This book marks the twentieth anniversary of the publication of the book Bose- Einstein Condensation by Cambridge University Press. The book was the result of the 1993 meeting in Levico-Terme, Italy, organized by Allan Griffin, David Snoke, and Sandro Stringari, with significant help from Andre Mysyrowicz. That meeting grew out of a desire by many theorists and experimentalists to discuss the general themes of Bose-Einstein condensation, to draw connections between different physical systems.

One of the major driving forces for that meeting was the desire to have another example of Bose-Einstein condensation besides liquid helium. There was serious discussion at the time of whether nature abhorred a condensate, and liquid helium was a special, anomalous case. Experiments on spin-polarized hydrogen, excitons in semiconductors, and optically trapped atoms had been going on for more than a decade, without success. To move the field forward, the organizers of the 1993 meeting brought together world experts on the general theory, and experimentalists of all types, to discuss the universal themes of Bose-Einstein condensation generally. There were fascinating and heated debates about such topics as the time scale for condensation (could it be possible that condensation will not occur in a system with finite lifetime?), the concept of spontaneous symmetry breaking (could there ever be a universal “phase standard” for condensates?), and how superfluidity and condensation are related.

The situation is quite changed now. We now have many experimental examples of Bose-Einstein condensation, most notably atoms at very low temperature in optical traps, which led to the Nobel Prize in Physics in 2001. This work of Eric Cornell and Carl Wieman was first announced at the second general meeting on Bose-Einstein condensation in 1995, in Mt. Ste. Odile, France. This led to the successful conference series on atomic Bose-Einstein condensation, which now takes place regularly in San Feliu de Guixols, Spain.

Because of this changed situation, the present book does not have the same form as the 1995 book. At that time, it was possible to survey a good fraction of all the experimental and theoretical efforts in the field. The field is now so large that no book can do that comprehensively, and this book leaves out a good many significant topics.

A Quantum Storm in a Teacup

A befitting title to this chapter could have been “a quantum storm in a teacup.” The storm refers to a turbulent state of a fluid, teeming with swirls and waves. Quantum refers to the fact that the fluid is not the classical viscous fluid of conventional storms but rather a quantum fluid in which viscosity is absent and the swirls are quantized. The quantum fluid in our story is a quantum-degenerate gas of bosonic atoms, an atomic Bose-Einstein condensate (BEC), formed at less than a millionth of a degree above absolute zero. And finally the teacup refers to the bowl-like potential used to confine the gas; this makes the fluid inherently inhomogeneous and finite-sized. A typical image of our quantum storm in a teacup is shown in Fig. 17.1a.

This chapter reviews quantum turbulence in atomic condensates, tracing its history (Section 17.2), introducing the main theoretical approach (Section 17.3) and the underyling quantum vortices (Section 17.4).We then turn to describing physical characteristics (Section 17.5), the experimental observations to date (Section 17.6), methods of generating turbulence (Section 17.7), and some exciting research directions (Section 17.8) before presenting an outlook (Section 17.9).

Origins

Turbulence refers to a highly agitated, disordered, and nonlinear fluid motion, characterized by the presence of eddies and energy across a range of length and time scales [3]. It occurs ubiquitously in nature, from blood flow and waterways to atmospheres and the interstellar medium, and is of practical importance in many industrial and engineering contexts. Since da Vinci's first scientific study of turbulent flow of water past obstacles, circa 1507, research into turbulence in classical viscous fluids continues with vigor; however, due to its rich complexities, the physical essence and mathematical description of turbulence remain a challenge.