Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link

We have created a long-lived (≈40 s) persistent current in a toroidal Bose-Einstein condensate held in an all-optical trap. A repulsive optical barrier across one side of the torus creates a tunable weak link in the condensate circuit, which can affect the current around the loop. Superflow stops abruptly at a barrier strength such that the local flow velocity at the barrier exceeds a critical velocity. The measured critical velocity is consistent with dissipation due to the creation of vortex-antivortex pairs. This system is the first realization of an elementary closed-loop atom circuit.     

Motion of a viscoelastic micellar fluid around a cylinder: flow and fracture

We present an experimental study of the motion of a viscoelastic micellar fluid around a moving cylinder, which ranges from fluidlike flow to solidlike tearing and fracture, depending on the cylinder radius and velocity. The observation of crack propagation driven by the cylinder indicates an extremely low tear strength, approximately equal to the steady state surface tension of the fluid. At the highest speeds a driven crack is observed in front of the cylinder, propagating with a fluctuating speed equal on average to the cylinder speed, here as low as 5% of the elastic wave speed.     

A Consistent Characteristic Boundary Condition for General Fluid Mixture and Its Implementation in a Preconditioning Scheme

Characteristic boundary conditions that are capable of handling general fluid mixtures flow at all flow speeds are developed. The formulation is based on fundamental thermodynamics theories incorporated into an efficient preconditioning scheme in a unified manner. Local one-dimensional inviscid (LODI) relations compatible to the preconditioning system are proposed to obtain information carried by incoming characteristic waves at boundaries accurately. The approach has been validated against a variety of sample problems at a broad range of fluid states and flow speeds. Both acoustic waves and hydrodynamic flow features can pass through the boundaries of computational domain transparently without any unphysical reflection or spurious distortion. The approach can be reliably applied to fluid flows at extensive thermodynamic states and flow speeds in numerical simulations. Moreover, the use of the boundary condition shows to improve the computational efficiency.     

Berry phase effects on the dynamics of quasiparticles in a superfluid with a vortex

We study quasiparticle dynamics in a Bose-Einstein condensate with a vortex by following the center of mass motion of a Bogoliubov wave packet, and find important Berry-phase effects due to the background flow. We show that the Berry phase invalidates the usual canonical relation between the mechanical momentum and position variables, leading to important modifications of quasiparticle statistics and thermodynamic properties of the condensates. Applying these results to a vortex in an infinite uniform superfluid, we find that the total transverse force acting on the vortex is proportional to the superfluid density. We propose an experimental setup to directly observe Berry phase effects through measuring local thermal atoms' momentum distribution around a vortex.     

Quantum tweezer for atoms

We propose a quantum tweezer for extracting a desired number of neutral atoms from a reservoir. A trapped Bose-Einstein condensate is used as the reservoir, taking advantage of its coherent nature, which can guarantee a constant outcome. The tweezer is an attractive quantum dot, which may be generated by red-detuned laser light. By moving at certain speeds, the dot can extract a desired number of atoms from the condensate through Landau-Zener tunneling. The feasibility of our quantum tweezer is demonstrated through realistic and extensive model calculations.     

Nonlinear resonant transport of Bose-Einstein condensates

The coherent flow of a Bose-Einstein condensate through a quantum dot in a magnetic waveguide is studied. By the numerical integration of the time-dependent Gross-Pitaevskii equation in the presence of a source term, we simulate the propagation process of the condensate through a double barrier potential in the waveguide. We find that resonant transport is suppressed in interaction-induced regimes of bistability, where multiple scattering states exist at the same chemical potential and the same incident current. We demonstrate, however, that a temporal control of the external potential can be used to circumvent this limitation and to obtain enhanced transmission near the resonance on experimentally realistic time scales.     

Dynamics of Bose–Einstein condensate in a harmonic potential and a Gaussian energy barrier

We have studied the dynamics of Bose–Einstein condensate by solving numerically the Gross-Pitaevskii (GP) equation. We examined the periodic behaviour of the condensate in a shifted harmonic potential, and further demonstrated the tunneling effect of a condensate through a Gaussian energy barrier, which is inserted after the condensate has been excited by shifting the harmonic trapping potential to a side. Moreover, it is shown that the initial condensate evolves dynamically into two separate moving condensates after the tunneling time under certain conditions.     

Analysis of a Bose-Einstein condensate double-well atom interferometer

Motivated by an open theoretical question in Bose-Einstein condensate atom interferometry, we introduce a novel computational method to describe the condensate order parameter in the presence of a central barrier. We are able to follow the full dynamics of the system during the raising of a barrier, from a single macroscopically occupied ground state to a state where imaging shows a split density and, finally, to the observation of a phase-controlled interference pattern. We are able to discriminate between a mean-field and a two-mode state via the Penrose-Onsager criterion. By simulating the first such experiment, where in spite of the observed splitting of the condensate density there is never more than a single macroscopically occupied state, we provide a definitive interpretation of these systems as a novel many-body form of Young's double-slit experiment.     

Backscattering suppression in supersonic 1D polariton condensates

We investigate the effect of disorder on the propagation of one-dimensional polariton condensates in semiconductor microcavities. We observe a strong suppression of the backscattering produced by the imperfections of the structure when increasing the condensate density. This suppression occurs in the supersonic regime and is simultaneous to the onset of parametric instabilities which enable the "hopping" of the condensate through the disorder. Our results evidence a new mechanism for the strong scattering reduction of polaritons at high speeds.     

Josephson effects in dilute bose-einstein condensates

We propose an experiment that would demonstrate the dc and ac Josephson effects in two weakly linked Bose-Einstein condensates. We consider a time-dependent barrier, moving adiabatically across the trapping potential. The phase dynamics are governed by a "driven-pendulum" equation, as in current-driven superconducting Josephson junctions. At a critical velocity of the barrier (proportional to the critical tunneling current), there is a sharp transition between the dc and ac regimes. The signature is a sudden jump of a large fraction of the relative condensate population. Analytical results are compared with a numerical integration of the Gross-Pitaevskii equation, in an experimentally realistic situation.     

Superfluid to Normal Fluid Phase Transition in the Bose Gas Trapped in Two-Dimensional Optical Lattices at Finite Temperature

We develop the Hartree-Fock-Bogoliubov theory at finite temperature for Bose gas trapped in the two-dimensional optical lattice with the on-site energy low enough that the gas presents superfluid properties. We obtain the condensate density as function of the temperature neglecting the anomalous density in the thermodynamics equation. The condensate fraction provides two critical temperature. Below the temperature \(T_{C1}\), there is one condensate fraction. Above two condensate fractions merger up to the critical temperature \(T_{C2}\). At temperatures larger than \(T_{C2}\), the condensate fraction is null and, therefore, the gas is normal fluid. We resume by a finite-temperature phase diagram where three domains can be identified: the normal fluid, the superfluid with one stable condensate fraction and the superfluid with two condensate fractions being unstable one of them.     

Nonlinear theory for a quantum diode in a dense Fermi magnetoplasma

We present a simple analytical nonlinear theory for quantum diodes in a dense Fermi magnetoplasma. By using the steady-state quantum hydrodynamical equations for a dense Fermi magnetoplasma, we derive coupled nonlinear Schr?dinger and Poisson equations. The latter are numerically solved to show the effects of the quantum statistical pressure, the quantum tunneling (or the quantum diffraction), and the external magnetic field strength on the potential and electron density profiles in a quantum diode at nanometer scales. It is found that the quantum statistical pressure introduces a lower bound on the steady electron flow in the quantum diode, while the quantum diffraction effect allows the electron tunneling at low flow speeds. The magnetic field acts as a barrier, and larger potentials are needed to drive currents through the quantum diode.     

Dipole oscillations of a Bose-Einstein condensate in the presence of defects and disorder

We consider dipole oscillations of a trapped dilute Bose-Einstein condensate in the presence of a scattering potential consisting either in a localized defect or in an extended disordered potential. In both cases the breaking of superfluidity and the damping of the oscillations are shown to be related to the appearance of a nonlinear dissipative flow. At supersonic velocities the flow becomes asymptotically dissipationless.     

Global Solutions to a Reactive Boussinesq System with Front Data on an Infinite Domain

We prove the existence of global solutions to a coupled system of Navier–Stokes, and reaction-diffusion equations (for temperature and mass fraction) with prescribed front data on an infinite vertical strip or tube. This system models a one-step exothermic chemical reaction. The heat release induced volume expansion is accounted for via the Boussinesq approximation. The solutions are time dependent moving fronts in the presence of fluid convection. In the general setting, the fronts are subject to intensive Rayleigh-Taylor and thermal-diffusive instabilities. Various physical quantities, such as fluid velocity, temperature, and front speed, can grow in time. We show that the growth is at most for large time t by constructing a nonlinear functional on the temperature and mass fraction components. These results hold for arbitrary order reactions in two space dimensions and for quadratic and cubic reactions in three space dimensions. In the absence of any thermal-diffusive instability (unit Lewis number), and with weak fluid coupling, we construct a class of fronts moving through shear flows. Although the front speeds may oscillate in time, we show that they are uniformly bounded for large t. The front equation shows the generic time-dependent nature of the front speeds and the straining effect of the flow field. Received: 15 January 1996 / Accepted: 2 September 1997     

Acoustics of a blocked duct with flow

An analysis is given for flow and acoustical motion of fluid in a duct, aimed at describing some features of the blowing mechanism of a woodwind instrument. The latter is simulated by a rigid rectangular duct, open at one end and nearly closed off at the other, where a local section of the side wall can undergo transverse displacement. It is supposed that such a piston-like oscillation superposes an acoustical perturbation on a steady flow through the duct. The principal results of the calculations, in which it is presupposed that the displacement amplitude is small compared to the piston width, which is in turn small compared with the duct width and wavelength, are contained in estimates for the natural frequencies and optimum flow speeds to excite these modes.     

Realization of a sonic black hole analog in a Bose-Einstein condensate

We have created an analog of a black hole in a Bose-Einstein condensate. In this sonic black hole, sound waves, rather than light waves, cannot escape the event horizon. A steplike potential accelerates the flow of the condensate to velocities which cross and exceed the speed of sound by an order of magnitude. The Landau critical velocity is therefore surpassed. The point where the flow velocity equals the speed of sound is the sonic event horizon. The effective gravity is determined from the profiles of the velocity and speed of sound. A simulation finds negative energy excitations, by means of Bragg spectroscopy.     

Consequence of superfluidity on the expansion of a rotating Bose-Einstein condensate

We propose an easily detectable signature of superfluidity in rotating, vortex-free gaseous Bose-Einstein condensates. We have studied the time evolution of the expansion of such a condensate after it is released from the confining trap. We find that if such a condensate is not initially rotating, then at some moment it will instantaneously achieve a circular cross section. If the condensate is initially rotating its irrotational flow and the conservation of angular momentum prevent the released condensate from attaining a circular cross section, since the instantaneous moment of inertia is then proportional to the asymmetry of this cross section.     

Ground-states and rotational properties of a spin–orbit-coupled spin-1 Bose–Einstein condensate in a concentrically coupled toroidal trap

We investigate the ground states of an antiferromagnetic spin-1 Bose–Einstein condensate with spin–orbit coupling in a concentrically coupled toroidal trap. A new necklace-type state with double-ring structure is created in the system due to the spin–orbit coupling. The petal number of the necklace state is increased with enhancing the strength of the spin–orbit coupling. When the rotation is introduced, the condensate can be dragged into the outer trough of the trap by increasing the rotation frequency, which makes it possible to realize the exotic ground state combined by the necklace state at the inner trough and the persistent flow at the outer one. Once the two troughs of the toroidal trap are populated by the persistent flow at the specific effective interactions between atoms, the hidden vortices may occur in the central region of the trap and at the barrier between the two troughs. In addition, the visible vortex with the laminar structure can be generated under the more effective atomic interaction.     

Flow of a Bose-Einstein condensate in a quasi-one-dimensional channel under the action of a piston

The problem of the flow of a Bose—Einstein condensate in a channel under the action of a piston is considered. Problems of this kind are topical in connection with experiments on condensate flow control in quasi-one-dimensional (cigar-shaped) traps, in wh ich the repulsive potential produced by a laser beam focused across the trap acts as a piston. A dispersive shock wave characterized by rapid oscillations of the condensate density and flow velocity is shown to be formed in the condensate flow after some instant of time for an arbitrary law of piston motion. The Whitham averaging method is used to obtain a solution for the main parameters of the dispersive shock wave in the case of a uniformly accelerated piston motion. The evolution of the dispersive shock wave immediately after the breaking time, when the dispersionless solution is well approximated by a cubic parabola for the coordinate dependence of the density, is analyzed in the case of an arbitrary piston motion. Comparison shows good agreement of the numerical calculation with the approximate analytical theory. The developed theory complements the previously considered case of a piston moving with a constant velocity and is important for describing the condensate transport in atomic chips.     

Oblique solitons generated by the flow of a polariton condensate past an obstacle

The formation of oblique solitons in a polariton condensate flowing past an obstacle is considered. Because of the finite lifetime of polaritons, the condensate flow is inhomogeneous, which leads to a significant modification of the conditions necessary for the generation of oblique solitons as compared to the conditions established earlier for the flow of an atomic condensate. In particular, it is established that oblique solitons in the polariton case can be generated by a subsonic flow of the condensate in agreement with the results of recent experiments [9]. The geometric shape and other parameters of oblique solitons are analytically calculated using a model based on the nonlinear Schr?dinger equation with damping, and the analytical results are confirmed by numerical simulations.