Collective excitations of a trapped Bose-condensed gas

Abstract

By taking the hydrodynamic limit we derive, at $T=0$, an explicit solution of the linearized time dependent Gross-Pitaevskii equation for the order parameter of a Bose gas confined in a harmonic trap and interacting with repulsive forces. The dispersion law $\omega ={\omega }_0(2n^2+2n\ell +3n+\ell {)}^{1/2}$ for the elementary excitations is obtained, to be compared with the prediction $\omega ={\omega }_0(2n+\ell )$ of the noninteracting harmonic oscillator model. Here $n$ is the number of radial nodes and $\ell$ is the orbital angular momentum. The effects of the kinetic energy pressure, neglected in the hydrodynamic approximation, are estimated using a sum rule approach. Results are also presented for deformed traps and attractive forces.

arXiv commentuuencoded file including 12 pages REVTEX and 1 figure

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• Twisted Phonons in Bose-Einstein condensates
• Collective oscillations in two-dimensional Bose-Einstein condensate
• Finite temperature oscillations of a Bose-Einstein condensate in a two-gas model
• Hydrodynamics of the Vacuum
• Vortices in Bose-Einstein Condensates: Theory
• Damping in two component Bose gas
• Damping of Confined Excitations Modes of 1D Condensates in an Optical Lattice
• Barrier effects on the collective excitations of split Bose-Einstein condensates
• Classical Dynamics of Harmonically Trapped Interacting Particles
• Dynamic structure function of two interacting atoms in 1D
• Dynamical Zeeman resonance in spin-orbit-coupled spin-1 Bose gases
• One-dimensional asymmetrically interacting quantum droplets in Bose-Bose mixtures
• Spatial and Temporal Periodic Density Patterns in Driven Bose-Einstein Condensates
• Dipole modes of a trapped bosonic mixture: Fate of the sum-rule approach
• Spin and mass currents near a moving magnetic obstacle in a two-component Bose-Einstein condensate
• Beats and Expansion of Two-Component Bose-Einstein Condensates in the Thomas-Fermi Limit
• Correlated spontaneous symmetry breaking induced by zero-point fluctuations in a quantum mixture
• Ground state and excited states of a trapped dilute condensed Bose gas
• Collective motions of a quantum gas confined in a harmonic trap
• Spin mixing in colliding spinor condensates: formation of an effective barrier
• Collective Oscillations of Bose-Einstein Condensates in a Synthetic Magnetic Field
• Supersolidity of dipolar Bose-Einstein condensates induced by coupling to fermions
• Effective Hamiltonian study of excitations in a boson- fermion mixture with attraction between components
• Cornwall-Jackiw-Tomboulis effective field theory to nonuniversal equation of state of an ultracold Bose gas
• The nonlinear damping of Bose-Einstein condensate oscillations at ultra-low temperatures
• Back-reaction of perturbation wave packets on gray solitons
• Vortex nucleation through edge states in finite Bose-Einstein condensates
• Orbital Variational Adiabatic Hyperspherical Method Applied to Bose-Einstein Condensates
• Melting Transition of Vortex Lattice in Point Vortex Systems
• Nonuniform Bose-Einstein condensate. II. Doubly coherent states
• Strong interaction induced dimensional crossover in 1D quantum gas
• Double unstable avoided crossings and complex domain patterns formation in spin-orbit coupled spin-1 condensates
• Anharmonicity-Induced Criticality of Collective Excitation in a Trapped Bose-Einstein Condensate
• Expansion dynamics of a cylindrical-shell-shaped strongly dipolar condensate
• Multi-component states for trapped spin-1 Bose-Einstein Condensates in the presence of magnetic field
• Bogoliubov spectrum and the dynamic structure factor in a quasi-two-dimensional spin-orbit coupled BEC
• Canonical quantization of classical systems with generalized entropies
• Collective excitations of trapped Fermi or Bose gases
• Propagation of collective modes in non-overlapping dipolar Bose-Einstein condensates
• Coupled oscillator model of a trapped Fermi gas at the BEC-BCS crossover
• Long-range s-wave interactions in Bose-Einstein Condensates: An exact correspondence between truncated free energy and dynamics
• Landau instability and mobility edges of the interacting one-dimensional Bose gas in weak random potentials
• Perfect Wave Transfer in Continuous Quantum Systems
• Dissipation Driven Coherent Dynamics Observed in Bose-Einstein Condensates
• Use of two-body correlated basis functions with van der Waals interaction to study the shape-independent approximation for a large number of trapped interacting bosons
• Hydrodynamics of compressible superfluids in confined geometries
• Probing the critical exponent of superfluid fraction in a strongly interacting Fermi gas
• Microscopic identification of dissipative modes in relativistic field theories
• Microstructure of He II in the presence of boundaries
• Condensate Oscillations, Kinetic Equations and Two-Fluid Hydrodynamics in a Bose Gas
• Dynamics of quantum vortices at finite temperature
• Breathing dynamics of the Bose polaron in a species-selective harmonic trap
• Breaking of Huygens-Fresnel principle in inhomogeneous Tomonaga-Luttinger liquids
• Scale Invariant Dynamics and Universal Quantum Beats in Bose Gases
• Collective modes of a quasi two-dimensional Bose condensate in large gas parameter regime
• Anomalous Doppler effect in two-component Bose-Einstein condensates
• Gauge equivalence among quantum nonlinear many body systems
• The method of moments for Nonlinear Schrodinger Equations: Theory and Applications
• Quench induced collective excitations: from breathing to acoustic modes
• Atomic scattering from Bose-Einstein condensates
• Collective modes of trapped spinor Bose condensates
• Turbulence in rotating Bose-Einstein condensates
• Controlled acoustic-driven vortex transport in coupled superfluid rings
• Efficient multipole representation for matter-wave optics
• Second Quantized Landau Variables in the Case of Dilute Bose-Einstein Condensates
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization
• Semiclassical Solution of the Quantum Hydrodynamic Equation for Trapped Bose-condensed Gas in the l=0 Case
• Nonlinear Mixing of Collective Modes in Harmonically Trapped Bose-Einstein Condensates
• Lattice-induced wavefunction effects on trapped superfluids
• Eigenvalues of a nonlinear ground state in the Thomas-Fermi approximation