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arXiv:cond-mat/0605711 · Physical Review A

Fragmentation of Bose-Einstein condensates

Erich J. Mueller, Tin-Lun Ho, Masahito Ueda, Gordon Baym

Published Sep 20, 2006• 294 citations
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Abstract

We present the theory of bosonic systems with multiple condensates, providing a unified description of various model systems that are found in the literature. We discuss how degeneracies, interactions, and symmetries conspire to give rise to this unusual behavior. We show that as degeneracies multiply, so do the varieties of fragmentation, eventually leading to strongly correlated states with no trace of condensation.

DOI
10.1103/physreva.74.033612

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We present the theory of bosonic systems with multiple condensates, providing a unified description of various model systems that are found in the literature. We discuss how degeneracies, interactions, and symmetries conspire to give rise to this unusual behavior. We show that as degeneracies multiply, so do the varieties of fragmentation, eventually leading to strongly correlated states with no trace of condensation.
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Chapter 17 first considers noninteracting elementary bosons for zero and finite temperatures and then discusses the effects of temperature and space dimension on Bose-Einstein condensation. Condensation of massive bosons in a potential trap is also discussed. Next, the chapter discusses condensate fragmentation, showing that the condensate stability against momentum fragmentation requires the introduction of a boson-boson repulsive interaction: exchange processes between the two parts of the fragmented condensate provide a positive extensive contribution to the N-boson energy, which stabilizes the unfragmented condensate. By contrast, spin fragmentation can occur: the condensate is “spin fragmented,” that is, unpolarized, for same-spin bosons undergoing repulsive interactions. The effect of interaction on the elementary boson ground-state energy is also presented, with emphasis on the physical origin of the singularity of the boson correlation energy, and its similarity with the singularity of the electron correlation energy.
Abstract Fragmented Bose–Einstein condensates are large systems of identical bosons displaying multiple macroscopic occupations of one-body states, in a suitable sense. The quest for an effective dynamics of the fragmented condensate at the leading order in the number of particles, in analogy to the much more controlled scenario for complete condensation in one single state, is deceptive both because characterising fragmentation solely in terms of reduced density matrices is unsatisfactory and ambiguous, and because as soon as the time evolution starts the rank of the reduced marginals generically passes from finite to infinite, which is a signature of a transfer of occupations on infinitely many more one-body states. In this work we review these difficulties, we refine previous characterisations of fragmented condensates in terms of marginals, and we provide a quantitative rate of convergence to the leading effective dynamics in the double limit of infinitely many particles and infinite energy gap.
Weakly interacting Bose gases usually form Bose-Einstein condensates in which most particles occupy the same single-particle state. However, when this state cannot realize a continuous symmetry of the many-body Hamiltonian, a fragmented condensate exhibiting the expected symmetry may emerge. Here, we produced a three-fragment condensate for a mesoscopic spin-1 gas of about 100 atoms, with anti-ferromagnetic interactions and vanishing collective spin. Using a spin-resolved detection approaching single-atom resolution, we show that the reconstructed state is close to the expected many-body ground state, whereas one-body observables are the same as for a completely mixed state. Our results highlight how the interplay between symmetry and interactions generates entanglement in a mesoscopic quantum system.
Abstract This volume introduces the basic concepts of Bose–Einstein condensation and superfluidity. It makes special reference to the physics of ultracold atomic gases; an area in which enormous experimental and theoretical progress has been achieved in the last twenty years. Various theoretical approaches to describing the physics of interacting bosons and of interacting Fermi gases, giving rise to bosonic pairs and hence to condensation, are discussed in detail, both in uniform and harmonically trapped configurations. Special focus is given to the comparison between theory and experiment, concerning various equilibrium, dynamic, thermodynamic, and superfluid properties of these novel systems. The volume also includes discussions of ultracold gases in dimensions, quantum mixtures, and long-range dipolar interactions.