Superfluid Flow Research Articles

Superfluid dark matter flow around cosmic strings

Superfluid dark matter flow around cosmic strings

Parylene-bonded micro-fluidic channels for cryogenic experiments at superfluid He-4 temperatures.

We present the manufacturing process of a (24.5 × 100) μm2-sized on-chipflow channel intended for flow experiments with normal and superfluid phases of 4He and showcase such a proof-of-concept experiment. This work proves the suitability of chip-to-chip bonding using a thin layer of Parylene-C for cryogenic temperatures as a simpler alternative to other techniques, such as anodic bonding. A monocrystalline silicon chip embeds the etched meander-shaped micro-fluidic channel and a deposited platinum heater and is bonded to a Pyrex glass top. We test the leak tightness of the proposed bonding method for superfluid 4He, reaching temperatures of ≈1.6K and evaluate its possible effects on flow experiments. We demonstrate that powering an on-chip platinum heater affects the superfluid flow rate by local overheating of a section of the micro-fluidic channel.

Critical velocity and arrest of a superfluid in a pointlike disordered potential

Superfluid flow past a potential barrier is a well studied problem in ultracold Bose gases, however, fewer studies have considered the case of flow through a disordered potential. Here we consider the case of a superfluid flowing through a channel containing multiple point-like barriers, randomly placed to form a disordered potential. We begin by identifying the relationship between the relative position of two point-like barriers and the critical velocity of such an arrangement. We then show that there is a mapping between the critical velocity of a system with two obstacles, and a system with a large number of obstacles. By establishing an initial superflow through a point-like disordered potential, moving faster than the critical velocity, we study how the superflow is arrested through the nucleation of vortices and the breakdown of superfluidity, a problem with interesting connections to quantum turbulence and coarsening. We calculate the vortex decay rate as the width of the barriers is increased, and show that vortex pinning becomes a more important effect for these larger barriers. Published by the American Physical Society 2024

Vorticity locking and pressure dynamics in finite-temperature superfluid turbulence

We present a numerical study of finite-temperature superfluid turbulence using the vortex filament model for superfluid helium. We examine the phenomenon of vorticity locking between the normal and superfluid components across a wide range of temperatures, using two different structures of external normal fluid drive. We show that vorticity locking increases with temperature leading to the superfluid flow being more influenced by the characteristics of the normal fluid. This also results in stronger superfluid polarization and turbulent intermittency. We also examine how these properties influence the pressure field and attempt to verify a long-standing $P_k\propto k^{-7/3}$ theoretical quantum signature within the spatial pressure spectrum.

Interpretation of Josephson junction fluctuations at very low temperatures by superfluid flow equations

The effect of fluctuations on the stability of the zero-voltage state in the Josephson junction has been extensively investigated in the last four decades, due to the fundamental interest in this macroscopic quantum system and in view of possible application as a detector and, more recently, as base for quantum logic. Thermal induced escape from the zero-voltage state is well explained by consolidated theories based on the standard junction electrical model. However, at very low temperatures, significant deviations have been experimentally observed, which have triggered additional theories based on quantization of the Josephson junction effective potential and on macroscopic quantum tunneling. By looking at experiments carried out in the last forty years, we show here that the reported experimental data can be well described by standard theories down to zero temperature, provided that the Josephson potential is shifted by a constant amount, related to the junction plasma frequency. An explanation of this shift is given in terms of Anderson equations, relating chemical potential to phases, energies, and particle numbers in a superfluid flow.

Controlling superfluid flows using dissipative impurities

We propose and analyze a protocol to create and control the superfluid flow in a one dimensional, weakly interacting Bose gas by noisy point contacts. Considering first a single contact in a static or moving condensate, we identify three different dynamical regimes: I. a linear response regime, where the noise induces a coherent flow in proportion to the strength of the noise, II. a Zeno regime with suppressed currents, and III. a regime of continuous soliton emission. Generalizing to two point contacts in a condensate at rest we show that noise tuning can be employed to control or stabilize the superfluid transport of particles along the segment which connects them.

Minimum critical velocity of a Gaussian obstacle in a Bose-Einstein condensate

When a superfluid flows past an obstacle, quantized vortices can be created in the wake above a certain critical velocity. In the experiment by Kwon et al. [Phys. Rev. A 91, 053615 (2015)], the critical velocity ${v}_{c}$ was measured for atomic Bose-Einstein condensates (BECs) using a moving repulsive Gaussian potential, and ${v}_{c}$ was minimized when the potential height ${V}_{0}$ of the obstacle was close to the condensate chemical potential $\ensuremath{\mu}$. Here we numerically investigate the evolution of the critical vortex shedding in a two-dimensional BEC with increasing ${V}_{0}$ and show that the minimum ${v}_{c}$ at the critical strength ${V}_{0c}\ensuremath{\approx}\ensuremath{\mu}$ results from the local density reduction and vortex-pinning effect of the repulsive obstacle. The spatial distribution of the superflow around the moving obstacle just below ${v}_{c}$ is examined. The particle density at the tip of the obstacle decreases as ${V}_{0}$ increases to ${V}_{c0}$, and at the critical strength, a vortex dipole is suddenly formed and dragged by the moving obstacle, indicating the onset of vortex pinning. The minimum ${v}_{c}$ exhibits power-law scaling with the obstacle size $\ensuremath{\sigma}$ as ${v}_{c}\ensuremath{\sim}{\ensuremath{\sigma}}^{\ensuremath{-}\ensuremath{\gamma}}$ with $\ensuremath{\gamma}\ensuremath{\approx}1/2$.

Identification of vortices in quantum fluids: Finite element algorithms and programs

We present finite-element numerical algorithms for the identification of vortices in quantum fluids described by a macroscopic complex wave function. Their implementation using the free software FreeFem++ is distributed with this paper as a post-processing toolbox that can be used to analyse numerical or experimental data. Applications for Bose-Einstein condensates (BEC) and superfluid helium flows are presented. Programs are tested and validated using either numerical data obtained by solving the Gross-Pitaevskii equation or experimental images of rotating BEC. Vortex positions are computed as topological defects (zeros) of the wave function when numerical data are used. For experimental images, we compute vortex positions as local minima of the atomic density, extracted after a simple image processing. Once vortex centers are identified, we use a fit with a Gaussian to precisely estimate vortex radius. For vortex lattices, the lattice parameter (inter-vortex distance) is also computed. The post-processing toolbox offers a complete description of vortex configurations in superfluids. Tests for two-dimensional (giant vortex in rotating BEC, Abrikosov vortex lattice in experimental BEC) and three-dimensional (vortex rings, Kelvin waves and quantum turbulence fields in superfluid helium) configurations show the robustness of the software. The communication with programs providing the numerical or experimental wave function field is simple and intuitive. The post-processing toolbox can be also applied for the identification of vortices in superconductors. Program summaryProgram Title: FFEM_postproc_data_2D, FFEM_postproc_data_3D and FFEM_postproc_imageCPC Library link to program files:https://doi.org/10.17632/bhrtdbkxmy.1Licensing provisions: Apache 2.0Programming language: FreeFem++ (v 4.12) free software (www.freefem.org)Nature of problem: The software is scoped to the identification of quantized vortices in 2D or 3D configurations described by a complex wave function. Either simulation data obtained through numerical resolution of the Gross-Pitaevskii equation or 2D experimental images of Bose-Einstein condensates (BEC) can be used as input data. Examples of vortex identification in rotating BECs and superfluid helium are illustrated in the paper.Solution method: We model the complex wave function using P1 (piece-wise linear) Galerkin triangular (in 2D) and tetrahedral (in 3D) finite elements. For simulation data, the zeros of the wave function are directly computed and the circulation of the velocity on triangles sides is assessed. Vortices are obtained when a zero is found in a triangle with non-zero circulation. In 3D, the algorithm is applied on tetrahedron faces and the zero points are linked using mesh connectivity to form vortex lines. For experimental images, vortices are identified as local minima of the atomic density and extracted using the image contrast.Additional comments including restrictions and unusual features: Running time is from seconds to minutes depending on the mesh resolution of the simulation/experimental data.

Local bistability under microwave heating for spatially mapping disordered superconductors

We theoretically study a strongly disordered superconducting layer heated by near-field microwave radiation from a nanometric metallic tip. The microwaves heat up the quasiparticles, which cool by phonon emission and conduction away from the heated area. Due to a bistability with two stable states of the electron temperature under the tip, the heating can be tuned to induce a submicrometer-sized normal region bounded by a sharp domain wall between high- and low-temperature states. We propose this as a local probe to access different physics from existing methods, for example, to map out inhomogeneous superfluid flow in the layer. The bistability-induced domain wall can significantly improve its spatial resolution.

Boost-invariant superfluid flows

We present some exact solutions to the ideal hydrodynamics of a relativistic superfluid with an almost-conformal equation of state. The solutions have stress tensors which are invariant under Lorentz boosts in one direction, and represent superfluid generalisations of the Bjorken and Gubser flows. We also study corrections to the flows in first-order hydrodynamics, arguing that dissipation is dominated by the shear viscosity. We present some simple numerical solutions for these viscous corrections. Finally, we estimate the size of corrections to the flows arising when the spontaneously broken U(1) symmetry responsible for superfluidity is only approximate, giving the corresponding Goldstone boson a small non-zero mass. We find that the massless solutions can still provide good approximations at sufficiently small spatial rapidities.

Dynamical Mechanisms of Vortex Pinning in Superfluid Thin Films.

We characterize the mechanisms of vortex pinning in a superfluid thin film described by the two-dimensional Gross-Pitaevskii equation. We consider a vortex "scattering experiment" whereby a single vortex in a superfluid flow interacts with a circular, uniform pinning potential. By an analogy with linear dielectrics, we develop an analytical hydrodynamic approximation that predicts vortex trajectories, the vortex fixed point and the unpinning velocity. We then solve the Gross-Pitaevskii equation to validate this model, and build a phase portrait of vortex pinning. We identify two different dynamical pinning mechanisms marked by distinctive phonon emission signatures: one enabled by acoustic radiation and another mediated by vortex dipoles nucleated within the pin. Relative to obstacle size, we find that pinning potentials on the order of the healing length are more effective for vortex capture. Our results could be useful in mitigating the negative effects of drag due to vortices in superfluid channels, in analogy to maximizing supercurrents in type-II superconductors.

Dissipative Josephson vortices in annular polariton fluids

We consider two concentric rings formed by bosonic condensates of exciton-polaritons. A circular superfluid flow of polaritons in one of the rings can be manipulated by acting upon the second annular polariton condensate. The complex coupling between the rings with different topological charges triggers nucleation of stable Josephson vortices (JVs) which are revealed as topological defects of the angular dependence of the relative phase between rings. Being dependent on the coupling strength, the structure of the JV governs the difference of the mean angular momenta of the inner and the outer rings. At the vanishing coupling the condensates rotate independently demonstrating no correlations of their winding numbers. At the moderate coupling, the interaction between two condensates tends to equalize their mean angular momenta despite of the mismatch of the winding numbers demonstrating the phenomenology of a drag effect. Above the critical coupling strength the synchronous rotation is established via the phase slip events.

Investigation of properties of superfluid He4 turbulence using a hot-wire signal

We report hot-wire measurements performed in two very different, co- and counter-rotating flows, in normal and superfluid helium at 1.6 K, 2 K, and 2.3 K. As recently reported, the power spectrum of the hot-wire signal in superfluid flows exhibits a significant bump at high frequency (Diribarne et al. [1]). We confirm that the bump frequency does not depend significantly on the temperature and further extend the previous analysis of the velocity dependence of the bump, over more than one decade of velocity. The main result is that the bump frequency depends on the turbulence intensity of the flow, and that using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both co- and counter-rotating flows. The vortex shedding model previously proposed, in its current form, does not account for this observation. This suggests that the physical origin of the bump is related to the small scale turbulence properties of the flow. We finally propose some qualitative physical mechanism by which the smallest structures of the flow, at intervortex distance, could affect the heat flux of the hot-wire.

Hydrodynamic attractor and novel fixed points in superfluid Bjorken flow

Extending the quantum effective approach of Son and Nicolis and incorporating dissipation, we develop a MIS formalism for describing a superfluid out of equilibrium by including the Goldstone boson and the condensate together with the hydrodynamic modes as the effective degrees of freedom. We find that the evolution of the superfluid undergoing Bjorken flow is governed by the conventional hydrodynamic attractor with unbroken symmetry and an even number of novel non-dissipative fixed points with broken symmetry. If the initial temperature is super-critical, then the condensate becomes exponentially small very rapidly and the system is trapped by the hydrodynamic attractor for a long intermediate time before it reheats rapidly and switches to one of the symmetry-breaking fixed points eventually. Finally, we show that the fixed points are unstable against inhomogeneous perturbations that should lead to spinodal decomposition. We conclude that these features should be generic beyond the MIS formalism.

Dynamical friction in Bose-Einstein condensed self-interacting dark matter at finite temperatures, and the Fornax dwarf spheroidal

Aims. The aim of the present work is to better understand the gravitational drag forces, also referred to as dynamical friction, acting on massive objects moving through a self-interacting Bose-Einstein condensate, also known as a superfluid, at finite temperatures. This is relevant for models of dark matter consisting of light scalar particles with weak self-interactions that require nonzero temperatures, or that have been heated inside galaxies. Methods. We derived expressions for dynamical friction using linear perturbation theory, and compared these to numerical simulations in which nonlinear effects are included. After testing the linear result, it was applied to the Fornax dwarf spheroidal galaxy, and two of its gravitationally bound globular clusters. Dwarf spheroidals are well-suited for indirectly probing properties of dark matter, and so by estimating the rate at which these globular clusters are expected to sink into their host halo due to dynamical friction, we inferred limits on the superfluid dark matter parameter space. Results. The dynamical friction in a finite-temperature superfluid is found to behave very similarly to the zero-temperature limit, even when the thermal contributions are large. However, when a critical velocity for the superfluid flow is included, the friction force can transition from the zero-temperature value to the value in a conventional thermal fluid. Increasing the mass of the perturbing object induces a similar transition to when lowering the critical velocity. When applied to two of Fornax’s globular clusters, we find that the parameter space preferred in the literature for a zero-temperature superfluid yields decay times that are in agreement with observations. However, the present work suggests that increasing the temperature, which is expected to change the preferred parameter space, may lead to very small decay times, and therefore pose a problem for finite-temperature superfluid models of dark matter.

Phase separation in a mixture of trapped charged Bose–Einstein condensates

We study the phase separation configurations and rotational properties of a mixture of two interacting charged Bose–Einstein condensates subjected to a magnetic field trapped in disc and Corbino geometries. We calculate the ground state energies of the azimuthal and radial phase separation configurations using the Gross–Pitaevskii and Thomas–Fermi approximations. We show that the results for the experimentally relevant system parameters of both approaches are in good agreement. For both geometries, an immiscible mixture with equal intracomponent interactions favors azimuthal phase separation for all intercomponent interactions. Only an imbalance in the intracomponent interactions can result in a transition to radial phase separation, for which the transition becomes sensitive to the shape of the trap. We present phase diagrams as functions of the inter- and intracomponent interactions. While radial phase separation is widely favoured in disc geometry, the azimuthal phase separation is favoured for narrower Corbino geometries. We explore the rotational properties of spatially separated condensates subjected to magnetic fields, studying their angular momenta and velocity fields. The quantization of circulation breaks down for azimuthal phase separation. In this case, the bulk region of the condensate continues to display superfluid flow behaviour, whereas the velocity field shows a rigid body behaviour along the phase boundaries.

Phase coherence in out-of-equilibrium supersolid states of ultracold dipolar atoms

A supersolid is a counterintuitive phase of matter that combines the global phase coherence of a superfluid with a crystal-like self-modulation in space. Recently, such states have been experimentally realized using dipolar quantum gases. Here we investigate the response of a dipolar supersolid to an interaction quench that shatters the global phase coherence. We identify a parameter regime in which this out-of-equilibrium state rephases, indicating superfluid flow across the sample as well as an efficient dissipation mechanism. We find a crossover to a regime where the tendency to rephase gradually decreases until the system relaxes into an incoherent droplet array. Although a dipolar supersolid is, by its nature, ‘soft’, we capture the essential behaviour of the de- and rephasing process within a rigid Josephson junction array model. Yet, both experiment and simulation indicate that the interaction quench causes substantial collective mode excitations that connect to phonons in solids and affect the phase dynamics. A supersolid is a phase of matter featuring both crystalline order as a solid and global phase coherence as a superfluid. Now an experiment shows how this global phase coherence can be established across the system in a non-equilibrium process.

Bathtub vortex in superfluid He4

We have investigated the structure of macroscopic suction flows in superfluid $^4$He. In this study, we primarily analyze the structure of the quantized vortex bundle that appears to play an important role in such systems. Our study is motivated by a series of recent experiments conducted by a research group in Osaka City University [Yano $\textit{et. al.}$, J. Phys. Conf. Ser. $\textbf{969}$, 012002 (2018)]; they created a suction vortex using a rotor in superfluid $^4$He. They also reported that up to $10^4$ quantized vortices accumulated in the central region of the rotating flow. The quantized vortices in such macroscopic flows are assumed to form a bundle structure; however, the mechanism has not yet been fully investigated. Therefore, we prescribe a macroscopic suction flow to the normal fluid and discuss the evolution of a giant vortex ($\textit{i.e.}$, one with a circulation quantum number exceeding unity) and a bundle of singly quantized vortices from a small number of seed vortices. Then, using numerical simulations, we discuss several possible characteristic structures of the bundle in such a flow, and we suggest that the actual steady-state bundle structure in the experiment can be verified by measuring the diffusion constant of the vortex bundle after the macroscopic normal flow has been switched off. By applying extensive knowledge of the superfluid $^4$He system, we elucidate a new type of macroscopic superfluid flow and identify a novel structure of quantized vortices.

Counterflow-Induced Inverse Energy Cascade in Three-Dimensional Superfluid Turbulence.

Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a nonzero-mean relative velocity. Such out-of-equilibrium state is known as counterflow superfluid turbulence. We report here the emergence of a counterflow-induced inverse energy cascade in three-dimensional superfluid flows by performing extensive numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. As the intensity of the mean counterflow is increased, an abrupt transition, from a fully three-dimensional turbulent flow to a quasi-two-dimensional system exhibiting a split cascade, is observed. The findings of this work could motivate new experimental settings to study quasi-two-dimensional superfluid turbulence in the bulk of three-dimensional experiments. They might also find applications beyond superfluids in systems described by more than one fluid component.

Experiments of superfluid helium flow in a channel with a monodisperse backfill

The experimental data on the superfluid helium flow in a U-shaped channel filled with a monodisperse backfill at a certain length is considered in this paper. The entire channel is immersed in a volume of superfluid helium. A flat heater is located in one end of the channel. When the heat load is applied, a vapor plug is formed in the channel. The column of superfluid helium begins to fluctuate in size with a constant amplitude and frequency. On the basis of the video recording of experiments, the dependence of the coordinate of the interfacial surface on time was plotted, and a qualitative analysis of heat and mass transfer processes is performed.