Simple derivation of the condition for the transition point from absolute instability of plane dark solitons to their convective instability is suggested. It is shown that unstable wave packet expands with velocity equal to the minimal group velocity of the disturbance waves propagating along a dark soliton. The growth rate of the length of dark solitons generated by the flow of Bose-Einstein condensate past an obstacle is estimated. Analytical theory is confirmed by the results of numerical simulations.
Dark solitons in superfluid Bose gases decay through the snake instability mechanism, unless they are strongly confined. Recent experiments in superfluid Fermi gases have also interpreted soliton decay via this mechanism. However, we show using both an effective field numerical simulation and a perturbative analysis that there is a qualitative difference between soliton decay in the BEC- and BCS-regimes. On the BEC-side of the interaction domain, the characteristic snaking deformations are induced by fluctuations of the amplitude of the order parameter, while on the BCS-side, fluctuations of t…
Here we revisit the topic of stationary and propagating solitonic excitations in self-repulsive three-dimensional Bose-Einstein condensates by quantitatively comparing theoretical analysis and associated numerical computations with our experimental results. Using fully 3d numerical simulations, we explore the existence, stability, and evolution dynamics of planar dark solitons, as well as their instability-induced decay products including solitonic vortices and vortex rings. In the trapped case and with no adjustable parameters, our numerical findings are in correspondence with experimentally …
Snake instability of dark solitons across the BEC-BCS crossover: an effective field theory perspective
本文利用最近发展起来的有效场论[Eur. B 88，122（2015）]。这种理论处理已被证明是适合于研究稳定的暗孤子在准一维设置跨越BEC-BCS交叉。在本文中，稳定孤子解的节面通过加入横向调制而被扰动。耦合的非线性微分方程描述的扰动的幅度的系统的数值解导致的不稳定谱计算的范围广泛的相互作用制度，并与其他理论预测。的最大横向尺寸，原子云可以有，以保持稳定性的估计，和自旋不平衡对这个临界长度的影响进行了检查，揭示了稳定的孤子与增加的不平衡。
In this paper, we formulate extended stream functions (ESFs) to describe the dynamics of Bose-Einstein condensations in the two-dimensional space. The ordinary stream function is applicable only for stationary and incompressible superfluids, whereas the ESFs can describe the dynamics of compressible and non-stationary superfluids. The ESFs are composed of two stream functions, i.e., one describes the compressible density modulations and the other the incompressible rotational superflow. As an application, we study the snake instability of the dark soliton in a rectangular potential in detail b…
By means of analytical and numerical methods, we address the modulational instability (MI) in chiral condensates governed by the Gross-Pitaevskiiequation including the current nonlinearity. The analysis shows that this nonlinearity partly suppresses off the MI driven by the cubic self-focusing, although the current nonlinearity is not represented in the system's energy (although it modifies the momentum), hence it may be considered as zero-energy nonlinearity. Direct simulations demonstrate generation of trains of stochastically interacting chiral solitons by MI. In the ring-shaped setup, the …
Gray solitons are a one-parameter family of solutions to the one-dimensional non-linear Schrödinger equation (NLSE) with positive cubic nonlinearity, as found in repulsively interacting dilute Bose-Einstein condensates or electromagnetic waves in the visible spectrum in waveguides described by Gross-Pitaevskii mean field theory. In two dimensions these solutions to the NLSE appear as a line or plane of depressed condensate density or light intensity, but numerical solutions show that this line is dynamically unstable to `snaking': the initially straight line of density or intensity minimum und…
We experimentally study universal nonequilibrium dynamics of two-dimensional atomic Bose gases quenched from repulsive to attractive interactions. We observe the manifestation of modulational instability that, instead of causing collapse, fragments a large two-dimensional superfluid into multiple wave packets universally around a threshold atom number necessary for the formation of Townes solitons. We confirm that the density distributions of quench-induced solitary waves are in excellent agreement with the stationary Townes profiles. Furthermore, our density measurements in the space and time…
