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Register a new userSuperfluid flow past an obstacle in annular Bose--Einstein condensates
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We investigate the flow of a one-dimensional nonlinear Schrodinger model with periodic boundary conditions past an obstacle, motivated by recent experiments with Bose--Einstein condensates in ring traps. Above certain rotation velocities, localized solutions with a nontrivial phase profile appear. In striking difference from the infinite domain, in this case there are many critical velocities. At each critical velocity, the steady flow solutions disappear in a saddle-center bifurcation. These interconnected branches of the bifurcation diagram lead to additions of circulation quanta to the phase of the associated solution. This, in turn, relates to the manifestation of persistent current in numerous recent experimental and theoretical works, the connections to which we touch upon. The complex dynamics of the identified waveforms and the instability of unstable solution branches are demonstrated.
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We study the flow of a spinor (F=1) Bose-Einstein condensate in the presence of an obstacle. We consider the cases of ferromagnetic and polar spin-dependent interactions and find that the system demonstrates two speeds of sound that are identified analytically. Numerical simulations reveal the nucleation of macroscopic nonlinear structures, such as dark solitons and vortex-antivortex pairs, as well as vortex rings in one- and higher-dimensional settings respectively, when a localized defect (e.g., a blue-detuned laser beam) is dragged through the spinor condensate at a speed larger than the second critical speed.
Stability of dark solitons generated by a supersonic flow of Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow velocity from absolute instability of dark solitons to their convective instability. This leads to decay of disturbances of solitons at fixed distance from the obstacle and formation of effectively stable dark solitons. This phenomenon explains surprising stability of the flow picture that has been observed in numerical simulations.
We theoretically show that the topology of a non-simply-connected annular atomic Bose-Einstein condensate enforces the inner surface waves to be always excited with outer surface excitations and that the inner surface modes are associated with induced vortex dipoles unlike the surface waves of a simply-connected one with vortex monopoles. Consequently, under stirring to drive an inner surface wave, a peculiar population oscillation between the inner and outer surface is generated regardless of annulus thickness. Moreover, a new vortex nucleation process by stirring is observed that can merge the inner vortex dipoles and outer vortex into a single vortex inside the annulus. The energy spectrum for a rotating annular condensate with a vortex at the center also reveals the distinct connection of the Tkachenko modes of a vortex lattice to its inner surface excitations.
We analyze the excitation spectrum of a superfluid Bose-Einstein condensate rotating in a ring trap. We identify two important branches of the spectrum related to outer and inner edge surface modes that lead to the instability of the superfluid. Depending on the initial circulation of the annular condensate, either the outer or the inner modes become first unstable. This instability is crucially related to the superfluid nature of the rotating gas. In particular we point out the existence of a maximal circulation above which the superflow decays spontaneously, which cannot be explained by invoking the average speed of sound.
We present experimental results and a systematic theoretical analysis of dark-br ight soliton interactions and multiple-dark-bright soliton complexes in atomic t wo-component Bose-Einstein condensates. We study analytically the interactions b etween two-dark-bright solitons in a homogeneous condensate and, then, extend ou r considerations to the presence of the trap. An effective equation of motion is derived for the dark-bright soliton center and the existence and stability of stationary two-dark-bright soliton states is illustrated (with the bright components being either in- or out-of-phase). The equation of motion provides the characteristic oscillation frequencies of the solitons, in good agreement with the eigenfrequencies of the anomalous modes of the system.
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