Quantum Turbulence Research Articles

Quantum turbulence, superfluidity, non-Markovian dynamics, and wave function thermalization

While quantum turbulence has been addressed both experimentally (predominantly for superfluid He4 and He3) and theoretically, the dynamics of various ensembles of quantized vortices has been followed in time only until the vortices have decayed into phonons. How this “thermalization” is achieved is still an unaddressed and thus an unelucidated question. The unitary Fermi gas (UFG) is a unique quantum system, which has no classical counterpart and is of relevance to neutron stars, cold atoms, condensed-matter and nuclear many-body systems. The non-Markovian evolution of an isolated UFG is put in evidence and its entire nonequilibrium evolution can be studied theoretically within a unified theoretical framework. The initial lattice of quantum vortices and antivortices evolves through a couple of vortex tangles and excitation of Kelvin waves, where vortices cross and reconnect, until very slowly thermalization sets in. Published by the American Physical Society 2024

Quantum analog to flapping of flags: interface instability for co-flow binary superfluids

We study the interface dynamics in immiscible binary superfluids using its holographic description, which naturally consists of an inviscid superfluid component and a viscous normal fluid component. We give the first theoretical realization of interface instability for two superfluid components moving with identical velocity, providing a quantum analog to the flapping of flags that is common in daily life. This behavior is in sharp contrast to the one from Gross-Pitaevskii equation for which no such co-flow instability develops in an isolated uniform system because of Galilean invariance. The real time evolution triggered by the dynamical instability exhibits intricate nonlinear patterns leading to quantum turbulence reminiscent of the quantum Kelvin-Helmholtz instability. Moreover, we show that such interface dynamics is essentially different from the Landau instability for which the frictionless flow becomes thermodynamically unstable above a critical superfluid velocity. Our study uncovers the rich interface dynamics of quantum fluids and the emergence of complex flow phenomena.

Stochastic approach to analysis of vortex dynamic and turbulence in superfluid

Stochastic approach to analysis of vortex dynamic and turbulence in superfluid

Vortex-pair dynamics in three-dimensional homogeneous dipolar superfluids

The static and dynamic properties of vortices in dipolar Bose-Einstein condensates (dBECs) can be considerably modified relative to their nondipolar counterparts by the anisotropic and long-ranged nature of the dipole-dipole interaction. Working in a uniform dBEC, we analyze the structure of single vortices and the dynamics of vortex pairs, investigating the deviations from the nondipolar paradigm. For a straight vortex line, we find that the induced dipolar interaction potential is axially anisotropic when the dipole moments have a nonzero projection orthogonal to the vortex line. This results in a corresponding elongation of the vortex core along this projection as well as an anisotropic superfluid phase and enhanced compressibility in the vicinity of the vortex core. Consequently, the trajectories of like-signed vortex pairs are described by a family of elliptical and oval-like curves rather than the familiar circular orbits. Similarly for opposite-signed vortex pairs their translation speeds along the binormal are found to be dipole-interaction dependent. We expect that these findings will shed light on the underlying mechanisms of many-vortex phenomena in dBECs such as quantum turbulence, vortex reconnections, and vortex lattices. Published by the American Physical Society 2024

Fermionic quantum turbulence: Pushing the limits of high-performance computing.

Ultracold atoms provide a platform for analog quantum computer capable of simulating the quantum turbulence that underlies puzzling phenomena like pulsar glitches in rapidly spinning neutron stars. Unlike other platforms like liquid helium, ultracold atoms have a viable theoretical framework for dynamics, but simulations push the edge of current classical computers. We present the largest simulations of fermionic quantum turbulence to date and explain the computing technology needed, especially improvements in the Eigenvalue soLvers for Petaflop Applications library that enable us to diagonalize matrices of record size (millions by millions). We quantify how dissipation and thermalization proceed in fermionic quantum turbulence by using the internal structure of vortices as a new probe of the local effective temperature. All simulation data and source codes are made available to facilitate rapid scientific progress in the field of ultracold Fermi gases.

Vortex polarization and circulation statistics in isotropic turbulence.

We carry out an in-depth analysis of a recently introduced vortex gas model of homogeneous and isotropic turbulence. Direct numerical simulations are used to provide a concrete physical interpretation of one of the model's constituent fields: the degree of vortex polarization. Our investigations shed light on the complexity underlying vortex interactions and reveal, furthermore, that despite some striking similarities, classical and quantum turbulence exhibit distinct structural characteristics, even at inertial range scales. Crucially, these differences arise due to correlations between the polarization and circulation intensity within vortex clusters.

On the emergent “Quantum” theory in complex adaptive systems

We explore the concept of emergent quantum-like theory in complex adaptive systems, and examine in particular the concrete example of such an emergent (or “mock”) quantum theory in the Lotka–Volterra system. In general, we investigate the possibility of implementing the mathematical formalism of quantum mechanics on classical systems, and what would be the conditions for using such an approach. We start from a standard description of a classical system via Hamilton–Jacobi (HJ) equation and reduce it to an effective Schrodinger-type equation, with a (mock) Planck constant ▪ , which is system-dependent. The condition for this is that the so-called quantum potential VQ, which is state-dependent, is canceled out by some additional term in the HJ equation. We consider this additional term to provide for the coupling of the classical system under consideration to the ‘environment’. We assume that a classical system could cancel out the VQ term (at least approximately) by fine tuning to the environment. This might provide a mechanism for establishing a stable, stationary states in (complex) adaptive systems, such as biological systems. In particular, we present a general argument as to why the non-equilibrium dynamics of a classical system could lead to a mock quantum description that ensures stability compatible with adaptability. In this context we emphasize the state dependent nature of the mock quantum dynamics and we also introduce the new concept of the mock quantum, state dependent, statistical field theory. We also discuss some universal features of the quantum-to-classical as well as the mock-quantum-to-classical transition found in the turbulent phase of the hydrodynamic formulation of our proposal. In this way we re-frame the concept of decoherence into the concept of ‘quantum turbulence’, i.e. that the transition between quantum and classical could be defined in analogy to the transition from laminar to turbulent flow in hydrodynamics.

Phenomenology of transition to quantum turbulence in flows of superfluid helium

Transition from laminar to turbulent states of classical viscous fluids is complex and incompletely understood. Transition to quantum turbulence (QT), by which we mean the turbulent motion of quantum fluids such as helium II, whose physical properties depend on quantum physics in some crucial respects, is naturally more complex. This increased complexity arises from superfluidity, quantization of circulation, and, at finite temperatures below the critical, the two-fluid behavior. Transition to QT could involve, as an initial step, the transition of the classical component, or the intrinsic or extrinsic nucleation of quantized vortices in the superfluid component, or a simultaneous occurrence of both scenarios—and the subsequent interconnected evolution. In spite of the multiplicity of scenarios, aspects of transition to QT can be understood at a phenomenological level on the basis of some general principles, and compared meaningfully with transition in classical flows.

On the dependence of thermodynamic variables on the relative velocity vns in a superfluid counterflowing helium

Based on the theory of the thermodynamic equilibrium in a system of quantum vortices in superfluids in the presence of a counterflow, the influence of a vortex tangle on various thermodynamic phenomena in quantum liquids is studied. Using the early calculated partition function, we study some of the properties of He II related to counterflow, such as the distribution of vortex loops in their length, the suppression of the superfluid density ρs, and the shift Tλ. The physics behind this issue is related to the fact that the partition function describing the ensemble of chaotic vortex filaments depends on the relative velocity vns. The partition function, in turn, depends on relative velocity due to the Gibbs distribution with the specific velocity-dependent Hamiltonian. Good agreement with the earlier obtained results is a fairly strong argument in favor of the point of view that a collection of chaotic quantum vortices can, indeed, be considered as a kind of gas of quasiparticles at high temperatures, especially near a phase transition. The work is closely related to nonlinear physics, which studies chaotic processes, and is currently in the stage of active development, resulting in many meaningful and expressive results. The application of the developed formalism to the theory of quantum turbulence is briefly discussed.

Exploring the Equivalence between Two-Dimensional Classical and Quantum Turbulence through Velocity Circulation Statistics.

We study the statistics of velocity circulation in two-dimensional classical and quantum turbulence. We perform numerical simulations of the incompressible Navier-Stokes and the Gross-Pitaevskii (GP) equations for the direct and inverse cascades. Our GP simulations display clear energy spectra compatible with the double cascade theory of two-dimensional classical turbulence. In the inverse cascade, we found that circulation intermittency in quantum turbulence is the same as in classical turbulence. We compare GP data to Navier-Stokes simulations and experimental data from Zhu etal. [Phys. Rev. Lett. 130, 214001 (2023)PRLTAO0031-900710.1103/PhysRevLett.130.214001]. In the direct cascade, for nearly incompressible GP flows, classical and quantum turbulence circulation displays the same self-similar scaling. When compressibility becomes important, quasishocks generate quantum vortices and the equivalence of quantum and classical turbulence only holds for low-order moments. Our results establish the boundaries of the equivalence between two-dimensional classical and quantum turbulence.

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

Asynchronous quantum Kármán vortex street in two-component Bose-Einstein condensate with PT symmetric potential

The dynamics of a miscible two-component Bose-Einstein condensate (BEC) with PT (parity-time) symmetric potential are investigated numerically. The dynamical behaviors of the system is described by Gross-Pitaevskii (GP) equations under the mean-field theory. Firstly, the ground state of the system is obtained by the imaginary-time propagation method. Then dynamical behaviors are numerically simulated by the time-splitting Fourier pseudo-spectral approach under periodic boundary conditions. By adjusting the width and velocity of the obstacle potential, various patterns such as no vortex, oblique drifting vortex dipole, V-shaped vortex pairs, irregular quantum turbulence and combined modes are studied. It is noted that the shedding vortex pairs in components 1 and 2 are staggered, which is called “the asynchronous quantum Kármán vortex street”. Here, the ratio of the distance between two vortex pairs in one row to the distance between vortex rows is approximately 0.18, which is less than the stability criterion 0.28 of classical fluid. We calculated the drag force acting on the obstacle potential during generation of the asynchronous quantum Kármán vortex street. It is found that periodical oscillation of the drag force is generated via drifting up or down of the vortex pairs. Meanwhile, we analyzed the influence of the imaginary part of the PT symmetric potential with gain-loss for wake. The trajectory and frequency of the vortex are changed, due to the imaginary part breaks the local symmetry of the system. In addition, the imaginary part affects the stability of the asynchronous quantum Kármán vortex street. Lots of numerical simulations are carried out to determine the parameter regions of various vortex shedding modes. We also proposed an experimental protocol to realize the asynchronous quantum Kármán vortex street in the miscible two-component BEC with PT symmetric potential.

Conformal invariance of 2D quantum turbulence in an exciton–polariton fluid of light

The similarities of quantum turbulence with classical hydrodynamics allow quantum fluids to provide essential models of their classical analog, paving the way for fundamental advances in physics and technology. Recently, experiments on 2D quantum turbulence observed the clustering of same-sign vortices in strong analogy with the inverse energy cascade of classical fluids. However, self-similarity of the turbulent flow, a fundamental concept in the study of classical turbulence, has so far remained largely unexplored in quantum systems. Here, thanks to the unique features of exciton–polaritons, we measure the scale invariance of velocity circulations and show that the cascade process follows the universal scaling of critical phenomena in 2D. We demonstrate this behavior from the statistical analysis of the experimentally measured incompressible velocity field and the microscopic imaging of the quantum fluid. These results can find wide application in both quantum and classical 2D turbulence.

Second sound resonators and tweezers as vorticity or velocity probes: Fabrication, model, and method.

An analytical model of open-cavity second sound resonators is presented and validated against simulations and experiments in superfluid helium using a new resonator design that achieves unprecedented resolution. The model incorporates diffraction, geometrical misalignments, and flow through the cavity and is validated using cavities operated up to their 20th resonance in superfluid helium. An important finding is that resonators can be optimized to selectively sense either the quantum vortex density carried by the throughflow-as typically done in the literature-or the mean velocity of the throughflow. We propose two velocity probing methods: one that takes advantage of misalignments between the tweezers' plates and other that drives the resonator non-linearly, beyond a threshold that results in the self-sustainment of a vortex tangle within the cavity. A new mathematical treatment of the resonant signal is proposed to adequately filter out parasitic signals, such as temperature and pressure drift, and accurately separate the quantum vorticity signal. This elliptic method consists in a geometrical projection of the resonance in the inverse complex plane. Its effectiveness is demonstrated over a wide range of operating conditions. The resonator model and elliptic method are being utilized to characterize a new design of resonators with high resolution, thanks to miniaturization and design optimization. These second-sound tweezers are capable of providing time-space resolved information similar to classical local probes in turbulence, down to sub-millimeter and sub-millisecond scales. The principle, design, and microfabrication of second sound tweezers are being presented, along with their potential for exploring quantum turbulence.

Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium

AbstractClosed quantum systems far from thermal equilibrium can show universal dynamics near attractor solutions, known as non-thermal fixed points, generically in the form of scaling behaviour in space and time. A systematic classification and comprehensive understanding of such scaling solutions are tasks of future developments in non-equilibrium quantum many-body theory. In this tutorial review, we outline several analytical approaches to non-thermal fixed points and summarise corresponding numerical and experimental results. The analytic methods include a non-perturbative kinetic theory derived within the two-particle irreducible effective action formalism, as well as a low-energy effective field theory framework. As one of the driving forces of this research field are numerical simulations, we summarise the main results of exemplary cases of universal dynamics in ultracold Bose gases. This encompasses quantum vortex ensembles in turbulent superfluids as well as recently observed real-time instanton solutions in one-dimensional spinor condensates.

Direct visualization of the quantum vortex lattice structure, oscillations, and destabilization in rotating 4He.

Quantum vortices are a core element of superfluid dynamics and elusively hold the keys to our understanding of energy dissipation in these systems. We show that we are able to visualize these vortices in the canonical and higher-symmetry case of a stationary rotating superfluid bucket. Using direct visualization, we quantitatively verify Feynman's rule linking the resulting quantum vortex density to the imposed rotational speed. We make the most of this stable configuration by applying an alternative heat flux aligned with the axis of rotation. Moderate amplitudes led to the observation of collective wave mode propagating along the vortices, and high amplitudes led to quantum vortex interactions. When increasing the heat flux, this ensemble of regimes defines a path toward quantum turbulence in rotating 4He and sets a baseline to consolidate the descriptions of all quantum fluids.

Vibrating Microwire Resonators Used as Local Probes of Quantum Turbulence in Superfluid $$^{4}$$He

Vibrating Microwire Resonators Used as Local Probes of Quantum Turbulence in Superfluid $$^{4}$$He

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.

Types of quantum turbulence

We collect and describe the observed geometrical and dynamical properties of turbulence in quantum fluids, particularly superfluid helium and atomic condensates for which more information about turbulence is available. Considering the spectral features, the temporal decay, and the comparison with relevant turbulent classical flows, we identify three main limiting types of quantum turbulence: Kolmogorov quantum turbulence, Vinen quantum turbulence, and strong quantum turbulence. This classification will be useful to analyze and interpret new results in these and other quantum fluids.

Coupling Navier-Stokes and Gross-Pitaevskii equations for the numerical simulation of two-fluid quantum flows

Numerical methods for solving the Navier-Stokes equations for classical (or normal) viscous fluids are well established. This is also the case for the Gross-Pitaevskii equation, governing quantum inviscid flows (or superfluids) in the zero temperature limit. In quantum flows, like liquid helium II at intermediate temperatures between zero and 2.17 K, a normal fluid and a superfluid coexist with independent velocity fields. The most advanced existing models for such systems use the Navier-Stokes equations for the normal fluid and a simplified description of the superfluid, based on the dynamics of quantized vortex filaments, with ad hoc reconnection rules. There was a single attempt (C. Coste, 1998 [22]) to couple Navier-Stokes and Gross-Pitaevskii equations in a global model intended to describe the compressible two-fluid liquid helium II. We present in this contribution a new numerical model to couple a Navier-Stokes incompressible fluid with a Gross-Pitaevskii superfluid. Coupling terms in the global system of equations involve new definitions of the following concepts: the regularized superfluid vorticity and velocity fields, the friction force exerted by quantized vortices to the normal fluid, the covariant gradient operator in the Gross-Pitaevskii model based on a slip velocity respecting the dynamics of vortex lines in the normal fluid. A numerical algorithm based on pseudo-spectral Fourier methods is presented for solving the coupled system of equations. Finally, we numerically test and validate the new numerical system against well-known benchmarks for the evolution in a normal fluid of different types or arrangements of quantized vortices (vortex crystal, vortex dipole and vortex rings). The new coupling model has the advantage to keep the full Gross-Pitaevskii model for the superfluid, and thus describe quantized vortex dynamics without any phenomenological approximation. This opens new possibilities to revisit and enrich existing numerical results for complex quantum fluids, such as quantum turbulent flows.