Observation of Faraday Waves in a Bose-Einstein Condensate

Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.

Figure 1

In-trap absorption images of Faraday waves in a BEC. Frequency labels for each image represent the driving frequency at which the transverse trap confinement is modulated.

Figure 2

Average spacing of adjacent maxima of the longitudinal patterns plotted versus the transverse driving frequency. Points are experimental data, while the line shows the theoretical values calculated for the longitudinal modes closest to half the driving frequency.

Figure 3

Onset of Faraday wave formation after driving the transverse breathing mode for only two cycles. Pattern visibility is quantified as described in 16.

Figure 4

Pattern domains observed in a very elongated BEC. The graph shows an integrated cross section of the BEC displayed in the inset.

Figure 5

Impact-oscillator behavior. Plot of BEC radius in the tight direction vs. time when continuously driving the transverse breathing mode. Points show experimental data, while the curve corresponds to numerical simulation. Inset: (a) Image of BEC after 5.2 driving periods, i.e., 16.2 ms. (b) Fourier transform of the image in (a).