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Journal of Atomic and Molecular Physics

Landau damping and frequency-shift of a monopole mode in a spherical rubidium Bose-Einstein condensate

Sheng Peng

Published Jan 1, 2015• 1 citation
OpenAlex

Abstract

The Landau damping and frequency- shift of a monopole mode in a spherical rubidium Bose- Einstein condensate are investigated by using the Hartree- Fock- Bogoliubov approximation. The damping rate and frequency- shift magnitude and their temperature dependence are analytically calculated by using the parameters of particle number and traping frequency in the study of numerical simulation and experiment in existence. In the calculation,the practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain the calculation formula for damping and frequency- shift,and the first approximation of Gaussian distribution function is employed for the ground- state wavefunction to eliminate the divergence of the three- mode coupling matrix elements. Our calculation results are directly and indirectly compared with the numerical simulation ones and experimental ones,respectively. And all the comparison illustrate that our method is reasonable.

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The Landau damping and frequency- shift of a monopole mode in a spherical rubidium Bose- Einstein condensate are investigated by using the Hartree- Fock- Bogoliubov approximation. The damping rate and frequency- shift magnitude and their temperature dependence are analytically calculated by using the parameters of particle number and traping frequency in the study of numerical simulation and experiment in existence. In the calculation,the practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain the calculation formula for damping and frequency- shift,and the first approximation of Gaussian distribution function is employed for the ground- state wavefunction to eliminate the divergence of the three- mode coupling matrix elements. Our calculation results are directly and indirectly compared with the numerical simulation ones and experimental ones,respectively. And all the comparison illustrate that our method is reasonable.
The Landau damping and frequency-shift of monopole mode in an elongated-rubidium Bose-Einstein condensate are investigated by using the time-dependent Hartree-Fock-Bogoliubov approximation. Improving the previous approach, We have taken into account the practical relaxations of elementary excitations and the orthogonal relation among them. With such an approach, we provide a new calculation formula for Landau damping rate and frequency-shift. In addition, our previous method of eliminating the divergence in three-mode coupling matrix elements is also improved by zeroing the kinetic energy at the condensate boundary instead of minimizing the ground-state energy. Based on these improvements, both the Landau damping rate and the frequency-shift of the monopole mode are analytically calculated and their temperature dependences are also discussed. And all the theoretical results are in agree meat with experimental data.
The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose—Einstein condensate are investigated by using the Hartree—Fock—Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements. According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.
The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose–Einstein condensate are investigated by using the Hartree–Fock–Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements.According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.更多还原
This paper proposes a method for calculating the Landau damping of a low-energy collective mode in a harmonically trapped Bose–Einstein condensate. Based on the divergence-free analytical solutions for ground-state wavefunction of the condensate and eigenvalues and eigenfunctions for thermally excited quasiparticles, obtained beyond Thomas–Fermi approximation, this paper calculates the coupling matrix elements describing the interaction between the collective mode and the quasiparticles. With these analytical results this paper evaluates the Landau damping rate of a monopole mode in a spherical trap and discusses its dependence on temperature, particle number and trapping frequency of the system.
We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hartree—Fock—Bogoliubov approximation. We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature, on transverse trapping frequency, on atom number in the condensate, and on length of the system. Different from the usual calculation method for the three dimension system, our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation. With little approximation, our theoretical calculation results agree with the experimental ones. Comparing with the usual calculation method, our theory is helpful to deduce the inter-particle interactions in damping phenomenon.
We investigate the Landau damping of the collective mode in a quasi-two-dimension repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hatree—Fock—Bogoliubov approximation and a complete and orthogonal eigenfunction set for the elementary excitation of the system. We calculate the three-mode coupling matrix element between the collective mode and the thermal excited quasi-particles and the Landau damping rate of the collective mode. We discuss the dependence of the Landau damping on temperature, on atom number in the condensate, on transverse trapping frequency and on the length of the condensate. The energy width of the collective mode is taken into account in our calculation. With little approximation, our theoretic calculation results agree well with the experimental ones and are helpful for deducing the damping mechanics and the inter-particle interaction.