# Phonons and Correlations

This area of research investigates the basic microscopic properties of an ultracold bose gas. The studies were part of the effort to observe Hawking radiation. However, the observations are rather interesting in themselves.

Firstly, we developed the technique of in situ observation of phonons in a BEC. Since the moving particles composing the phonons interfere with the large condensate wavefunction, the signal is increased by a factor of relative to the usual time-of-flight technique, where is the number of atoms in the condensate. This gives orders of magnitude more signal. This allowed for a very precise study of the dispersion relation and static structure factor. We thus discovered that the group velocity has a minimum, caused by 1D behavior of the excitations at long wavelength. In this work, we created the phonons by the novel technique of short Bragg pulses, and then watched them oscillate and decay in time.

Secondly, we observed phonons which occur naturally in the BEC. This is the Planck distribution of thermal phonons. We observed these phonons in situ by computing the Fourier transform of the image. The resulting power spectrum (the static structure factor) agreed with the Planck distribution with no free parameters. However, if the condensate is cooled too quickly, then extra phonons are created. In this case, the condensate is not as cold as one might think.

Thirdly, by applying our in situ Fourier transform technique above , we made the first calibrated observation of the bunching effect in a 3D bose gas. The bunching phenomenon is an increased probability of finding two particles close together in an ideal bose gas. This phenomenon is thought to result from the quantum mechanical exchange symmetry. This effect is difficult to observe quantitatively, because the bunching only occurs for particle separations which are below the spatial resolution of experimental systems. However, with our Fourier transform technique, the short range effect in position space produces a broad spectrum in -space. This is easily resolvable, allowing for the first quantitative measurement. This confirms the fact that the bunching indeed results from the exchange symmetry, rather than from interactions, light-assisted collisions, or losses.

#### Related Publications

Shammass, I., Rinott, S., Berkovitz, A., Schley, R. & Steinhauer, J. Phonon Dispersion Relation of an Atomic Bose-Einstein Condensate. Phys. Rev. Lett. 109, 195301 (2012).

Schley, R., Berkovitz, A., Rinott, S., Shammass, I., Blumkin, A. & Steinhauer, J. Planck Distribution of Phonons in a Bose-Einstein Condensate. Phys. Rev. Lett. 111, 055301 (2013).

Blumkin, A., Rinott, S., Schley, R., Berkovitz, A., Shammass, I. & Steinhauer, J. Observing Atom Bunching by the Fourier Slice Theorem. Phys. Rev. Lett. 110, 265301 (2013).