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7 - Formation of Bose-Einstein Condensates
- from Part II - General Topics
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- By M. J. Davis, School of Mathematics and Physics, University of Queensland, T. M. Wright, School of Mathematics and Physics, University of Queensland, St. Lucia QLD 4072, Australia, T. Gasenzer, Universität Heidelberg, S. A. Gardiner, Department of Physics, Durham University, N. P. Proukakis, School of Mathematics and Statistics, Newcastle University
- Edited by Nick P. Proukakis, Newcastle University, David W. Snoke, University of Pittsburgh, Peter B. Littlewood, University of Chicago
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- Book:
- Universal Themes of Bose-Einstein Condensation
- Published online:
- 18 May 2017
- Print publication:
- 27 April 2017, pp 117-150
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Summary
The problem of understanding how a coherent, macroscopic Bose- Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently, there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases.
Introduction
The equilibrium phase diagram of the dilute Bose gas exhibits a continuous phase transition between condensed and noncondensed phases. The order parameter characteristic of the condensed phase vanishes above some critical temperature Tc and grows continuously with decreasing temperature below this critical point. However, the dynamical process of condensate formation has proved to be a challenging phenomenon to address both theoretically and experimentally. This formation process is a crucial aspect of Bose systems and of direct relevance to all condensates discussed in this book, despite their evident system-specific properties. Important questions leading to intense discussions in the early literature include the time scale for condensate formation and the role of inhomogeneities and finite-size effects in “closed” systems. These issues are related to the concept of spontaneous symmetry breaking, its causes, and implications for physical systems (see, for example, Chapter 5 by Snoke and Daley).
In this chapter, we give an overview of the dynamics of condensate formation and describe the present understanding provided by increasingly well-controlled cold-atom experiments and corresponding theoretical advances over the past twenty years. We focus on the growth of BECs in cooled Bose gases, which, from a theoretical standpoint, requires a suitable nonequilibrium formalism.
1 - Universality and Bose-Einstein Condensation: Perspectives on Recent Work
- from Part I - Introduction
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- By D. W. Snoke, University of Pittsburgh, USA, N. P. Proukakis, Joint Quantum Centre Durham-Newcastle, Newcastle University, UK, T. Giamarchi, University of Geneva, P. B. Littlewood, University of Chicago, USA
- Edited by Nick P. Proukakis, Newcastle University, David W. Snoke, University of Pittsburgh, Peter B. Littlewood, University of Chicago
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- Book:
- Universal Themes of Bose-Einstein Condensation
- Published online:
- 18 May 2017
- Print publication:
- 27 April 2017, pp 3-21
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Summary
The study of Bose-Einstein condensation has undergone a remarkable expansion during the last twenty years. Observations of this phenomenon have been reported in a number of diverse atomic, optical, and condensed matter systems, facilitated by remarkable experimental advances. The synergy of experimental and theoretical work in this broad research area is unique, leading to the establishment of Bose-Einstein condensation as a universal interdisciplinary area of modern physics. This chapter reviews the broad expansion of Bose-Einstein condensation physics in the past two decades.
Introduction
The field of Bose-Einstein condensation (BEC) has undergone an explosive expansion during the past twenty years. Newcomers to this field are now often introduced to this as a universal phenomenon, which nonetheless exhibits diverse (and sometimes strikingly different) manifestations. Despite such differences, the common underlying theme creates a unique identity across many different energy and length scales.
The study of BEC as a universal phenomenon was highlighted in a focused conference in 1993, leading to the publication of the well-known “green book” [1], which surveyed the breadth of the field of condensate physics at that time. The success of the conference led to a second meeting in 1995, at which Eric Cornell and Carl Wieman announced the achievement of Bose-Einstein condensation of ultracold 87Rb atoms in a harmonic trap. That work began an explosion of new research in the field of cold atoms, which has continued to this day, and this very success inevitably led many of those studying cold atoms to pay less attention to other types of condensates. Wolfgang Ketterle gives a historical overview of this exciting period of time in Chapter 3. Recently, various scientific meetings have worked to re-establish the physical connections across different BEC systems, and in 2013 a workshop was held with the focused goal of improving communications across disciplines. This present book is an outgrowth of that meeting.
The Situation Before the Revolution
Because of the great success of the cold atom BEC and other BEC systems in the past twenty years, it may be hard for young scientists to understand the climate of BEC research in the early 1990s. At that time, there was only one known example of BEC, namely liquid helium-4, and there was a small but vocal minority of scientists who questioned whether BEC was established even in that system.
17 - Quantum Turbulence in Atomic Bose-Einstein Condensates
- from Part III - Condensates in Atomic Physics
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- By N. G. Parker, Newcastle University, Newcastle upon Tyne, A. J. Allen, Newcastle University, Newcastle upon Tyne, C. F. Barenghi, Newcastle University, Newcastle upon Tyne, N. P. Proukakis, Newcastle University, Newcastle upon Tyne
- Edited by Nick P. Proukakis, Newcastle University, David W. Snoke, University of Pittsburgh, Peter B. Littlewood, University of Chicago
-
- Book:
- Universal Themes of Bose-Einstein Condensation
- Published online:
- 18 May 2017
- Print publication:
- 27 April 2017, pp 348-370
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Summary
The past decade has seen atomic Bose-Einstein condensates emerge as a promising prototype system to explore the quantum mechanical form of turbulence, buoyed by a powerful experimental toolbox to control and manipulate the fluid, and the amenity to describe the system from first principles. This chapter presents an overview of this topic, from its history and fundamental motivations, its characteristics and key results to date, and finally to some promising future directions.
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.