Binary Quantum Turbulence Arising from Countersuperflow Instability in Two-Component Bose-Einstein Condensates

Abstract

We theoretically study the development of quantum turbulence from two counter-propagating superfluids of miscible Bose-Einstein condensates by numerically solving the coupled Gross-Pitaevskii equations. When the relative velocity exceeds a critical value, the countersuperflow becomes unstable and quantized vortices are nucleated, which leads to isotropic quantum turbulence consisting of two superflows. It is shown that the binary turbulence can be realized experimentally in a trapped system.PACS numbers: 03.75. Mn, 67.25.dk, 47.27.Cn Hydrodynamic instability develops into turbulence or turbulent flow due to the complicated dynamics of eddies of various length scales [1]. This phenomenon appears in diverse fields of physics, such as magneto-hydrodynamic fluids in plasma physics [2], relativistic fluids in astrophysics [3], and quantum fluids in low temperature physics [4,5]. Turbulence has been studied thoroughly in classical fluid dynamics as the most important unsolved problem of classical physics. Recently, quantum turbulence (QT), turbulence in superfluids, has attracted interest in low temperature physics [6]. QT consists of topological defects, vortices with definite quantized circulation, and can provide a simple prototype for understanding classical turbulence. QT has been historically studied in superfluid 4 He and 3 He and has been numerically studied in atomic Bose-Einstein condensates (BECs) [7,8] and has recently been realized in experiments [9].Early studies on QT were devoted primarily to thermal counterflow in superfluid 4 He, where the hydrodynamics is usually described using a two-fluid model in which the system consists of an inviscid superfluid component and a viscous normal fluid component [10]. Thermal counterflow is driven by an injected heat current, where the two components flow in opposite directions. For a sufficiently large relative velocity between the two components, the laminar counterflow state becomes unstable, developing into a superfluid turbulent state. In the transition, remnant vortices, quantized vortices attached to the container wall, are stretched by the mutual friction between the superfluid and normal fluid components, growing into a tangle through reconnections with other vortices [11,12].We consider a similar case in two-component BECs, QT arising from the instability of the counterflow of two superfluids, namely, countersuperflow instability. Counter-superflow instability has been theoretically studied in several multicomponent miscible superfluid systems, such as helium superfluids [13][14][15][16], mixture BECs of cold atoms [17], and nucleon superflows in rotating neutron stars [18]. Atomic BEC systems have great advantages over other superfluid systems, because modern experimental techniques enable us to easily control superflows and directly visualize the dynamics of topological defects therein. Recently, Hamner et al. experimentally realized countersuperflow instability for the first time, and observed that shocks and dark-bright solitons nucleate via the in...

Numerical Studies of Quantum Turbulence

“…In this turbulence, not only the velocity field but also the spin density vector field is disturbed, so we call it spin turbulence. Though QT in the binary [151,152,153,154,155,156,157] and spin-2 spinor BECs [136,158] have been studied, we do not address these in this review.…”

“…Recently, studies of QT in this system have been carried out [136,151,152,153,154,155,156,157,158], in which correlation functions for the velocity field and spin density vector were investigated and some power laws were reported. However, these address binary QT in limited parameter regions, and QT in a mass imbalance system or QT with spin-orbit coupling have never been investigated.…”

Generation of Dark-Bright Soliton Trains in Superfluid-Superfluid Counterflow

“…Together with the long lifetime of the observed dark-bright solitons, this opens the door to future experiments with these interesting coherent nonlinear structures. While the dynamics considered in this Letter are effectively one-dimensional, a very recent theoretical analysis has shown that superfluid counterflow in higher dimensions can lead to binary quantum turbulence, providing another example of the exceptional dynamical richness of the two-component system [21]. Fig.…”

Bouncing motion and penetration dynamics in multicomponent Bose-Einstein condensates

“…Employing such adjustability and selectability, intriguing phenomena that depend on the degree of miscibility have been experimentally observed, e.g., soliton generation in a counterflow of miscible fluids [8,9], quantum tunneling across spin domains [10] and suppression of relative flow by multiple domains [11] in immiscible systems. Theoretically, quantum turbulence in a counterflow of miscible BECs [12,13] and pattern formation by instabilities at interfaces in immiscible BECs [14][15][16][17][18] have been predicted.…”