Parametric Excitation of a Bose-Einstein Condensate: From Faraday Waves to Granulation

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 an 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 wave functions computed by a beyond-mean-field theory at zero temperature, the multiconfigurational time-dependent Hartree for bosons method.

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Plain Language Summary

In 1831, Michael Faraday observed a pattern of ripples on the surface of a bucket of fluid that was shaken vertically. These patterns, known as Faraday waves, arise when the shaking frequency is tuned to some critical value, and they take the form of stripes, crosses, or a mash-up of various, but regular, geometric shapes. While they can arise in any fluid, the Faraday pattern depends on the properties of the fluid. To better understand how these patterns emerge, we study Faraday waves in a tiny quantum fluid of ultracold atoms, known as a Bose-Einstein condensate (BEC).

As expected, we observe regular Faraday wave patterns when the shaking frequency is close to one of the critical values, but surprisingly, we find that far from those, the BEC fragments into an irregular granular array. This granulation effect is similar to the unpredictable distribution of sizes of shards falling from a broken glass. Each time the glass, or the BEC, breaks, a different and fundamentally unpredictable distribution of fragments is created. The appearance of grains suggests that the shaking creates quantum correlations.

Physicists are interested in how interactions between atoms in a BEC create correlations. The transition from a predictable, regular array of the Faraday pattern to a highly irregular granulation is a challenge to explain and understand. Standard theoretical approaches are unable to reproduce the observations, particularly the broad distribution of grain sizes. Instead, we employ a sophisticated theoretical method that accounts for quantum fluctuations and correlations, effects that are unaccounted for in the usual theories, and we find remarkable agreement with the experimental observations.

These results may have important implications for understanding turbulence in quantum fluids.