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 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. 1 arXiv:1707.04055v4 [cond-mat.quant-gas]

Spatial structure of the pair wave function and the density correlation functions throughout the BEC-BCS crossover

“…Combination of the first two equations, (5) and (6), into the third one, (7), and using a recursion relation of Legendre functions, yields the following closed expression of e 0 in terms of the four thermodynamic quantities n, µ, a and ∆,…”

“…To conclude we would like to briefly address the consequences of the long range behavior near unitarity and in the BCS limit on current experimental studies with confined ultracold gases. Typically, specially in the BEC side [7,39,40] and in gases with bosons such as 87 Rb [41] and 7 Li, [42], the local density approximation has been shown to be quite accurate.…”

Management of the correlations of UltracoldBosons in triple wells

“…Therefore, we use MCTDHB to obtain an optimized problem-adapted basis to investigate tilted lattices. MCTDHB is in principle exact [36,39], has been verified with experimental results [40], can describe both coherent and fragmented condensates, and includes the GP theory as an extreme case when only one single-particle state is considered; see [38,41,42] for details on MCTDHB.…”

Faraday and Resonant Waves in Dipolar Cigar-Shaped Bose-Einstein Condensates

“…In the context of ultracold gases, Faraday waves were first investigated theoretically in 2002 by Staliunas [11]. After these theoretical and numerical results for the systems with contact interaction, where it was assumed that the interaction strength is harmonically modulated, the Faraday waves were first measured in BEC experiments with 87 Rb in 2007 by Engels [12], and more recently with 7 Li by Hulet and Bagnato [13,14]. In the first experiment, the radial part of the harmonic trap was modulated, while the other two experiments have modulated the contact interaction strength.…”