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arXiv:cond-mat/0410398 · Physical Review Letters

Comment on “Dynamical Role of Anyonic Excitation Statistics in Rapidly Rotating Bose Gases”

Pijush K. Ghosh

Published May 26, 2005• 2 citations
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Abstract

We comment on the work of Fischer, Phys. Rev. Lett. 93, 160403 (2004). Contrary to the claim in the letter, we argue that the anyonic excitation statistics does not play any dynamical role in stabilizing attractive bose gases under rapid rotation in a fractional quantum Hall state. We also point out that the assertion of obtaining exact solutions of the self-dual equation that saturates the Bogomol'nyi bound is invalid for non-zero external field.

DOI
10.1103/physrevlett.94.208903

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We comment on the work of Fischer, Phys. Rev. Lett. 93, 160403 (2004). Contrary to the claim in the letter, we argue that the anyonic excitation statistics does not play any dynamical role in stabilizing attractive bose gases under rapid rotation in a fractional quantum Hall state. We also point out that the assertion of obtaining exact solutions of the self-dual equation that saturates the Bogomol'nyi bound is invalid for non-zero external field.
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.
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.
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.
We demonstrate the experimental feasibility of incompressible fractional quantum Hall-like states in ultracold two-dimensional rapidly rotating dipolar Fermi gases. In particular, we argue that the state of the system at filling fraction nu = 1/3 is well described by the Laughlin wave function and find a substantial energy gap in the quasiparticle excitation spectrum. Dipolar gases, therefore, appear as natural candidates of systems that allow us to realize these very interesting highly correlated states in future experiments.
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.
It is mentioned that anyon thermodynamic potential Q(α,N)Q(\alpha, N)Q(α,N) could not be factorized in terms characteristic of the ideal boson α=0\alpha =0α=0 and fermion α=1\alpha =1α=1 gases by the relation Q(α,N)=(1−α)Q(0,Nb)+αQ(1,Nf)Q(\alpha, N) = (1-\alpha) Q(0, N_b)+ \alpha Q(1, N_f)Q(α,N)=(1−α)Q(0,Nb​)+αQ(1,Nf​) in which N=Nf+NbN=N_f +N_bN=Nf​+Nb​, that claimed in Phys. Rev. Lett. 78, 3233 (1997). Our analyses indicate that the thermodynamic quantities of anyon gas may be factorized as Q(α)=αQ(1)+(1−α)Q(0)Q(\alpha) = \alpha Q(1) + (1-\alpha) Q(0)Q(α)=αQ(1)+(1−α)Q(0) only in the two-dimension system.