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Quantum Hall Effect in a Rotating Bose-Einstein Condensate: An Atomic Twin of the Electronic Brother?

Zeng‐Bing Chen, Bo Zhao, Zhang, Yong-De

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.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.

arXiv:cond-mat/0211187Nov 10, 20021 citation

Quantum Hall Phases and Plasma Analogy in Rotating Trapped Bose Gases

Nicolas Rougerie, Sylvia Serfaty, Jakob Yngvason

arXiv:1301.1043Journal of Statistical PhysicsMay 17, 201333 citations

Rotating trapped Bose-Einstein condensates

Alexander L. Fetter

After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, I discuss the effect of interactions on the formation of a Bose-Einstein condensate (BEC), along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity Omega, one or several vortices nucleate, with many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For Omega near the radial trap frequency omega_perp, the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as Omega approaches omega_perp, the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, I discuss the effect of interactions on the formation of a Bose-Einstein condensate (BEC), along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity Omega, one or several vortices nucleate, with many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For Omega near the radial trap frequency omega_perp, the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as Omega approaches omega_perp, the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.

arXiv:0801.2952Jan 18, 20082 citations

On the quantum phase transition of a quantum Hall liquid

Adriaan M. J. Schakel

Nuclear Physics BOct 1, 19954 citations

Quantum Hall States in Rotating Spin-1 Bose Systems

N. Read

APSMar 1, 20030 citations

Quantum Hall physics in rotating Bose–Einstein condensates

Susanne Viefers

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.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.

arXiv:0801.4856Journal of Physics Condensed MatterFeb 25, 2008125 citations

Analogy between rotating Bose-Einstein condensate and quantum Hall liquid(Fundamental Problems and Applications of Quantum Field Theory)

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