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Physical Review Letters

Collective Excitations of a Confined Bose Condensate

Kanwal G. Singh, Daniel S. Rokhsar

Published Aug 26, 1996• 107 citations
Publisher

Abstract

We discuss the collective excitation spectrum and condensate depletion of a dilute, interacting Bose condensate confined to a harmonic potential, within the Bogoliubov approximation. The spectrum is calculated explicitly for weak coupling based on a variational condensate. We discuss the qualitative nature of this spectrum and make quantitative predictions for future experiments.

DOI
10.1103/physrevlett.77.1667

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We discuss the collective excitation spectrum and condensate depletion of a dilute, interacting Bose condensate confined to a harmonic potential, within the Bogoliubov approximation. The spectrum is calculated explicitly for weak coupling based on a variational condensate. We discuss the qualitative nature of this spectrum and make quantitative predictions for future experiments.
The density of states of a Bose-condensed gas confined in a harmonic trap is investigated. The predictions of Bogoliubov theory are compared with those of Hartree-Fock theory and of the hydrodynamic model. We show that the Hartree-Fock scheme provides an excellent description of the excitation spectrum in a wide range of energy, revealing a major role played by single-particle excitations in these confined systems. The crossover from the hydrodynamic regime, holding at low energies, to the independent-particle regime is explicitly explored by studying the frequency of the surface mode as a function of their angular momentum. The applicability of the semiclassical approximation for the excited states is also discussed. We show that the semiclassical approach provides simple and accurate formulas for the density of states and the quantum depletion of the condensate.
Abstract Using the time-dependent Hartree–Fock–Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings computed by quantum Monte Carlo simulations. We present also a systematic investigation of the collective modes of a Bose condensate confined in an external trap. Our predictions are in qualitative agreement with previous experimental and theoretical results. We show in particular that our theory is capable of explaining the so-called anomalous behavior of the m = 0 mode.
In this paper, we investigate the collective excitations of an attractively interacting Bose–Einstein condensate confined in a two-channel potential. Using the Bogoliubov approximation, we derive the Bogoliubov–de Gennes equations and determine the excitation spectrum numerically. Two distinct modes are identified: the well-known Josephson mode, associated with periodic inter-channel tunneling, and a novel antisymmetric translational mode, describing out-of-phase oscillations of the condensate center of mass. Unlike conventional dipole oscillations, the latter arises from the interplay between inter-channel coupling and attractive nonlinearity and does not follow the Kohn theorem. We then employ the variational approximation to describe the condensate dynamics under these excitations and to extract the corresponding mode frequencies. The results are further validated by real-time simulations of the governing Gross–Pitaevskii equations, showing good agreement between analytical and numerical approaches.
With the help of a set of exact closed-form solutions to the stationary Gross—Pitaevskii (GP) equation, we calculate the collective excitation and quantum depletion of a weakly interacting Bose gas in the presence of a periodic array of quantum wells. The excitation spectrum (Bogoliubov spectrum) is obtained from the solution of the linearized time-dependent GP equation, which develops energy bands ħω j ( p ) periodic in quasi-momentum space. Moreover, we calculate the excitation strengths Z j ( p ) relative to the density operator and then the dynamic structure factor S ( p , ω). Accordingly, the analytical expressions of quantum depletion of the system are obtained. We find that the quantum depletion is enhanced when the interatomic interactions become larger and the potential is sufficiently deep. The conditions for the possible experimental realization of our scenario are also proposed.
The effective interaction energy of quasiparticles in the Bose fluid, which is described by ”ladder state diagrams” in the Bogoliubov approximation, was studied for a model potential. It is shown that in the Bogoliubov approximation, the interaction of excitations in liquid He can not be described even qualitatively. It means that a model of the weakly interacting dilute Bose gas fails in describing the interaction between excitation in Bose-condensed liquid, although this model qualitatively incorporates superfluidity in itself.
Abstract In the work the problem of phenomenon of superfluidity is considered within the framework of Bose-Einshtein condensation, theoretically. We discuss the main features of the excitation spectrum in a weakly interacting Bose gas. Our analysis will show that the healing length, which determines the length scale below which collective phenomena are physically more relevant than free-particle-like ones. Since the weakly interacting gas of Bose particles has been mapped onto a gas of noninteracting quasiparticles, we are able to analyze the thermodynamics of the system and find how temperature affect the depletion of the condensate.