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arXiv:cond-mat/0007209

Collective excitation frequencies of a Bose - Einstein condensate with electromagnetically induced $1/r$ attraction

I. E. Mazets

Published Jul 12, 2000• 1 citation
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Abstract

We investigate collective excitations of an atomic Bose-Einstein condensate in a recently discovered regime [D.O'Dell et al., Phys. Rev. Lett. 84, 5687 (2000)] of a balance between electromagnetically induced $1/r$ attraction and a short-range interatomic repulsion. The corresponding frequencies for monopole, dipole, and quadrupole modes are calculated numerically in the zero temperature case.

DOI
10.48550/arxiv.cond-mat/0007209

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Collective excitation frequencies of a Bose - Einstein condensate with electromagnetically induced 1/r1/r1/r attraction
We investigate collective excitations of an atomic Bose-Einstein condensate in a recently discovered regime [D.O'Dell et al., Phys. Rev. Lett. 84, 5687 (2000)] of a balance between electromagnetically induced 1/r1/r1/r attraction and a short-range interatomic repulsion. The corresponding frequencies for monopole, dipole, and quadrupole modes are calculated numerically in the zero temperature case.
We study the collective excitations of a neutral atomic Bose-Einstein condensate with gravitylike 1/r1/r1/r interatomic attraction induced by an electromagnetic wave. Using the time-dependent variational approach, we derive an analytical spectrum for monopole and quadrupole mode frequencies of a gravitylike self-bound Bose condensed state at zero temperature. We also analyze the excitation frequencies of the Thomas-Fermi--gravity (TF-G) and gravity (G) regimes. Our result agrees excellently with that of Giovanazzi et al. [Europhysics Lett., 56, 1 (2001)], which is obtained within the sum-rule approach. We also consider the vortex state. We estimate the superfluid coherence length and the critical angular frequencies to create a vortex around the z axis. We find that the TF-G regime can exhibit the superfluid properties more prominently than the G regime. We find that the monopole mode frequency of the condensate decreases due to the presence of a vortex.
We investigate the collective excitations of an atomic Bose-Einstein condensate in the self-binding regime produced by electromagnetically induced "gravity" (1/ r attraction). Analytical expressions for the frequencies of the monopole and quadrupole modes are obtained at zero temperature, using the sum-rule approach, and compared with the exact results available in the Thomas-Fermi limit. The low-energy dynamics of such condensates is shown to be dominated by the effective "plasma" frequency. An analog of the Jeans gravitational instability is analyzed.
Finite-temperature simulations are used to study quadrupole excitations of a trapped Bose-Einstein condensate. We focus specifically on the m = 0 mode, where a long-standing theoretical problem is to account for an anomalous variation of the mode frequency with temperature. We explain this behavior in terms of the excitation of two separate modes, corresponding to the coupled motion of the condensate and the thermal cloud. The relative amplitude of the modes depends sensitively on the temperature and on the frequency of the harmonic drive used to excite them. Good agreement with experiment is found for appropriate drive frequencies.
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 excite the lowest-lying quadrupole mode of a Bose-Einstein condensate by modulating the atomic scattering length via a Feshbach resonance. Excitation occurs at various modulation frequencies, and resonances located at the natural quadrupole frequency of the condensate and at the first harmonic are observed. We also investigate the amplitude of the excited mode as a function of modulation depth. Numerical simulations based on a variational calculation agree with our experimental results and provide insight into the observed behavior.