1207.3440 (I. Shammass et al.)

The phonon dispersion relation of a Bose-Einstein condensate    [PDF]

I. Shammass, S. Rinott, A. Berkovitz, R. Schley, J. Steinhauer

We measure the dispersion relation of a Bose-Einstein condensate. We present the technique of short Bragg pulses, in which a sinusoidal potential is applied for a time much shorter than the period of oscillation of the phonons. This pulse results in a standing wave of phonons. The time evolution of this standing wave is observed in-situ, giving the oscillation frequency as a function of the wavenumber; the dispersion relation. This technique is particularly suitable for long-wavelength phonons. This technique is thus complementary to Bragg spectroscopy, which gives the excitation spectrum rather than the dispersion relation, and is particularly suitable for short wavelengths. The static structure factor is also measured in the long-wavelength regime. Furthermore, the high sensitivity of the technique gives an order of magnitude more precision than the previous Bragg spectroscopy results. Deviations from the local-density approximation are seen at the 10% level, suggesting a violation of the f-sum rule (the Bijl-Feynman relation). Furthermore, the lifetime of the oscillations is significantly longer than predicted by the local-density approximation, suggesting that discrete radial modes are playing a role.

View original: http://arxiv.org/abs/1207.3440