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Counterflow induced modulational instability in miscible, two-component Bose-Einstein condensates

Mark A. Hoefer, Chris Hamner, Peter Engels

Published Jul 28, 2010• 0 citations
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Abstract

Washington State University, Department of Physics and Astronomy, Pullman, Washington 99164, USA(Dated: July 29, 2010)Modulational instability (MI) due to relative motion of two superfluids is found for a miscible,binary Bose-Einstein condensate (BEC). For sufficiently large relative speeds of the BEC compo-nents, we experimentally observe the onset of counterflow induced MI leading to the proliferationof dark-dark vector solitons which can experience a transverse (snake) instability. This is in con-trast to nonlinear self-steepening and intercomponent shock formation previously observed at lowcounterflow speeds. Our experimental results are complemented by a linear stability analysis andby multi-dimensional numerical simulations that reveal an intriguing dynamical richness of the su-perfluid counterflow.

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Washington State University, Department of Physics and Astronomy, Pullman, Washington 99164, USA(Dated: July 29, 2010)Modulational instability (MI) due to relative motion of two superfluids is found for a miscible,binary Bose-Einstein condensate (BEC). For sufficiently large relative speeds of the BEC compo-nents, we experimentally observe the onset of counterflow induced MI leading to the proliferationof dark-dark vector solitons which can experience a transverse (snake) instability. This is in con-trast to nonlinear self-steepening and intercomponent shock formation previously observed at lowcounterflow speeds. Our experimental results are complemented by a linear stability analysis andby multi-dimensional numerical simulations that reveal an intriguing dynamical richness of the su-perfluid counterflow.
We investigate the dynamics of two miscible superfluids experiencing fast counterflow in a narrow channel. The superfluids are formed by two distinguishable components of a trapped dilute-gas Bose-Einstein condensate (BEC). The onset of counterflow-induced modulational instability throughout the cloud is observed and shown to lead to the proliferation of dark-dark vector solitons. These solitons do not exist in single-component systems, exhibit intriguing beating dynamics, and can experience a transverse instability leading to vortex line structures. Experimental results and multidimensional numerical simulations are presented.
The dynamics of two penetrating superfluids exhibit an intriguing variety of nonlinear effects. Using two distinguishable components of a Bose-Einstein condensate, we investigate the counterflow of two superfluids in a narrow channel. We present the first experimental observation of trains of dark-bright solitons generated by the counterflow. Our observations are theoretically interpreted by three-dimensional numerical simulations for the coupled Gross-Pitaevskii equations and the analysis of a jump in the two relatively flowing components' densities. Counterflow-induced modulational instability for this miscible system is identified as the central process in the dynamics.
We investigate nonlinear dynamics induced by the modulation instability of a two-component mixture in an atomic Bose-Einstein condensate. The nonlinear dynamics is examined using numerical simulations of the time-dependent coupled Gross-Pitaevskii equations. The unstable modulation grows from initially miscible condensates into various types of vector solitary waves, depending on the combinations of the sign of the coupling constants (intracomponent and intercomponent). We discuss the detailed features of the modulation instability, dynamics of solitary wave formation, and an analogy with the collapsing dynamics in a single-component condensate with attractive interactions.
We study theoretically the instability of countersuperflow, i.e., two counterpropagating miscible superflows, in uniform two-component Bose-Einstein condensates. Countersuperflow instability causes mutual friction between the superfluids, causing a momentum exchange between the two condensates, when the relative velocity of the counterflow exceeds a critical value. The momentum exchange leads to nucleation of vortex rings from characteristic density patterns due to the nonlinear development of the instability. Expansion of the vortex rings drastically accelerates the momentum exchange, leading to a highly nonlinear regime caused by intervortex interaction and vortex reconnection between the rings. For a sufficiently large interaction between the two components, rapid expansion of the vortex rings causes isotropic turbulence and the global relative motion of the two condensates relaxes. The maximum vortex line density in the turbulence is proportional to the square of the relative velocity.
We investigate the effect of higher-order interactions induced by shape-dependent confinement in the modulational instability (MI) of a binary mixture of Bose-Einstein condensates. For this, we present and compute both analytically and numerically a system of coupled Gross-Pitaevskii equations with residual nonlinearity that rule the dynamics of the mixture. Using the linear stability approach, we obtain the instability criteria of the mixture and find that the MI can be excited in miscible condensates and altered in immiscible condensates due to the effect of residual nonlinearity. Direct numerical calculations are performed to support the analytical predictions, and a good agreement is found. The space-time evolution of the condensate density is displayed in both cases when the mixture is miscible and immiscible, showing the generation of bright solitons for modes predicted to be unstable.
Modulational instability (MI) is a fundamental phenomenon in the study of nonlinear dynamics, spanning diverse areas such as shallow water waves, optics, and ultracold atomic gases. In particular, the nonlinear stage of MI has recently been a topic of intense exploration and has been shown to manifest, in many cases, in the generation of dispersive shock waves (DSWs). In this Letter, we experimentally probe the MI dynamics in an immiscible two-component ultracold atomic gas with exclusively repulsive interactions, catalyzed by a hard-wall-like boundary produced by a repulsive optical barrier. We analytically describe the expansion rate of the DSWs in this system, generalized to arbitrary intercomponent interaction strengths and species ratios. We observe excellent agreement among the analytical results, an effective 1D numerical model, full 3D numerical simulations, and experimental data. Additionally, we extend this scenario to the interaction between two counterpropagating DSWs, which leads to the production of Peregrine soliton structures. These results further demonstrate the versatility of atomic platforms toward the controlled realization of DSWs and rogue waves.