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arXiv:0801.4856 · Journal of Physics Condensed Matter

Quantum Hall physics in rotating Bose–Einstein condensates

Susanne Viefers

Published Feb 25, 2008• 125 citations
arXivHTMLPDF

Abstract

The close theoretical analogy between the physics of rapidly rotating atomic Bose condensates and the quantum Hall effect (i.e. a two-dimensional electron gas in a strong magnetic field) was first pointed out ten years ago. As a consequence of this analogy, a large number of strongly correlated quantum-Hall-type states have been predicted to occur in rotating Bose systems, and suggestions have been made for how to manipulate and observe their fractional quasiparticle excitations. Due to a very rapid development in experimental techniques over the past years, experiments on BEC now appear to be close to reaching the quantum Hall regime. This paper reviews the theoretical and experimental work done to date in exploring quantum Hall physics in cold bosonic gases. Future perspectives are discussed briefly, in particular the idea of exploiting some of these strongly correlated states in the context of topological quantum computing.

DOI
10.1088/0953-8984/20/12/123202

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The close theoretical analogy between the physics of rapidly rotating atomic Bose condensates and the quantum Hall effect (i.e. a two-dimensional electron gas in a strong magnetic field) was first pointed out ten years ago. As a consequence of this analogy, a large number of strongly correlated quantum-Hall-type states have been predicted to occur in rotating Bose systems, and suggestions have been made for how to manipulate and observe their fractional quasiparticle excitations. Due to a very rapid development in experimental techniques over the past years, experiments on BEC now appear to be close to reaching the quantum Hall regime. This paper reviews the theoretical and experimental work done to date in exploring quantum Hall physics in cold bosonic gases. Future perspectives are discussed briefly, in particular the idea of exploiting some of these strongly correlated states in the context of topological quantum computing.
This chapter reviews the theoretical understanding of Bose and Fermi superfluids under rotation (or in an effective magnetic field) while placing this in context of the current experimental status. It focuses on theoretical predictions of the novel phases that can appear. One goal is to establish the connections with the physics of the fractional quantum Hall effect of electrons in semiconductors. As the chapter is intended to be tutorial in nature, it concentrates on the qualitative features and simple model calculations to present the essential ideas in as physically transparent a way as possible. It begins with a brief review of the properties of Bose–Einstein condensates subjected to rotation.
The emergence of macroscopic quantum coherence appears through Bose–Einstein condensation (BEC), which was first seen in superfluid helium and later achieved in ultracold atomic gases as a weakly interacting quantum fluid. This article aims to provide a study of the rotational properties of a two-component ultracold bosonic mixture with homogeneous and inhomogeneous interactions in the fractional quantum Hall (FQH) regime, where strong effective magnetic fields or rapid rotation drive the system into a strongly correlated quantum fluid state. Ultracold atomic gases offer a versatile experimental platform to realize and test the predictions of the composite fermion approach, bridging condensed matter physics with atomic physics through the unifying concept of weakly interacting quantum fluids emerging from strong correlations. A quantum interference-based atom laser in a two-component BEC is scientifically original and technologically promising, following recent advances in multi-species condensates. In this article, we explore the possibility of realizing an atom laser from ultracold binary atomic gases via their rotational properties in the FQH regime, where the controlled emission of quasiholes or coherent matter waves from the correlated state may provide a route toward an atom-laser scheme based on strongly correlated FQH states.
We exploit the analogy with the quantum Hall (QH) effect for electrons to study the possible atomic QH states of a rapidly-rotating Bose-Einstein condensate. Actually, there is a nearly perfect map of the present problem in the QH regime to the QH physics for electrons. The profound map enables one to give a physically appealing definitions of the filling fraction and the "atomic Hall conductance" that is quantized for atomic Laughlin states. This quantization might imply an exotic fractionalization of atomic mass. We also briefly discuss an effective Chern-Simons theory for describing the atomic QH liquids where a gravitational-like field naturally emerges.
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In this article, we review developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single-component atomic Bose gas, which (at least at rest) forms a Bose–Einstein condensate. Rotation leads to the formation of quantized vortices which order into a vortex array, in close analogy with the behaviour of superfluid helium. Under conditions of rapid rotation, when the vortex density becomes large, atomic Bose gases offer the possibility to explore the physics of quantized vortices in novel parameter regimes. First, there is an interesting regime in which the vortices become sufficiently dense that their cores, as set by the healing length, start to overlap. In this regime, the theoretical description simplifies, allowing a reduction to single-particle states in the lowest Landau level. Second, one can envisage entering a regime of very high vortex density, when the number of vortices becomes comparable to the number of particles in the gas. In this regime, theory predicts the appearance of a series of strongly correlated phases, which can be viewed as bosonic versions of fractional quantum Hall states. In this article, we describe the equilibrium properties of rapidly rotating atomic Bose gases in both the mean-field and the strongly correlated regimes, and related theoretical developments for Bose gases in lattices, for multi-component Bose gases and for atomic Fermi gases. The current experimental situation and outlook for the future are discussed in light of these theoretical developments.
Cold atomic gases of interacting bosons subject to rapid rotation and confined in anharmonic traps can theoretically exhibit analogues of the fractional quantum Hall effect for electrons in strong magnetic fields. In this setting the Coriolis force due to the rotation mimics the Lorentz force on charged particles but artificial gauge fields can also be obtained by coupling the internal structure of the atoms to light fields. The chapter discusses mathematical aspects of transitions to different strongly correlated phases that appear when the parameters of a model Hamiltonian are varied.