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Anyonic Excitations in Fast Rotating Bose Gases

Jean-Christophe Wallet

Published Jul 11, 2005• 0 citations
OpenAlex

Abstract

The role of anyonic excitations in fast rotating harmonically trapped Bose gases in a fractional Quantum Hall State is examined. Standard Chern-Simons anyons as well as \"non standard\" anyons obtained from a statistical interaction having Maxwell-Chern-Simons dynamics and suitable non minimal coupling to matter are considered. Their respective ability to stabilize attractive Bose gases under fast rotation in the thermodynamical limit is studied. Stability can be obtained for standard anyons while for non standard anyons, stability requires that the range of the corresponding statistical interaction does not exceed the typical wavelength for the atoms.

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•Jan 1, 2006•0 citations
The role of anyonic excitations in fast rotating harmonically trapped Bose gases in a fractional Quantum Hall State is examined. Standard Chern-Simons anyons as well as "non standard" anyons obtained from a statistical interaction having Maxwell-Chern-Simons dynamics and suitable non minimal coupling to matter are considered. Their respective ability to stabilize attractive Bose gases under fast rotation in the thermodynamical limit is studied. Stability can be obtained for standard anyons while for non standard anyons, stability requires that the range of the corresponding statistical interaction does not exceed the typical wavelength for the atoms.
The role of anyonic excitations in fast rotating harmonically trapped Bose gases in a fractional quantum Hall state is examined. Standard Chern-Simons anyons as well as ``nonstandard'' anyons obtained from a statistical interaction having Maxwell-Chern-Simons dynamics and suitable nonminimal coupling to matter are considered. Their respective ability to stabilize attractive Bose gases under fast rotation in the thermodynamical limit is studied. Stability can be obtained for standard anyons while for nonstandard anyons, stability requires that the range of the corresponding statistical interaction does not exceed the typical wavelength of the atoms.
We show that for rotating harmonically trapped Bose gases in a fractional quantum Hall state, the anyonic excitation statistics in the rotating gas can effectively play a dynamical role. For particular values of the two-dimensional coupling constant g=-2pih2(2k-1)/m, where k is a positive integer, the system becomes a noninteracting gas of anyons, with exactly obtainable solutions satisfying Bogomol'nyi self-dual order parameter equations. Attractive Bose gases under rapid rotation thus can be stabilized in the thermodynamic limit due to the anyonic statistics of their quasiparticle excitations.
We use a Chern Simons Landau-Ginzburg (CSLG) framework related to hierarchies of composite bosons to describe 2D harmonically trapped fast rotating Bose gases in Fractional Quantum Hall Effect (FQHE) states. The predicted values for ννν (ratio of particle to vortex numbers) are ννν===pq{{p}\over{q}}qp​ (ppp, qqq are any integers) with even product pqpqpq, including numerically favored values previously found and predicting a richer set of values. We show that those values can be understood from a bosonic analog of the law of the corresponding states relevant to the electronic FQHE. A tentative global phase diagram for the bosonic system for ννν$
Anyons are low-dimensional quasiparticles that obey fractional statistics, hence interpolating between bosons and fermions. In two dimensions, they exist as elementary excitations of fractional quantum Hall states and they are believed to enable topological quantum computing. One-dimensional (1D) anyons have been theoretically proposed, but their experimental realization has proven to be difficult. Here, we observe anyonic correlations, which emerge through the phenomenon of spin-charge separation, in a 1D strongly-interacting quantum gas. The required spin degree of freedom is provided by a mobile impurity, whose effective anyonic correlations are associated with an experimentally tunable statistical angle. These anyonic correlations are measured by monitoring the impurity momentum distribution, whose asymmetric feature demonstrates the transmutation of bosons via anyons to fermions. Going beyond equilibrium conditions, we study the dynamical properties of the anyonic correlations via dynamical fermionization of the anyons. Our work opens up the door to the exploration of non-equilibrium anyonic phenomena in a highly controllable setting.
Ultracold atomic gases in rapidly rotating traps display a wealth of interesting physics. One of the most striking achievements in this field is the observation of th e Abrikosov lattice of vortices. When the rotation frequency is equal to the harmonic trap frequency, the atomic gases is similar to charged particles in a magnetic f ield. It has been predicted that for weak interactions and strong confinement along the rotation axis, this system will exhibit quantum phases equivalent to the one o f the fractional quantum Hall effect. The talk will be focused on bosonic atoms with only one hyperfine species (i.e spinless bosons). We will give numerical evidences of the fractional quantum Hall states in these systems. We will describe how they can be understood using the Laughlin wave function and the Jain's composite fermion theory. We will also discuss about more exotic quantum phases that have also been predicted in such regime. These quantum phases are described by the Read-Rezayi wave functions whose one of the most remarkable properties is that their excitations obey non-abelian statistics.