Ultracold Bosonic and Fermionic Gases

Kathy Levin, Alexander Fetter, Dan Stamper-Kurn

• Publisher: Elsevier
• Year: 2012
• Print ISBN:
  9780444538574
• eBook ISBN:
  9780444538628
• Topic: Physical Sciences
• Subtopic: Thermodynamics

The rapidly developing topic of ultracold atoms has many actual and potential applications for condensed-matter science, and the contributions to this book emphasize these connections. Ultracold Bose and Fermi quantum gases are introduced at a level appropriate for first-year graduate students and non-specialists such as more mature general physicists. The reader will find answers to questions like: how are experiments conducted and how are the results interpreted? What are the advantages and limitations of ultracold atoms in studying many-body physics? How do experiments on ultracold atoms facilitate novel scientific opportunities relevant to the condensed-matted community? This volume seeks to be comprehensible rather than comprehensive; it aims at the level of a colloquium, accessible to outside readers, containing only minimal equations and limited references. In large part, it relies on many beautiful experiments from the past fifteen years and their very fruitful interplay with basic theoretical ideas. In this particular context, phenomena most relevant to condensed-matter science have been emphasized. - Introduces ultracold Bose and Fermi quantum gases at a level appropriate for non-specialists - Discusses landmark experiments and their fruitful interplay with basic theoretical ideas - Comprehensible rather than comprehensive, containing only minimal equations

Contemporary Concepts of Condensed Matter Science, Vol. 5, No. suppl (C), 2012

ISSN: 1572-0934

doi: 10.1016/B978-0-444-53857-4.00001-5

Chapter 1 Experimental Methods of Ultracold Atomic Physics

Dan M. Stamper-Kurn^a,b, J.H. Thywissen^c,d

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^a Department1 of Physics, University of California, Berkeley, CA 94720

^b Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

^c Department of Physics, University of Toronto, Ontario, Canada M5S 1A7

^d Canadian Institute for Advanced Research, Toronto, Ontario, Canada M5G 1Z8

Abstract

Experiments on solid-state materials and atomic quantum gases are increasingly investigating similar concepts in many-body quantum physics. Yet, the flavor of experiments on the gaseous atomic materials is different from that of conventional materials research. Here, we summarize some aspects of atomic physics and some of the common technical elements of cold atom experiments which underlie the investigations described in the remaining chapters of this volume.

Keywords

• ultracold atomic physics • atomic structure basics • trapping • optical lattice • Feshbach resonance

The broad appeal of research on quantum gases relies on the universality of many-body quantum physics. For example, regardless of whether it is constructed using electrons (as in superconductors), neutrons (as in neutron stars), or neutral atoms of different hyperfine spin (as in ultracold lithium gases), a system of strongly interacting mobile fermions will show the same phenomenology. Similarly, nonlinear and quantum optics can be treated in a common theoretical scheme, regardless of whether the bosonic fields under investigation correspond to massless photons or massive rubidium atoms. Such universality allows ultracold atomic physics to contribute significantly to fields as diverse as condensed matter physics, high energy astrophysics, and quantum optics. As such, the collection of works within this book is meant to bridge the gap between practitioners of these diverse fields so as to make the exchange among them more productive.

Yet, despite these appealing similarities, there do remain system-specific considerations that must be kept in mind in comparing physical systems built from different basic ingredients. This chapter discusses some of the atom-specific aspects of ultracold atomic physics experiments. We focus on two main topics: the common experimental techniques of quantum gas experiments and the nature of atom–atom interactions.

1 Introduction: Why so Cold?

There is little variety in temperature and density among the quantum degenerate neutral gases produced currently in over 100 laboratories in 17 countries. This commonality may be surprising because, unlike solids, gases have no lower bound in density. However, to within a factor of 10, the density of an ultracold gas is

cm⁻³, about six orders of magnitude lower than the density of an ideal gas at standard temperature and pressure. Why is this the typical density? For

cm⁻³, loss processes, such as a three-particle collision leading to the formation of a deeply bound molecule, become faster than rethermalization from elastic collisions. For

cm⁻³, the characteristic energy and temperature scales of the quantum gas become impractically small, particularly if one is interested in anything beyond the noninteracting ideal gas, and the thermalization rate of the gas becomes slow compared to parasitic heating rates and the vacuum-limited lifetimes of the frigid gas samples.

This common density sets a common characteristic energy and length scale for experiments on cold gases. From the interparticle spacing

, typically 300nm, one would guess the energy scale for the physics of such gases to be

, where

is Planck’s constant and M is the atomic mass; more formally, one often takes the Fermi energy

, where

is the Fermi wave vector. For ⁸⁷Rb, this energy scale is around

eV, corresponding to a temperature of about 500nK, and a frequency of about 10kHz.¹

This energy scale also (roughly) defines the temperature at which a gas becomes quantum degenerate. The onset of quantum degeneracy can also be considered from the comparison of length scales. From the system temperature, we can define the thermal de Broglie wavelength,

(1)

where k_B is the Boltzmann constant. When the de Broglie wavelength is comparable to the interparticle spacing, the coherent matter waves associated with the various particles in the gas are forced to overlap, meaning (pictorially) that the number of independent quantum states in the gas becomes comparable to the number of gas particles. At this point, the quantum statistics of particles come into play in describing the nature of the gas. The ultra-low temperature of quantum gases is therefore simply a consequence of their necessarily low density. Since the gases in question are roughly a billion times less dense than liquid helium, they are degenerate at a temperature a million times lower than the lambda point of helium.

The low temperature scale required for the study of quantum degenerate gases has been, and continues to be, the prime technical challenge in ultracold atom research. As discussed in Section 4.1, cooling gases from room temperature to quantum degeneracy relies on a hybrid of cooling methods. These methods took decades to develop. Even today, with cutting-edge techniques, gases cannot match the extreme quantum degeneracy of electrons within a solid in a dilution refrigerator, where the ratio

is around 10⁻⁶; in contrast, for cold atom experiments to date, this ratio goes no lower than 10⁻². Thus, advancing the frontier cold atom experiments still requires the continued development of cooling techniques. Pursuing this frontier is tremendously appealing, as one expects that neutral gases would be able to explore the rich physics of spin liquids, topological quantum matter, pure BCS superfluidity, and perhaps d-wave pairing in lattices [1].

However, even within the current technical limits, the combination of low density and ultracold temperature creates an extraordinary opportunity t...

Table of contents

• Cover image
• Table of Content
• Edited by
• Copyright page
• List of Contributors
• Series Preface
• Volume Preface
• Chapter 1 Experimental Methods of Ultracold Atomic Physics
• Chapter 2 Bose Gas: Theory and Experiment
• Chapter 3 The Fermi Gases and Superfluids: Experiment and Theory
• Chapter 4 Low-Dimensional Atomic Bose Gases
• Chapter 5 Ultracold Atoms and Molecules in Optical Lattices
• Chapter 6 Unitary Fermi Gases
• Chapter 7 Potential Insights into Nonequilibrium Behavior from Atomic Physics
• Index