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arXiv:2306.05048 · Europhysics Letters (EPL)

Stationary transport above the critical velocity in a one-dimensional superflow past an obstacle

Juliette Huynh, F. Hébert, Pierre-Élie Larré, Mathias Albert

Published Aug 1, 2023• 1 citation
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Abstract

Abstract We consider in this work the different possible stationary flows of a one-dimensional quantum fluid in the mean-field regime. We focus on the supersonic regime where a transition from a time-dependent flow to a stationary diffractive flow occurs at a given critical velocity. We give nonperturbative results for this critical velocity in the presence of a localised obstacle of arbitrary size and strength. In addition, we discuss the existence of superfluid-like solution in the supersonic regime due to resonant transport and provide a complete map of the different regimes of stationary transport of a quantum fluid.

DOI
10.1209/0295-5075/acf15a

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Abstract We consider in this work the different possible stationary flows of a one-dimensional quantum fluid in the mean-field regime. We focus on the supersonic regime where a transition from a time-dependent flow to a stationary diffractive flow occurs at a given critical velocity. We give nonperturbative results for this critical velocity in the presence of a localised obstacle of arbitrary size and strength. In addition, we discuss the existence of superfluid-like solution in the supersonic regime due to resonant transport and provide a complete map of the different regimes of stationary transport of a quantum fluid.
We determine in a nonperturbative way the critical velocity for superfluidity of a generic quantum fluid flowing past a localized obstacle in the one-dimensional mean-field regime. We get exact expressions in the narrow- and wide-obstacle limits and interpolate them numerically using an original relaxation algorithm for the stationary problem. The existence of a Josephson-type critical current across a very high and slowly varying obstacle is discussed. Particle losses, if present, are treated within an adiabatic approach of the dynamics giving results in excellent agreement with full numerics. Relevant for experiments with quantum fluids of matter, of mixed matter-light, and of light, our study paves the way for further nonperturbative investigations in higher dimensions and beyond mean-field theory.
The one-dimensional flow of a continuous beam of Bose-Einstein condensed atoms in the presence of an obstacle is studied as a function of the beam velocity and of the type of perturbing potential (representing the interaction of the obstacle with the atoms of the beam). We identify the relevant regimes: stationary/time-dependent and superfluid/dissipative; the absence of drag is used as a criterion for superfluidity. There exists a critical velocity below which the flow is superfluid. For attractive obstacles, we show that this critical velocity can reach the value predicted by Landau's approach. Besides, for penetrable obstacles, it is shown that superfluidity is recovered at large beam velocity. Finally, enormous differences in drag occur when switching from repulsive to attractive potential.
Motivated by recent experiments, we theoretically analyze the flow past an obstacle of a one-dimensional ``quantum fluid of light,'' which is resonantly driven, and exhibits bistability. The flow is found to abruptly change several times when the fluid velocity or the obstacle potential strength is increased. These transitions display unusual features. In contrast to the cases of usual fluids and superfluids, the transitions take place between stationary states. They involve the fluid bistability in an essential way. Remarkably, at the transitions points, the fluid in the obstacle wake lies in the unstable intermediate density state.
The frictionless motion of an object through a fluid medium is commonly viewed as a hallmark of superfluidity. According to Landau, kinematic constraints prohibit superfluid behavior in one-dimensional (1D) bosonic systems. Here, using ultracold atoms, we show how a microscopic impurity can propagate through a strongly interacting 1D Bose gas without any friction, at odds with conventional expectations. We inject the impurity with initial velocities ranging from the subsonic to supersonic regime, and subsequently track its dynamics. For supersonic initial velocities, we observe the formation of a shock wave and a remarkably fast relaxation to a stationary regime, on a time scale that increases with decreasing impurity velocity. After reaching the stationary state, the impurity continues its motion through the system with a finite velocity. Our findings demonstrate how quantum effects can conspire to eliminate dissipation of a microscopic object immersed in a quantum fluid, thereby bringing novel insights into the propagation of matter and information in the quantum realm.
Abstract We investigate the flow of a one-dimensional nonlinear Schrödinger 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.
We investigate the problem of an ultracold atomic gas in the superfluid phase flowing in the presence of a potential barrier or a periodic potential. We use a hydrodynamic scheme in the local density approximation (LDA) to obtain an analytic expression for the critical current as a function of the barrier height or the lattice intensity, which applies to both Bose and Fermi superfluids. In this scheme, the stationary flow becomes energetically unstable when the local superfluid velocity is equal to the local sound velocity at the point where the external potential is maximum. We compare this prediction with the results of the numerical solutions of the Gross-Pitaevskii and Bogoliubov-de Gennes equations. We discuss the role of long-wavelength excitations in determining the critical velocity. Our results allow one to identify the different regimes of superfluid flow, namely, the LDA hydrodynamic regime, the regime of quantum effects beyond LDA for weak barriers and the regime of tunneling between weakly coupled superfluids for strong barriers. We finally discuss the relevance of these results in the context of current experiments with ultracold gases.