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A Variational Sum-Rule Approach to Collective Excitations of a Trapped Bose-Einstein condensate

弘樹斎藤, Hiroki Saito

Jan 1, 19990 citations

Variational Calculations for the Spectrum of Finite Bosons in Harmonic Potentials

Ma Yong-Li, Zhongzhou Chen

Using both the Gaussian and Fetter's variational calculations for the N -body ground-state wavefunction of the trapped Bose-Einstein condensate, we give explicit analytic formulae for the spectrum of finite bosons in harmonic potentials based on the corrected sum rules and generalized virial identities. We compare the low-lying excitation spectra among the Gaussian and Fetter's variational calculations and the exact numerical results. The Gaussian approximation has the simplest reasonable results, valid for N → ∞ and high-lying excitations.Using both the Gaussian and Fetter's variational calculations for the N -body ground-state wavefunction of the trapped Bose-Einstein condensate, we give explicit analytic formulae for the spectrum of finite bosons in harmonic potentials based on the corrected sum rules and generalized virial identities. We compare the low-lying excitation spectra among the Gaussian and Fetter's variational calculations and the exact numerical results. The Gaussian approximation has the simplest reasonable results, valid for N → ∞ and high-lying excitations.

Chinese Physics LettersAug 29, 20035 citations

Collective Excitations of a Trapped Bose–Einstein Condensate at Finite Large Atom Numbers

Yong-li Ma, S. T. Chui, John C. Kimball

Journal of Low Temperature PhysicsOct 1, 20029 citations

Breathing modes of Bose-Einstein condensates in highly asymmetric traps

T. Kimura

The breathing mode collective-excitation frequency of a Bose-Einstein condensate is studied in a highly asymmetric (two- or one-dimensional) trap by using a sum-rule method and a time-dependent variational method. The collective-excitation frequency of the breathing mode in the Thomas-Fermi limit for a purely two- or one-dimensional trap is reproduced by a general result for a three-dimensional trap. In the case of a two- or one-dimensional trap, we obtain the lowest-order correction for the excitation frequency due to the finiteness of the trap frequency in the tightly trapped direction or the finiteness of the number of atoms.The breathing mode collective-excitation frequency of a Bose-Einstein condensate is studied in a highly asymmetric (two- or one-dimensional) trap by using a sum-rule method and a time-dependent variational method. The collective-excitation frequency of the breathing mode in the Thomas-Fermi limit for a purely two- or one-dimensional trap is reproduced by a general result for a three-dimensional trap. In the case of a two- or one-dimensional trap, we obtain the lowest-order correction for the excitation frequency due to the finiteness of the trap frequency in the tightly trapped direction or the finiteness of the number of atoms.

Physical Review AJul 18, 20028 citations

Elementary excitations of the trapped Bose-condensed gas

Patrik Öhberg, E.L. Surkov, Ilkka Juhani Tittonen +3 more

Jan 1, 19970 citations

Elementary excitation spectrum of a trapped weakly interacting Bose-Einstein condensate

Mircea Marinescu, Anthony F. Starace

An analytic expression is presented for the elementary excitation spectrum of the Bose-Einstein condensate of a trapped boson system in the weakly interacting, low-density limit. Explicit analytic formulas for the elementary excitation spectrum are obtained for harmonic-oscillator traps. These formulas provide information about the behavior of the elementary excitation levels as a function of the number of atoms and their interaction strength for a given trap geometry. They also provide a low-density benchmark for results of fully numerical calculations.An analytic expression is presented for the elementary excitation spectrum of the Bose-Einstein condensate of a trapped boson system in the weakly interacting, low-density limit. Explicit analytic formulas for the elementary excitation spectrum are obtained for harmonic-oscillator traps. These formulas provide information about the behavior of the elementary excitation levels as a function of the number of atoms and their interaction strength for a given trap geometry. They also provide a low-density benchmark for results of fully numerical calculations.

Physical Review AJul 1, 19978 citations

Corrected Sum Rule, Generalized Virial Identity and Elementary Excitation Spectrum of Bose–Einstein Condensates at Any Trapped Atom Number

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Corrected Sum Rule, Generalized Virial Identity and Elementary Excitation Spectrum of Bose–Einstein Condensates at Any Trapped Atom Number

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