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Theory of Low-Energy Collective Excitations in a Trapped Bose-Einstein Condensate at Finite Temperatures

正人大矢

We present the theory of low-energy collective excitations of a trapped Bose-Einstein condensate which includes the dynamics of thermal quasiparticles. A general expression of the mode frequency and the damping rate is obtained for trapped Bose gases at finite temperatures.

Mar 5, 20030 citations

Temperature-dependent frequency shifts in collective excitations of a Bose-Einstein condensate

Hualin Shi, Wei‐Mou Zheng

By including the contribution of the thermal cloud in the Lagrangian of the condensate of a Bose gas, we extend the time-dependent variational method at zero temperature to study temperature-dependent low collective excitation modes. A Gaussian trial wave function of the condensate and a static distribution density of the thermal cloud are used and analytical expressions for temperature-dependent excitation frequencies obtained. Theoretical results are compared with measurements in the JILA and MIT experiments.By including the contribution of the thermal cloud in the Lagrangian of the condensate of a Bose gas, we extend the time-dependent variational method at zero temperature to study temperature-dependent low collective excitation modes. A Gaussian trial wave function of the condensate and a static distribution density of the thermal cloud are used and analytical expressions for temperature-dependent excitation frequencies obtained. Theoretical results are compared with measurements in the JILA and MIT experiments.

arXiv:cond-mat/9804108Physical Review AFeb 1, 19998 citations

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

弘樹斎藤, Hiroki Saito

Jan 1, 19990 citations

Low Energy Excitations of a Bose-Einstein Condensate: A Time-Dependent Variational Analysis

Víctor M. Pérez‐García, Humberto Michinel, J. I. Cirac +2 more

We solve the time-dependent Gross-Pitaevskii equation by a variational ansatz to calculate the excitation spectrum of a Bose-Einstein condensate in a trap. The trial wave function is a Gaussian which allows an essentially analytical treatment of the problem. Our results reproduce numerical calculations over the whole range from small to large particle numbers, and agree exactly with the Stringari results in the strong interaction limit. Excellent agreement is obtained with the recent JILA experiment and predictions for the negative scattering length case are also made.We solve the time-dependent Gross-Pitaevskii equation by a variational ansatz to calculate the excitation spectrum of a Bose-Einstein condensate in a trap. The trial wave function is a Gaussian which allows an essentially analytical treatment of the problem. Our results reproduce numerical calculations over the whole range from small to large particle numbers, and agree exactly with the Stringari results in the strong interaction limit. Excellent agreement is obtained with the recent JILA experiment and predictions for the negative scattering length case are also made.

Physical Review LettersDec 30, 1996422 citations

Collapses and revivals of collective excitations in trapped Bose condensates

R. Graham, Daniel F. Walls, Matthew J. Collett +2 more

We present a quantum theory of low-lying excitations in a trapped Bose condensate with finite particle numbers. We find that even at zero temperature condensate number fluctuations and/or fluctuations of the excitation frequency due to quantum uncertainties of the mode occupation lead to a collapse of the collective modes due to dephasing. Coherent revivals of the collective excitations are predicted on a much longer time scale. Depletion of collective modes due to second-harmonic generation is discussed.We present a quantum theory of low-lying excitations in a trapped Bose condensate with finite particle numbers. We find that even at zero temperature condensate number fluctuations and/or fluctuations of the excitation frequency due to quantum uncertainties of the mode occupation lead to a collapse of the collective modes due to dephasing. Coherent revivals of the collective excitations are predicted on a much longer time scale. Depletion of collective modes due to second-harmonic generation is discussed.

arXiv:cond-mat/9612060Physical Review AJan 1, 199817 citations

Collective Excitations of a Dipolar Bose-Einstein Condensate

G. Bismut, Benjamin Pasquiou, É. Maréchal +4 more

We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical predictions based on the Thomas-Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simulations based on a Gaussian ansatz.We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical predictions based on the Thomas-Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simulations based on a Gaussian ansatz.

arXiv:1005.2493Physical Review LettersJul 23, 201075 citations

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

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

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