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Journal of the Physical Society of Japan

Alternate Oscillation between Scissors and Quadrupole Modes in Sodium Bose–Einstein Condensates

Masahiro Yamazaki, Kazuki Wakayama, Miho Harada, Atsuo Morinaga

Published Mar 9, 2015• 1 citation
Publisher

Abstract

Using an additional off-axis Helmholtz coil, we modulated the strength of a magnetic field at the center of a cloverleaf trap for sodium Bose–Einstein condensates so that it passed through zero for a few milliseconds. At a modulation time of 1 ms, a scissors mode and a high-lying quadrupole mode were generated independently, which had the same Landau damping rates of 39(10) 1/s. However, at 2 ms, alternate oscillation between the scissors mode and the high-lying quadrupole mode, whose frequency was twice that of the scissors mode, was observed with the frequency of the low-lying quadrupole mode.

DOI
10.7566/jpsj.84.044001

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Using an additional off-axis Helmholtz coil, we modulated the strength of a magnetic field at the center of a cloverleaf trap for sodium Bose–Einstein condensates so that it passed through zero for a few milliseconds. At a modulation time of 1 ms, a scissors mode and a high-lying quadrupole mode were generated independently, which had the same Landau damping rates of 39(10) 1/s. However, at 2 ms, alternate oscillation between the scissors mode and the high-lying quadrupole mode, whose frequency was twice that of the scissors mode, was observed with the frequency of the low-lying quadrupole mode.
We report the observation of the scissors mode of a Bose-Einstein condensed gas of 87Rb atoms in a magnetic trap, which gives direct evidence of superfluidity in this system. The scissors mode of oscillation is excited by a sudden rotation of the anisotropic trapping potential. For a gas above T(c) (normal fluid) we detect the occurrence of oscillations at two frequencies, with the lower frequency corresponding to the rigid body value of the moment of inertia. Well below T(c) the condensate oscillates at a single frequency, without damping, as expected for a superfluid.
We study nonlinear mixing effects among quadrupole modes and scissors modes in a harmonically trapped Bose-Einstein condensate. Using a perturbative technique in conjunction with a variational approach with a Gaussian trial wave function for the Gross-Pitaevskii equation, we find that mode mixing occurs selectively. Our perturbative approach is useful in gaining a qualitative understanding of the recent experiment [M. Yamazaki et al., J. Phys. Soc. Jpn. 84, 44001 (2015)], exhibiting a beating phenomenon of the scissors mode as well as a modulation phenomenon of the low-lying quadrupole mode by the high-lying quadrupole mode frequency. Within the second-order treatment of the nonlinear mode coupling terms, our approach predicts all the spectral peaks obtained by the numerical simulation of the Gross-Pitaevskii equation.
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We report the first experimental observation of Beliaev coupling between collective excitations of a Bose-Einstein condensed gas. Beliaev coupling is not predicted by the Gross-Pitaevskii equation and so this experiment tests condensate theory beyond the mean field approximation. Measurements of the amplitude of a high frequency scissors mode show that the Beliaev process transfers energy to a lower-lying mode and then back and forth between these modes, unlike Landau processes which lead to a monotonic decrease in amplitude. To enhance the Beliaev process we adjusted the geometry of the magnetic trapping potential to give a frequency ratio of 2 to 1 between the two scissors modes.
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