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Institute of Physics eBooks

Bose–Einstein condensates

Richard A. Dunlap

Published May 1, 2023• 0 citations
Publisher

Abstract

This chapter discusses the way in which the cooling and trapping methods presented in the previous chapter can be used to create a Bose–Einstein condensate. This discussion begins with an overview of the basic properties of this condensate and the necessary requirements for its formation. The means by which it can be unequivocally identified are presented. Finally, some potential applications of the Bose–Einstein condensate are considered.

DOI
10.1088/978-0-7503-5482-0ch8

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This chapter discusses the way in which the cooling and trapping methods presented in the previous chapter can be used to create a Bose–Einstein condensate. This discussion begins with an overview of the basic properties of this condensate and the necessary requirements for its formation. The means by which it can be unequivocally identified are presented. Finally, some potential applications of the Bose–Einstein condensate are considered.
With the prevalence of quantum theory, many physicists have focused on the Bose-Einstein condensation (BEC) because it reveals the quantum behavior macroscopically. This article discusses briefly the discovery of BEC and the difficulties to achieve BEC. After that, the general procedures to achieve BEC are introduced while the mechanism of important techniques to accomplish each procedure is illustrated, such as laser cooling, trapping, and evaporative cooling. Besides, the unique physical properties of BEC are introduced in this article. Finally, the possible application of BEC in the field of an atom laser, simulation, and the atomic clock is evaluated.
This chapter introduces basic notions about Bose-Einstein condensates (BECs). One first studies ideal Bose gases, putting an emphasis on the role of the trapping geometry and of the dimensionality. One also introduces the correlation functions characterizing coherence. The second section deals with weakly-interacting BECs, which are described, in a mean-field approach, by the so-called Gross-Pitaevskii equation. This equation is derived and applied to a variety of experimentally relevant situations. The third section deals with beyond-mean-field effects that appear when the interactions are stronger, and introduces in particular the Bogolubov approximation. The last section is devoted to the study of BECs in double-well potentials, a situation inspired from condensed matter systems where beyond-mean-field effects can appear quite easily, and which remains simple enough to be studied theoretically in details.
This chapter introduces the fundamental concepts of Bose–Einstein condensates (BECs), providing a comprehensive theoretical foundation for subsequent investigation on their localization and numerical simulation. It begins with a historical overview of BECs, tracing their theoretical origins and experimental realization. The chapter then focuses on the theoretical perspective of scalar BECs and how it can be modelled by a single-component Gross–Pitaevskii (GP) equation in the mean-field description, a variable-coefficient nonlinear Schrödinger (NLS) equation encompassing a trapping potential and interatomic interaction. The mean-field description is then extended to govern the dynamics of vectorial condensates described by a coupled GP equation with intra and inter-species (atomic) interactions. Subsequently, the chapter discusses the origin of fermionic condensates, highlighting their distinct pairing mechanisms. Beyond mean-field approaches are then introduced to address the limitations of the GP framework, incorporating quantum fluctuations and correlations. The chapter concludes with an outline of the textbook, setting the stage for analytical and numerical investigations of ultracold atoms in ensuing chapters.
Besides the enormous opportunities offered by spectroscopy and atom interferometry, laser cooling has opened up the possibility of experimentally realizing and manipulating quantum degenerate gases: Bose–Einstein condensates and degenerate Fermionic systems. This chapter starts with an illustration of key experimental techniques, such as magnetic trapping, evaporative cooling, and Feshbach resonances. It then turns to the physics of atomic Bose–Einstein condensates, discussing their superfluid behaviour, their coherence properties, and their application to precise measurements. It also describes the experimental investigation of ultracold Fermi gases and fermionic superfluidity, as well as ongoing research into ultracold polar molecules.