dipoles always features a transient stripe pattern, which eventually breaks into a metastable soliton gas. Finally, we demonstrate how a dipolar BEC in a shallow trap can eventually be turned into a self-trapped matter wave by an adiabatic approach involving the tuning of the tilting angle.