Time-dependent multi-orbital mean-field for fragmented Bose-Einstein condensates

Abstract

The evolution of Bose-Einstein condensates is usually described by the famous time-dependent Gross-Pitaevskii equation, which assumes all bosons to reside in a single time-dependent orbital. In the present work we address the evolution of fragmented condensates, for which two (or more) orbitals are occupied, and derive a corresponding time-dependent multi-orbital mean-field theory. We call our theory TDMF($n$), where $n$ stands for the number of evolving fragments. Working equations for a general two-body interaction between the bosons are explicitly presented along with an illustrative numerical example.

16 pages, 1 figure

References in corpus (16)

• Dynamics of a Bright Soliton in Bose-Einstein condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential
• Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate
• Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity
• Fragmentation of Bose-Einstein Condensates
• The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond
• General variational many-body theory with complete self-consistency for trapped bosonic systems
• Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions
• Bose-Einstein Condensates in Optical Quasicrystal Lattices
• Pathway from condensation via fragmentation to fermionization of cold bosonic systems
• Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices
• Best mean-field for condensates
• Ground state fragmentation of repulsive BEC in double-trap potentials
• Multiconfigurational Hartree-Fock theory for identical bosons in a double well
• Collisions of solitons and vortex rings in cylindrical Bose-Einstein condensates
• Self-consistent fragmented excited states of trapped condensates
• Properties of fragmented repulsive condensates

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