arXiv:cond-mat/9805068 · Physical Review Letters

Quantized Vortices and Collective Oscillations of a Trapped Bose-Einstein Condensate

Francesca Zambelli, S. Stringari

Published Aug 31, 1998• 127 citations

Abstract

Using a sum rule approach we calculate the frequency shifts of the quadrupole oscillations of a harmonically trapped Bose gas due to the presence of a quantized vortex. Analytic results are obtained for positive scattering lengths and large $N$ where the shift relative to excitations of opposite angular momentum is found to be proportional to the quantum circulation of the vortex and to decrease as ${N}^{\ensuremath{-}2/5}$. Results are also given for smaller values of $N$ covering the transition between the ideal gas and the Thomas-Fermi limit. The splitting of the collective frequencies in toroidal configurations is also discussed.

DOI: 10.1103/physrevlett.81.1754

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arXiv:cond-mat/9805068 · Physical Review Letters

Quantized Vortices and Collective Oscillations of a Trapped Bose-Einstein Condensate

Francesca Zambelli, S. Stringari

Published Aug 31, 1998• 127 citations

arXiv HTML PDF

Abstract

N

where the shift relative to excitations of opposite angular momentum is found to be proportional to the quantum circulation of the vortex and to decrease as

{N}^{\ensuremath{-}2/5}

. Results are also given for smaller values of

N

covering the transition between the ideal gas and the Thomas-Fermi limit. The splitting of the collective frequencies in toroidal configurations is also discussed.

DOI: 10.1103/physrevlett.81.1754

Related papers

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Arup Banerjee, B. Tanatar

We study the effect of lower dimensional geometry on the frequency splitting of the quadrupole oscillations of a harmonically trapped Bose-Einstein condensate due to the presence of a quantized vortex. To study the effect of two-dimensional geometry we consider a pancake-shaped condensate and employ various models for the coupling parameter depending on the thickness of the condensate relative to the value of the scattering length. Using these models and the sum-rule approach we obtain analytical expressions for the frequency splitting. These expressions are valid for positive scattering length and large $N$ . We show that the frequency splitting of the quadrupole oscillations are significantly altered by the reduced dimensionality and also study the evolution of the splitting as the system makes transition from one scattering regime to the other.We study the effect of lower dimensional geometry on the frequency splitting of the quadrupole oscillations of a harmonically trapped Bose-Einstein condensate due to the presence of a quantized vortex. To study the effect of two-dimensional geometry we consider a pancake-shaped condensate and employ various models for the coupling parameter depending on the thickness of the condensate relative to the value of the scattering length. Using these models and the sum-rule approach we obtain analytical expressions for the frequency splitting. These expressions are valid for positive scattering length and large $N$. We show that the frequency splitting of the quadrupole oscillations are significantly altered by the reduced dimensionality and also study the evolution of the splitting as the system makes transition from one scattering regime to the other.

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Tarun Kanti Ghosh

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N

where the shift relative to excitations of opposite angular momentum is found to be proportional to the quantum circulation of the vortex and to decrease as

{N}^{\ensuremath{-}2/5}

. Results are also given for smaller values of

N

covering the transition between the ideal gas and the Thomas-Fermi limit. The splitting of the collective frequencies in toroidal configurations is also discussed.

N

. We show that the frequency splitting of the quadrupole oscillations are significantly altered by the reduced dimensionality and also study the evolution of the splitting as the system makes transition from one scattering regime to the other.

a

. We calculate the leading corrections to the frequencies from quantum fluctuations around the mean field. The semiclassical correction is proportional to

{N}^{1/5}{a}^{6/5}

, where

N

is the number of atoms in the condensate. The correction is positive semidefinite and is zero for surface modes whose eigenfunctions have a vanishing Laplacian. The shift in the frequency of the lowest quadrupole mode for an axially symmetric trap is large enough that it should be measurable in future experiments.

Ω

of the trap, the tendency of the system to exhibit spontaneous deformation is shown to lower the barrier which inhibits the nucleation of vortices at smaller

Ω

. The corresponding value of the critical angular velocity

Ω_c

is calculated as a function of the deformation of the trap and of the chemical potential. The theoretical predictions for

Ω_c

refer to the case of a sudden switch-on of the deformed rotating trap and they are compared with recent experimental data.

We study the collective excitations of a neutral atomic Bose-Einstein condensate with gravitylike

1/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.