On an exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions

Abstract

We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein condensate which has dipole-dipole interactions as well as the usual s-wave contact interaction, in a harmonic trap. Remarkably, despite the non-local anisotropic nature of the dipolar interaction the solution is an inverted parabola, as in the pure s-wave case, but with a different aspect ratio. Various properties such as electrostriction and stability are discussed.

11 pages, 5 figures

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Cited by in corpus (105)

• The physics of dipolar bosonic quantum gases
• Spinor Bose-Einstein condensates
• A Strongly Dipolar Bose-Einstein Condensate of Dysprosium
• Condensed Matter Theory of Dipolar Quantum Gases
• Observation of dipole-dipole interaction in a degenerate quantum gas
• Stabilizing a purely dipolar quantum gas against collapse
• Dipolar physics: A review of experiments with magnetic quantum gases
• Quantum Fluctuations in Dipolar Bose Gases
• Radial and angular rotons in trapped dipolar gases
• Ground-state phase diagram of a dipolar condensate with quantum fluctuations
• Beyond Mean-Field Low-Lying Excitations of Dipolar Bose Gases
• Bogoliubov modes of a dipolar condensate in a cylindrical trap
• Einstein--de Haas Effect in Dipolar Bose-Einstein Condensates
• Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates
• Comparing contact and dipolar interaction in a Bose-Einstein condensate
• Fortran and C programs for the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap
• Collective excitations of self-bound droplets of a dipolar quantum fluid
• Pattern Formation in Quantum Ferrofluids: from Supersolids to Superglasses
• Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions
• Liquid quantum droplets of ultracold magnetic atoms
• s-wave scattering lengths of the strongly dipolar bosons ${}^{162}$Dy and ${}^{164}$Dy
• Dipolar Bose gases: Many-body versus mean-field description
• Tuning the dipole-dipole interaction in a quantum gas with a rotating magnetic field
• Structure formation during the collapse of a dipolar atomic Bose-Einstein condensate
• Expansion dynamics of a dipolar Bose-Einstein condensate
• Supersolidity in Two-Dimensional Trapped Dipolar Droplet Arrays
• Vortices in dipolar condensates with dominant dipolar interactions
• Two-dimensional dipolar Bose gas with the roton-maxon excitation spectrum
• Dipolar condensates confined in a toroidal trap: ground state and vortices
• Dipolar and spinor bosonic systems
• Properties of a dipolar condensate with three-body interactions
• Vortex in a trapped Bose-Einstein condensate with dipole-dipole interactions
• Distribution of eigenfrequencies for oscillations of the ground state in the Thomas--Fermi limit
• Dynamical Instability of a Rotating Dipolar Bose-Einstein Condensate
• Bose-Einstein condensation of 162Dy and 160Dy
• Thomas-Fermi versus one- and two-dimensional regimes of a trapped dipolar Bose-Einstein condensate
• Order parameter and detection for crystallized dipolar bosons in lattices
• Hydrodynamics of cold atomic gases in the limit of weak nonlinearity, dispersion and dissipation
• Dipolar Bose-Einstein condensates at Finite temperature
• Vortices and vortex lattices in quantum ferrofluids
• Collective excitation frequencies and stationary states of trapped dipolar Bose-Einstein condensates in the Thomas-Fermi regime
• Catalyzation of supersolidity in binary dipolar condensates
• Ground states of spin-3 Bose-Einstein condensates for conserved magnetization
• Correlations of strongly interacting ultracold dipolar bosons in optical lattices
• Stability and structure of an anisotropically trapped dipolar Bose-Einstein condensate: angular and linear rotons
• Exact solutions and stability of rotating dipolar Bose-Einstein condensates in the Thomas-Fermi limit
• Collapse times of dipolar Bose-Einstein condensates
• Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. II. Applications
• Aligned dipolar Bose-Einstein condensate in a double-well potential: From cigar-shaped to pancake-shaped
• Critical Temperature of Weakly Interacting Dipolar Condensates
• Instabilities leading to vortex lattice formation in rotating Bose-Einstein condensates
• Vortex Lattice Formation in Dipolar Bose-Einstein Condensates via Rotation of the Polarization
• Dipolar Fermi gases in anisotropic traps
• Bose-Einstein Condensation Temperature of Dipolar Gas in Anisotropic Harmonic Trap
• Quantum dilute droplets of dipolar bosons at finite temperature
• Vortices in dipolar Bose-Einstein condensates
• Mean-field description of dipolar bosons in triple-well potentials
• Detecting One-Dimensional Dipolar Bosonic Crystal Orders via Full Distribution Functions
• Instability of Rotationally Tuned Dipolar Bose-Einstein Condensates
• Finite-temperature trapped dipolar Bose gas
• Phase separation of a two-component dipolar Bose-Einstein condensate in the quasi-one-dimensional and quasi-two-dimensional regime
• Ultracold dipolar few-boson ensembles in a triple well trap
• Spin squeezing in dipolar spinor condensates
• Three-dimensional vortex structures in a rotating dipolar Bose-Einstein condensate
• Properties of dipolar bosonic quantum gases at finite temperatures
• Finite temperature stability of a trapped dipolar Bose gas
• A magic tilt angle for stabilizing two-dimensional solitons by dipole-dipole interactions
• Collective oscillations of dipolar Bose-Einstein condensates and accurate comparison between contact and dipolar interaction
• Groundstate and Collective Modes of a Spin-Polarized Dipolar Bose-Einstein Condensate in a Harmonic Trap
• Arbitrary-angle rotation of the polarization of a dipolar Bose-Einstein condensate
• Magnetostriction and exchange effects in trapped dipolar Bose and Fermi gases
• Anisotropic collisions of dipolar Bose-Einstein condensates in the universal regime
• Infrared behavior of dipolar Bose systems at low temperatures
• Exact analytical soliton solutions in dipolar BEC
• Production and stabilization of a spin mixture of ultracold dipolar Bose gases
• Singlet and Triplet Superfluid Competition in a Mixture of Two-Component Fermi and One-Component Dipolar Bose Gases
• Off-axis Vortex in a Rotating Dipolar Bose-Einstein Condensation
• Thermal spin fluctuations in spinor Bose-Einstein condensates
• Quantum rotor model for a Bose-Einstein condensate of dipolar molecules
• Ultra-low threshold polariton condensation
• Loss features in ultracold ${}^{162}$Dy gases: two- versus three-body processes
• Dispersion properties of transverse waves propagating in the electrically polarized BECs
• Stability of the density-wave state of a dipolar condensate in a pancake trap
• Self-consistent field theory of polarized BEC: dispersion of collective excitation
• Interaction of a Bose-Einstein Condensate and a Superconductor via Eddy Currents
• Effects of quantum fluctuations on the dynamics of dipolar Bose polarons
• Critical Trap Aspect Ratios For Dipolar BEC
• Vortex pair dynamics in three-dimensional homogeneous dipolar superfluids
• Low-density expansions for the homogeneous dipolar Bose gas at zero temperature
• Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions
• On cold gases with anisotropic interactions
• Energy barriers for vortex nucleation in dipolar condensates
• Dipolar Bose gas with three-body interactions at finite temperature
• Vortices in Bose-Einstein Condensates: Theory
• Dynamics of a dipolar Bose-Einstein condensate in the vicinity of a superconductor
• The field-induced interaction between non-resonant magnetic dipoles
• Reflections on dipolar quantum fluids
• Retardation effects in induced atomic dipole-dipole interactions
• Rotons and their damping in elongated dipolar Bose-Einstein condensates
• Anomalous non-thermal fixed point in a quasi-two-dimensional dipolar Bose gas
• Anisotropic potential immersed in a dipolar Bose-Einstein condensate
• Finite temperature instabilities of 2D dipolar Bose gas at arbitrary tilt angle
• Quasiparticle spectra of mixtures of dipolar and non-dipolar condensates at zero and finite temperatures
• Eigenvalues of a nonlinear ground state in the Thomas-Fermi approximation
• Crow instability of vortex lines in dipolar superfluids