Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 The non-interacting Bose gas
- 3 Atomic properties
- 4 Trapping and cooling of atoms
- 5 Interactions between atoms
- 6 Theory of the condensed state
- 7 Dynamics of the condensate
- 8 Microscopic theory of the Bose gas
- 9 Rotating condensates
- 10 Superfluidity
- 11 Trapped clouds at non-zero temperature
- 12 Mixtures and spinor condensates
- 13 Interference and correlations
- 14 Optical lattices
- 15 Lower dimensions
- 16 Fermions
- 17 From atoms to molecules
- Appendix: Fundamental constants and conversion factors
- Index
12 - Mixtures and spinor condensates
Published online by Cambridge University Press: 25 January 2011
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 The non-interacting Bose gas
- 3 Atomic properties
- 4 Trapping and cooling of atoms
- 5 Interactions between atoms
- 6 Theory of the condensed state
- 7 Dynamics of the condensate
- 8 Microscopic theory of the Bose gas
- 9 Rotating condensates
- 10 Superfluidity
- 11 Trapped clouds at non-zero temperature
- 12 Mixtures and spinor condensates
- 13 Interference and correlations
- 14 Optical lattices
- 15 Lower dimensions
- 16 Fermions
- 17 From atoms to molecules
- Appendix: Fundamental constants and conversion factors
- Index
Summary
In preceding chapters we have explored properties of Bose–Einstein condensates with a single macroscopically occupied quantum state, and spin degrees of freedom of the atoms were assumed to play no role. In the present chapter we extend the theory to systems in which two or more quantum states are macroscopically occupied.
The simplest example of such a multi-component system is a mixture of two different species of bosons, for example two isotopes of the same element, or two different atoms. The theory of such systems can be developed along the same lines as that for one-component systems developed in earlier chapters, and we do this in Sec. 12.1.
Since alkali atoms have spin, it is also possible to make mixtures of the same isotope, but in different internal spin states. This was first done experimentally by the JILA group, who made a mixture of 87Rb atoms in hyperfine states F = 2, mF = 2 and F = 1, mF = −1. Mixtures of hyperfine states of the same isotope differ from mixtures of distinct isotopes because atoms can undergo transitions between hyperfine states, while transitions that convert one isotope into another may be neglected. Transitions between different hyperfine states can influence equilibrium properties markedly if the interaction energy per particle is comparable with or larger than the energy difference between hyperfine levels. In magnetic traps it is difficult to achieve such conditions, since the trapping potential depends on the particular hyperfine state.
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- Bose–Einstein Condensation in Dilute Gases , pp. 348 - 364Publisher: Cambridge University PressPrint publication year: 2008