Quantized Vortices and Quantum Turbulence

Abstract

Abstract. We review recent important topics in quantized vortices and quantum turbulence in atomic Bose-Einstein condensates (BECs). They have previously been studied for a long time in superfluid helium. Quantum turbulence is currently one of the most important topics in low-temperature physics. Atomic BECs have two distinct advantages over liquid helium for investigating such topics: quantized vortices can be directly visualized and the interaction parameters can be controlled by the Feshbach resonance. A general introduction is followed by a description of the dynamics of quantized vortices, hydrodynamic instability, and quantum turbulence in atomic BECs. IntroductionBose-Einstein condensation is often considered to be a macroscopic quantum phenomenon because bosons occupy the same single-particle ground state below the critical temperature for Bose-Einstein condensation so that they have a macroscopic wave function (order parameter) Ψ (r, t) = |Ψ (r, t)|e iθ(r,t) that extends over the entire system. Here, the absolute squared amplitude |Ψ | 2 = n gives the condensate density and the gradient of the phase θ(r, t) gives the superfluid velocity field v s = (h/m)∇θ with boson mass m as the potential flow. Since the macroscopic wave function should be single-valued for the space coordinate r, the circulation Γ = v s · dℓ for an arbitrary closed loop in the fluid will be quantized with the quantum κ = h/m. A vortex with such quantized circulation is known as a quantized vortex. Any rotational motion of a superfluid is sustained only by quantized vortices. Hydrodynamics dominated by quantized vortices is called quantum hydrodynamics (QHD), and turbulence comprised of quantized vortices is known as quantum turbulence (QT).A quantized vortex is a stable topological defect that is a characteristic of a Bose-Einstein condensate (BEC). It differs from a vortex in a classical

Decay of two-dimensional quantum turbulence in binary Bose-Einstein condensates

“…In order to study the characteristics of the emergent quantum turbulence (as a result of our preparation procedure), we calculate the incompressible and compressible kinetic energy spectrum, E ic (k) and E c (k) [7,70,71], for the case of y1 = 0.025, g 11 = g 22 , and various values of g 12 (see appendix E). The incompressible fluid part of the condensate represents the divergence free component of the condensate velocity.…”

“…The precise control over the parameters such as the trapping frequencies and atomic interactions renders Bose-Einstein condensates (BECs) one of the widely used nonlinear systems to study the turbulent dynamics in quantum fluids, where the turbulence is referred to as quantum turbulence [5][6][7][8][9][10][11][12]. In 2D quantum fluids, a topological excitation is a vortex with a quantized circulation around the vortex core with a finite size.…”

Experimental Methods for Generating Two-Dimensional Quantum Turbulence in Bose–einstein Condensates

“…See also the relevant simulations of Refs. [7] and [32] that involve an obstacle repeatedly sweeping through a BEC.…”

“…In this respect, Bose-Einstein condensates may be ideally suited for investigating quantum turbulence and the dynamics of interacting quantized vortices in compressible quantum fluids; for recent reviews of this subject see Refs. [6] and [7] and the references therein. In superfluids, vorticity appears in the form of superfluid-free vortex cores about which there is quantized flow circulation [2].…”

Experimental setup for the production of ultracold strongly correlated fermionic superfluids of 6Li

“…As a future perspective, we plan to study topological and hydrodynamic excitations such as quantized vortices (see for instance [48,49] and references therein). We specifically want to understand how the dynamics of these systems depend on the interacting regime as well as on the temperature of the cloud.…”