Abstract
We explore, both experimentally and theoretically, the response of an elongated Bose-Einstein condensate to modulated interactions. We identify two distinct regimes differing in modulation frequency and modulation strength. Longitudinal surface waves are generated either resonantly or parametrically for modulation frequencies near the radial trap frequency or twice the trap frequency, respectively. The dispersion of these waves, the latter being a Faraday wave, is well-reproduced by a mean-field theory that accounts for the 3D nature of the elongated condensate. In contrast, in the regime of lower modulation frequencies we find that no clear resonances occur, but with increased modulation strength, the condensate forms an irregular granulated distribution that is outside the scope of a mean-field approach. We find that the granulated condensate is characterized by large quantum fluctuations and correlations, which are well-described with single-shot simulations obtained from wavefunctions computed by a beyond mean-field theory at zero temperature, the multiconfigurational time-dependent Hartree for bosons method.
Highlights
Spatial patterns frequently emerge in driven fluids in a variety of contexts, including chemistry, biology, and nonlinear optics [1]
We find that the granulated condensate is characterized by large quantum fluctuations and correlations, which are well described with single-shot simulations obtained from wave functions computed by a beyondmean-field theory at zero temperature, the multiconfigurational time-dependent Hartree for bosons method
We find that the Faraday pattern is suppressed during axial compression but subsequently revives as the condensate returns to its original size
Summary
Spatial patterns frequently emerge in driven fluids in a variety of contexts, including chemistry, biology, and nonlinear optics [1] Instabilities in these systems can generally be categorized as Rayleigh-Benard convection, Taylor-Couette flow, or parametric surface waves. In the BEC experiments, the transverse breathing mode, excited at a frequency of 2ωr, strongly couples to the density and, to the nonlinear interactions of the condensate This coupling produces the longitudinal sound waves responsible for creating Faraday waves [18,19]. We explore a different modulation regime, both experimentally and theoretically, where ω is far from any trap frequency The behavior in this regime is distinctly different; no clear resonances are observed, and much larger modulation amplitude and time are needed to obtain a significant response. The discrepancies between the Gross-Pitaevskii mean-field description and both the experimental observations and our MCTDHB results hint that granulation emerges concurrently with many-body correlations
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