Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions
arXiv:1006.4950 · doi:10.1103/PhysRevA.82.043623
Abstract
We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the strongly confined atoms. In addition, our equations introduce a nonlocal potential, which is anisotropic for pancake-shaped condensates. We propose to observe this anisotropy via measurement of the condensate aspect ratio. We also derive analytically approximate density profiles from our equations. Both the numerical solutions of our reduced mean-field equations and the analytical density profiles agree well with numerical solutions of the full Gross-Pitaevskii equation while being more efficient to compute.
arXiv comment11 pages, 5 figures. Updated references
References in corpus (42)
- Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
- A High Phase-Space-Density Gas of Polar Molecules
- The physics of dipolar bosonic quantum gases
- Bose-Einstein condensation of chromium
- A toolbox for lattice spin models with polar molecules
- Realization of Bose-Einstein condensates in lower dimensions
- Regimes of quantum degeneracy in trapped 1D gases
- Numerical Solution of the Gross-Pitaevskii Equation for Bose-Einstein Condensation
- Bose-Einstein condensation in trapped dipolar gases
- Quantum phases of dipolar bosons in optical lattices
- Roton-maxon spectrum and stability of trapped dipolar condensates
- Optical Production of Ultracold Polar Molecules
- Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential
- Strong dipolar effects in a quantum ferrofluid
- Observation of dipole-dipole interaction in a degenerate quantum gas
- Stabilizing a purely dipolar quantum gas against collapse
- Two-dimensional bright solitons in dipolar Bose-Einstein condensates
- Tuning the dipolar interaction in quantum gases
- Bose-Einstein condensation with magnetic dipole-dipole forces
- Trapped atomic condensates with anisotropic interactions
- Ultracold dense gas of deeply bound heteronuclear molecules
- Trapped condensates of atoms with dipole interactions
- Spontaneously modulated spin textures in a dipolar spinor Bose-Einstein condensate
- Controlling atom-atom interaction at ultralow temperatures by dc electric fields
- Stability of quasi-two-dimensional Bose-Einstein condensates with dominant dipole-dipole interactions
- Dipolar gases in quasi one-dimensional geometries
- Exact hydrodynamics of a trapped dipolar Bose-Einstein condensate
- One-dimensional Bosons in Three-dimensional Traps
- Ground state solution of Bose-Einstein condensate by directly minimizing the energy functional
- Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates
- On an exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions
- Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates
- Novel vortex structures in dipolar condensates
- Magnetic dipolar interaction in an atomic Bose Einstein condensate interferometer
- Phonon instability in two-dimensional dipolar Bose-Einstein Condensates
- On the Gross-Pitaevskii equation for trapped dipolar quantum gases
- Instabilities and the roton spectrum of a quasi-1D Bose-Einstein condensed gas with dipole-dipole interactions
- Low energy atomic collision with dipole interactions
- Vortex lattices in Bose-Einstein condensates with Dipolar Interactions Beyond the Weak Interaction Limit
- Thomas-Fermi versus one- and two-dimensional regimes of a trapped dipolar Bose-Einstein condensate
- One-Dimensional Behavior of Dilute, Trapped Bose Gases
- Generalized nonpolynomial Schrodinger equations for matter waves under anisotropic transverse confinement
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- Mathematical theory and numerical methods for Bose-Einstein condensation
- Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations
- Anisotropic and long-range vortex interactions in two-dimensional dipolar Bose gases
- Dipolar Bose-Einstein Condensates in Weak Anisotropic Disorder
- Mathematical models and numerical methods for spinor Bose-Einstein condensates
- Order parameter and detection for crystallized dipolar bosons in lattices
- Hydrodynamics of cold atomic gases in the limit of weak nonlinearity, dispersion and dissipation
- Vortices and vortex lattices in quantum ferrofluids
- Correlations of strongly interacting ultracold dipolar bosons in optical lattices
- Rotational properties of dipolar Bose-Einstein condensates confined in anisotropic harmonic potentials
- A general theory of flattened dipolar condensates
- Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT
- Two-dimensional Bose gas of tilted dipoles: roton instability and condensate depletion
- Engineering Bright Matter-Wave Solitons of Dipolar Condensates
- Detecting One-Dimensional Dipolar Bosonic Crystal Orders via Full Distribution Functions
- Vortex patterns and the critical rotational frequency in rotating dipolar Bose-Einstein condensates
- Dynamical excitation of maxon and roton modes in a Rydberg-Dressed Bose-Einstein Condensate
- Bright solitons in quasi-one dimensional dipolar condensates with spatially modulated interactions
- Higher-order effective interactions for bosons near a two-body zero crossing
- Graph states as ground states of two-body frustration-free Hamiltonians
- Self trapping of a dipolar Bose-Einstein condensate in a double well
- Vortices in the two-dimensional dipolar Bose gas
- Anomalous oscillations of dark solitons in trapped dipolar condensates
- Exact analytical soliton solutions in dipolar BEC
- Effective dipole-dipole interactions in multilayered dipolar Bose-Einstein condensates
- A robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose-Einstein condensates
- Ground state properties and excitation spectrum of a two dimensional gas of bosonic dipoles
- A Jacobi spectral method for computing eigenvalue gaps and their distribution statistics of the fractional Schrödinger operator
- Dynamics of ultracold dipolar particles in a confined geometry and tilted fields
- Interwires polar soliton molecules in a biwire system
- Exploring the Berezinskii-Kosterlitz-Thouless Transition in a Two-dimensional Dipolar Bose Gas
- Dissipation effect in the double-well Bose-Einstein Condensate
- Dispersion properties of transverse waves propagating in the electrically polarized BECs
- Self-consistent field theory of polarized BEC: dispersion of collective excitation
- Mean-field regime and Thomas-Fermi approximations of trapped Bose-Einstein condensates with higher order interactions in one and two dimensions
- Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions
- Stability of dipolar bosons in a quasiperiodic potential
- Rotons and their damping in elongated dipolar Bose-Einstein condensates
- Beyond-mean-field phases of rotating dipolar condensates
- Vortices in fermion droplets with repulsive dipole-dipole interactions
- Analysis of two and three dipolar bosons in a spherical harmonic trap
- Soliton Dimer-soliton scattering in coupled Quasi-one-dimensional Dipolar Bose-Einstein Condensates
- Mathematical Models and Numerical Methods for Bose-Einstein Condensation