Quantized vortices in superfluid helium

Abstract Chapter 3 focuses on the physics of quantized vortices in superfluid helium. We begin by introducing the unique properties of 4He, including its phase diagram, the superfluid transition (lambda transition), and the phenomenon of superfluidity. Following this, we will discuss the two-fluid model, a foundational and widely used phenomenological framework. Next, we delve into thermal counterflow, a crucial area that spurred the initial research on quantum turbulence, superfluid turbulence, and quantized vortices. We will then explore the dynamics of quantized vortices, often described by the Vortex Filament Model (VFM), which plays a central role in understanding quantum turbulence. The equations of motion and basic dynamics of vortices will be presented, and since the vortex motion is both nonlinear and nonlocal, numerical simulations are essential for accurately describing quantum turbulence. We will cover the computational methods used in these simulations, including both “two-way” and “one-way” approaches. In addition to quantum turbulence, we will examine the quantized vortex lattice under rotation, another key phenomenon in superfluidity. Early experiments on vortex lattice formation, the realization of rigid-body rotation, and simple examples of vortex dynamics under rotation will be introduced. Finally, we will discuss recent advancements in visualization experiments in superfluid helium, highlighting the results of visualizing quantized vortices, which have greatly enhanced our understanding of vortex dynamics.