Quantum turbulence by vortex stirring in a spinor Bose-Einstein condensate

Abstract

We introduce a novel mechanism to develop a turbulent flow in a spinor Bose-Einstein condensate, consisting in the stirring of a single line vortex by means of an external magnetic field. We find that density and velocity fluctuations have white-noise power spectra at large frequencies and that Kolmogorov 5/3 law is obeyed in the turbulent region. As the stirring is turned off, the flow decays to an agitated non-equilibrium state that shows an energy bottleneck crossover at small length scales. We demonstrate our findings by numerically solving two-state spinor coupled 3D Gross-Pitaevskii equations. We suggest that this mechanism may be experimentally implemented in spinor ultracold gases confined by optical traps. PACS numbers: 67.85.De, 67.85.Fg,67.25.dk 1 arXiv:1309.6218v1 [cond-mat.quant-gas] 24 Sep 2013Ever since Kolmogorov seminal ideas on classical turbulence [1], stochastic and universal laws have been sought for and discovered to be obeyed by highly complex fluid flows. Among the most celebrated predictions is the so-called "5/3" energy cascade. Although turbulence in general has remained as a fascinating topic of study both classically [2] and in helium superfluids [3,4], there has been an enormous recent interest in the study of turbulence in ultracold superfluid gases, see for recent reviews. Of notorious relevance are the experimental realizations of quantum turbulence (QT) in a superfluid ultracold 87 Rb gas in a pure magnetic trap [8], and in a 2D version confined by an annular trap [9]. In the theoretical side, a lot of effort has been devoted to understand QT as a "vortex tangle" as well as the velocity statistics of the turbulent state [10][11][12][13][14].Following the findings of Ref. [15], where it was shown that Gross-Pitaevskii (GP) spinor Bose-Einstein condensates (s-BEC) in inhomogenous optical traps can support vortices "on demand" in the presence of external magnetic fields, we study here the dynamics generated by the simple stirring of a single vortex in a 3D, spin 1/2, s-BEC. We shall show that even for mild stirrings a turbulent flow is developed in both components of s-BEC. In what follows, we describe the system and the temporal excitation protocol, as well as the nonequilibrium stationary state that it is reached once the excitation is turned-off. We discuss several scenarios.As succinctly put in Ref. [16], the study of quantum turbulence should address the following three questions: i) the generation of turbulence; ii) the statistical steady state; and, iii) the decay of turbulence. In this Letter, we analyze a novel, simple and realizable stirring procedure to produce turbulence in ultracold gases. The lack of a dissipative mechanism in GP superfluids makes it difficult to produce a true turbulent steady state, yet a turbulent phase is clearly obtained during and after the stirring process. When the latter is turned off, one finds that the flow decays to a non-equilibrium stationary state with turbulence remnants and an energy bottleneck contribution at small length scales [17]...

Quantum turbulence in trapped atomic Bose–Einstein condensates

“…In an independent work, the authors of Ref. [227] showed how a gas of two spin states driven by an oscillating magnetic field shows Kolmogorov power spectra. However, this is still hydrodynamic turbulence and not of the type of spin turbulence proposed in the references above.…”

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.…”

Macroscopic Excitations in Confined Bose–Einstein Condensates, Searching for Quantum Turbulence

“…Most notorious is the cascade of energy 1 through vortices or eddies, in the classical case, or by a tangle of vortices 2 in the quantum version. Among the relevant questions one must deal with, specially in the quantum regime, is the initiation or generation of such a complex state 3,4,5,6 and its characterization. 7,8 These issues motivate the study presented in this article.…”