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 (GP) 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.PACS numbers: 03.75. Kk, 67.85.De, 47.40.x, 05.45.Yv Nonlinear structures in dilute-gas Bose-Einstein condensates (BECs) have been the focus of intense research efforts, deepening our understanding of quantum dynamics and providing intriguing parallels between atomic physics, condensed matter and optical systems. For superfluids that are confined in a narrow channel, one of the most prominent phenomena of nonlinear behavior is the existence of solitons in which a tendency to disperse is counterbalanced by the nonlinearities of the system. In single-component BECs, dark and bright solitons, forming local density suppressions and local bumps in the density, resp., have attracted great interest [1]. In twocomponent BECs, the dynamics are even richer as a new degree of freedom, the relative flow between the two components, is possible.In this Letter, we investigate novel dynamics of superfluid-superfluid counterflow, which is in contrast to the extensively studied counterflow of a superfluid and normal fluid in liquid helium [2]. Previous theoretical analysis has demonstrated that spatially uniform, counterflowing superfluids exhibit modulational instability (MI) when the relative speed exceeds a critical value [3]. Modulational instability is characterized by a rapid growth of long wavelength, small amplitude perturbations to a carrier wave into large amplitude modulations. The growth is due to the nonlinearity in the system [4]. Our experiments and analysis reveal that by carefully tuning the relative speed slightly above the critical value, we can enhance large amplitude density modulations at the overlap interface between two nonlinearly coupled BEC components while mitigating the effects of MI in the slowly varying background regions. A dark-bright soliton train then results.In two previous experiments, individual dark-bright solitons were engineered in two stationary components using a wavefunction engineering technique [5,6]. In our experiment we find that trains of dark-bright solitons can occur quite naturally in superfluid counterflow. This novel method of generating dark-bright solitons turns out to be robust and repeatable. In single-component, attractive BECs the formation of a bright soliton train from an initial density jump has been predicted [7]. However, both condensate collapse and the effects of MI in the density backgro...

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 BoseEinstein 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, which we observe for the first time in a BEC, 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 multi-dimensional numerical simulations are presented.PACS numbers: 03.75. Kk, 67.85.De, 47.40.x, 03.75.Lm, 05.45.Yv Superfluids are a robust model system for the investigation of nonlinear fluid flow. Governed by an underlying macroscopic wavefunction, superfluids can display a large variety of nonlinear wave phenomena in the context of matterwaves. In Bose-Einstein condensates (BECs), nonlinear structures including solitons, vortices and vortex rings have been the focus of intense research efforts [1, 2]. In this work, we investigate the regime of fast counterflow between two distinguishable superfluids in a narrow channel and observe dynamics leading to novel structures. Modulational instability (MI), in which small perturbations to a carrier wave, reinforced by nonlinearity, experience rapid growth [3], plays a key role in the dynamics. In many nonlinear systems, MI leads to the breakup of periodic wavetrains, as in sufficiently deep water [4], as well as the formation of localized structures in optics [5] and BECs [6]. In our case, MIinduced regular density modulations, formed throughout the BEC, lead to the emergence of a large number of beating dark-dark solitons. These solitons-which exhibit periodic energy exchange between the two condensate components [4]-are a generalization of static dark-dark solitons [3]. They are distinctly different from all previously observed solitons in BECs, including dark-bright solitons which were generated in a two-component mixture by marginally critical counterflow-induced MI near a density edge [9]. We perform three-dimensional (3D) numerical simulations to corroborate this interpretation and furthermore identify a subsequent transverse instability resulting in multi-dimensional structures such as vortex lines (see [10] for the scalar counterpart).We study superfluid counterflow with an experimental system consisting of BECs with typically 8 × 10

Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton "molecules," composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark-and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons. This equation provides equilibrium positions and characteristic oscillation frequencies of the solitons, which are found to be in good agreement with the eigenfrequencies of the anomalous modes of the system.

The processes of merging and splitting dilute-gas Bose-Einstein condensates are studied in the nonadiabatic, high-density regime. Rich dynamics are found. Depending on the experimental parameters, uniform soliton trains containing more than ten solitons or the formation of a highdensity bulge as well as quantum (or dispersive) shock waves are observed experimentally within merged BECs. Our numerical simulations indicate the formation of many vortex rings. In the case of splitting a BEC, the transition from sound-wave formation to dispersive shock-wave formation is studied by use of increasingly stronger splitting barriers. These experiments realize prototypical dispersive shock situations.

Spin-orbit-coupled Bose-Einstein condensates (BECs) provide a powerful tool to investigate interesting gauge field-related phenomena. Here we study the ground state properties of such a system and show that it can be mapped to the well-known Dicke model in quantum optics, which describes the interactions between an ensemble of atoms and an optical field. A central prediction of the Dicke model is a quantum phase transition between a superradiant phase and a normal phase. We detect this transition in a spin-orbit-coupled BEC by measuring various physical quantities across the phase transition. These quantities include the spin polarization, the relative occupation of the nearly degenerate single-particle states, the quantity analogous to the photon field occupation and the period of a collective oscillation (quadrupole mode). The applicability of the Dicke model to spin-orbit-coupled BECs may lead to interesting applications in quantum optics and quantum information science.