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AIP conference proceedings

Introduction to the Basic-Concepts of Bose-Einstein Condensation

Vanderlei Salvador Bagnato, K. M. F. Magalhães, Jorge Amin Seman, E. A. L. Henn, E. R. F. Ramos, Rocio R. Jauregui, J. Récamier, Óscar Rosas-Ortiz

Published Jan 1, 2008• 3 citations
Publisher

Abstract

This text corresponds to part of the course presented at the ELAF XXXVIII. It is composed of work previously done along the years. The level of this introduction follows the last year of undergraduate and first year of graduate courses. We apologize to the experts on this field, but the idea here is to provide the basic principles and tools for students just getting involved with this topic. For those interested in a deeper reading on the subject, we strongly recommend the review article published by Courteille, Bagnato and Yukalov [1] from which part of this text was extracted. The lecture is divided in three parts: an introduction, the basic concepts of Bose‐Einstein Condensation and information about making and probing BECs.

DOI
10.1063/1.2907761

Related papers

Nobel Lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments

Eric Cornell, Carl Wieman

Bose-Einstein condensation, or BEC, has a long and rich history dating from the early 1920s. In this article we will trace briefly over this history and some of the developments in physics that made possible our successful pursuit of BEC in a gas. We will then discuss what was involved in this quest. In this discussion we will go beyond the usual technical description to try and address certain questions that we now hear frequently, but are not covered in our past research papers. These are questions along the lines of: How did you get the idea and decide to pursue it? Did you know it was going to work? How long did it take you and why? We will review some our favorites from among the experiments we have carried out with BEC. There will then be a brief encore on why we are optimistic that BEC can be created with nearly any species of magnetically trappable atom. Throughout this article we will try to explain what makes BEC in a dilute gas so interesting, unique, and experimentally ${\mathrm{challenging}.}^{1}$

Reviews of Modern Physics•Aug 19, 2002•837 citations

Introduction

Christopher C. Gerry, P. L. Knight

Scope and aims of this book Quantum optics is one of the liveliest fields in physics at present. While it has been a dominant research field for at least two decades, with much graduate activity, in the past few years it has started to impact the undergraduate curriculum. This book developed from courses we have taught to final year undergraduates and beginning graduate students at Imperial College London and City University of New York. There are plenty of good research monographs in this field, but we felt that there was a genuine need for a straightforward account for senior undergraduates and beginning postgraduates, which stresses basic concepts. This is a field which attracts the brightest students at present, in part because of the extraordinary progress in the field (e.g. the implementation of teleportation, quantum cryptography, Schrödinger cat states, Bell violations of local realism and the like). We hope that this book provides an accessible introduction to this exciting subject. Our aim was to write an elementary book on the essentials of quantum optics directed to an audience of upper-level undergraduates, assumed to have suffered through a course in quantum mechanics, and for first-or second-year graduate students interested in eventually pursuing research in this area. The material we introduce is not simple, and will be a challenge for undergraduates and beginning graduate students, but we have tried to use the most straightforward approaches. Nevertheless, there are parts of the text that the reader will find more challenging than others.

Cambridge University Press eBooks•Oct 28, 2004•1 citation

Bose-Einstein condensation

Vyacheslav I. Yukalov

The basic notions and the main historical facts on the Bose-Einstein condensation are surveyed.

arXiv:cond-mat/0503668•Mar 29, 2005•0 citations

Bose-Einstein condensation: Analysis of problems and rigorous results

Alessandro Michelangeli

This work is an up-to-date and partially improved analysis of the basics of the mathe- matical description of Bose-Einstein condensation in terms of first principles of Quantum Mechanics. The main aims are: 1) to provide a compact, yet coherent overview: - of the basic mathematical tools used to formalise Bose-Einstein condensation, - of the mathematical techniques for studying several features of this physical phenomenon, - and of how such means emerge as the natural ones in connection with their physical interpretation; 2) to discuss and to place in the above perspective some new contributions and improvements: - on equivalent characterizations of Bose-Einstein condensation, - on the strength of the convergence for some currently available asymptotic results, - and on the effects of interparticle correlations on the energy and the dynamics of the many-body condensate.

•Oct 16, 2007•10 citations

The Geometric Phase in Quantum Systems

Saverio Pascazio

The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke `after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is inexperienced in such matters and needs to look at details. This book is addressed to graduate physics and chemistry students and was written thinking of students. However, I would recommend it also to young and mature physicists, even those who are already `into' the subject. It is a comprehensive work, jointly written by five researchers. After a simple introduction to the subject, the book gradually provides deeper concepts, more advanced theory and finally an interesting introduction and explanation of recent experiments. For its multidisciplinary features, this work could not have been written by one single author. The collaborative effort is undoubtedly one of its most interesting qualities. I would definitely recommend it to anyone who wants to learn more on the geometric phase, a topic that is both beautiful and intruiguing.

Journal of Physics A Mathematical and General•Nov 26, 2003•27 citations

Experimental Aspects of Bose-Einstein Condensation

A. C. Wilson, Callum R. McKenzie

An introductory level review of experimental techniques essential for producing and probing Bose condensates formed with dilute alkali vapours is presented. This discussion includes a summary of evaporative cooling techniques, condensate imaging schemes, and a review of current BEC technology.

Modern Physics Letters B•Sep 1, 2000•1 citation
This text corresponds to part of the course presented at the ELAF XXXVIII. It is composed of work previously done along the years. The level of this introduction follows the last year of undergraduate and first year of graduate courses. We apologize to the experts on this field, but the idea here is to provide the basic principles and tools for students just getting involved with this topic. For those interested in a deeper reading on the subject, we strongly recommend the review article published by Courteille, Bagnato and Yukalov [1] from which part of this text was extracted. The lecture is divided in three parts: an introduction, the basic concepts of Bose‐Einstein Condensation and information about making and probing BECs.
Bose-Einstein condensation, or BEC, has a long and rich history dating from the early 1920s. In this article we will trace briefly over this history and some of the developments in physics that made possible our successful pursuit of BEC in a gas. We will then discuss what was involved in this quest. In this discussion we will go beyond the usual technical description to try and address certain questions that we now hear frequently, but are not covered in our past research papers. These are questions along the lines of: How did you get the idea and decide to pursue it? Did you know it was going to work? How long did it take you and why? We will review some our favorites from among the experiments we have carried out with BEC. There will then be a brief encore on why we are optimistic that BEC can be created with nearly any species of magnetically trappable atom. Throughout this article we will try to explain what makes BEC in a dilute gas so interesting, unique, and experimentally challenging.1{\mathrm{challenging}.}^{1}challenging.1
Scope and aims of this book Quantum optics is one of the liveliest fields in physics at present. While it has been a dominant research field for at least two decades, with much graduate activity, in the past few years it has started to impact the undergraduate curriculum. This book developed from courses we have taught to final year undergraduates and beginning graduate students at Imperial College London and City University of New York. There are plenty of good research monographs in this field, but we felt that there was a genuine need for a straightforward account for senior undergraduates and beginning postgraduates, which stresses basic concepts. This is a field which attracts the brightest students at present, in part because of the extraordinary progress in the field (e.g. the implementation of teleportation, quantum cryptography, Schrödinger cat states, Bell violations of local realism and the like). We hope that this book provides an accessible introduction to this exciting subject. Our aim was to write an elementary book on the essentials of quantum optics directed to an audience of upper-level undergraduates, assumed to have suffered through a course in quantum mechanics, and for first-or second-year graduate students interested in eventually pursuing research in this area. The material we introduce is not simple, and will be a challenge for undergraduates and beginning graduate students, but we have tried to use the most straightforward approaches. Nevertheless, there are parts of the text that the reader will find more challenging than others.
This work is an up-to-date and partially improved analysis of the basics of the mathe- matical description of Bose-Einstein condensation in terms of first principles of Quantum Mechanics. The main aims are: 1) to provide a compact, yet coherent overview: - of the basic mathematical tools used to formalise Bose-Einstein condensation, - of the mathematical techniques for studying several features of this physical phenomenon, - and of how such means emerge as the natural ones in connection with their physical interpretation; 2) to discuss and to place in the above perspective some new contributions and improvements: - on equivalent characterizations of Bose-Einstein condensation, - on the strength of the convergence for some currently available asymptotic results, - and on the effects of interparticle correlations on the energy and the dynamics of the many-body condensate.
The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke `after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is inexperienced in such matters and needs to look at details. This book is addressed to graduate physics and chemistry students and was written thinking of students. However, I would recommend it also to young and mature physicists, even those who are already `into' the subject. It is a comprehensive work, jointly written by five researchers. After a simple introduction to the subject, the book gradually provides deeper concepts, more advanced theory and finally an interesting introduction and explanation of recent experiments. For its multidisciplinary features, this work could not have been written by one single author. The collaborative effort is undoubtedly one of its most interesting qualities. I would definitely recommend it to anyone who wants to learn more on the geometric phase, a topic that is both beautiful and intruiguing.