Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping

Abstract

Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive $1/r$ interaction, we point out that the instance of self-trapping of the condensate, without external trap potential, is physically best understood by introducing appropriate "atomic" units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters $N^{2}a/a_u$ and $\gamma /N^2$, where $N$ is the particle number, $a$ the scattering length, $a_u$ the "Bohr" radius and $\gamma$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, for energies, sizes and peak densities, and compare with previous variational results. As a novel feature we point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.

7 pages, 7 figures, to appear in Phys. Rev. A

References in corpus (21)

• Bose-Einstein condensation of chromium
• Bose-Einstein condensation in trapped dipolar gases
• Quantum phases of dipolar bosons in optical lattices
• Roton-maxon spectrum and stability of trapped dipolar condensates
• Observation of dipole-dipole interaction in a degenerate quantum gas
• Gravitation and quantummechanical localization of macroobjects
• Tuning the dipolar interaction in quantum gases
• Bose-Einstein condensation with magnetic dipole-dipole forces
• Stationary solutions of the one-dimensional nonlinear Schroedinger equation: II. Case of attractive nonlinearity
• Ground state and elementary excitations of single and binary Bose-Einstein condensates of trapped dipolar gases
• Bose Condensates with 1/r Interatomic Attraction: Electromagnetically Induced ``Gravity''
• Exact hydrodynamics of a trapped dipolar Bose-Einstein condensate
• Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions
• Ultracold dipolar gases - a challenge for experiments and theory
• Quantum phases of dipolar spinor condensates
• Newtonian Quantum Gravity
• Ground-state structure and stability of dipolar condensates in anisotropic traps
• Stability and Decay Rates of Non-Isotropic Attractive Bose-Einstein Condensates
• Self-Binding Transition in Bose Condensates with Laser-Induced ``Gravitation''
• Continuous configuration-interaction for condensates in a ring
• Gravitational self-localization in quantum measurement

Cited by in corpus (24)

• The physics of exceptional points
• Pattern Formation in Quantum Ferrofluids: from Supersolids to Superglasses
• Interference of Dark Matter Solitons and Galactic Offsets
• Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive 1/r-interaction
• Bifurcations and exceptional points in dipolar Bose-Einstein condensates
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Spatial solitons in thermo-optical media from the nonlinear Schrodinger-Poisson equation and dark matter analogues
• Stable periodic density waves in dipolar Bose-Einstein condensates trapped in optical lattices
• Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. II. Applications
• Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept
• Coherent and incoherent structures in fuzzy dark matter halos
• Symmetry breaking in dipolar matter-wave solitons in dual-core couplers
• Pitchfork bifurcations in blood-cell shaped dipolar Bose-Einstein condensates
• Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction
• Bifurcations, order, and chaos in the Bose-Einstein condensation of dipolar gases
• Rotating three-dimensional solitons in Bose Einstein condensates with gravity-like attractive nonlocal interaction
• Bose-Einstein Condensates with Derivative and Long-Range Interactions as Set-Ups for Analog Black Holes
• Relation between the eigenfrequencies of Bogoliubov excitations of Bose-Einstein condensates and the eigenvalues of the Jacobian in a time-dependent variational approach
• High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices
• Transition state theory for wave packet dynamics. II. Thermal decay of Bose-Einstein condensates with long-range interaction
• Macroscopic quantum tunneling of Bose-Einstein condensates with long-range interaction
• Spectral Singularities and Zero Energy Bound States
• Schrödinger-Newton-Hooke system in higher dimensions. Part I: Stationary states
• Tightly bound solitons and vortices in three-dimensional bosonic condensates with the electromagnetically-induced gravity