Emergence of Fractional Statistics for Tracer Particles in a Laughlin Liquid

Lundholm, Douglas; Rougerie, Nicolas

doi:10.1103/physrevlett.116.170401

Cited by 49 publications

(47 citation statements)

References 45 publications

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“…Both of them were predicted to be realized in certain fractional quantum Hall systems [15][16][17][18][19][20]. In particular, non-Abelian statistics has received a significant amount of attention, as it enables unitary gate operations necessary for quantum computation [21][22][23][24] (also see Ref.…”

Section: Arxiv:171200308v2 [Cond-matquant-gas] 3 Jul 2018mentioning

confidence: 99%

Anyonic statistics of quantum impurities in two dimensions

Yakaboylu

Lemeshko

2018

Phys. Rev. B

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We demonstrate that identical impurities immersed in a two-dimensional many-particle bath can be viewed as flux-tube-charged-particle composites described by fractional statistics. In particular, we find that the bath manifests itself as an external magnetic flux tube with respect to the impurities, and hence the time-reversal symmetry is broken for the effective Hamiltonian describing the impurities. The emerging flux tube acts as a statistical gauge field after a certain critical coupling. This critical coupling corresponds to the intersection point between the quasiparticle state and the phonon wing, where the angular momentum is transferred from the impurity to the bath. This amounts to a novel configuration with emerging anyons. The proposed setup paves the way to realizing anyons using electrons interacting with superfluid helium or lattice phonons, as well as using atomic impurities in ultracold gases.

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Section: Arxiv:171200308v2 [Cond-matquant-gas] 3 Jul 2018mentioning

confidence: 99%

Anyonic statistics of quantum impurities in two dimensions

Yakaboylu

Lemeshko

2018

Phys. Rev. B

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“…In [35], the authors find that a pair of bosonic atoms immersed in a fractional quantum Hall state possesses a fractional relative angular momentum provided certain conditions are satisfied. This work was further studied in [36,37]. In ref.…”

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confidence: 99%

The fractional angular momentum realized by a neutral cold atom

et al. 2019

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Inspired by the electromagnetic duality, we propose an approach to realize the fractional angular momentum by using a cold atom which possesses a permanent magnetic dipole moment. This atom interacts with two electric fields and is trapped by a harmonic potential which enable the motion of the atom to be planar and rotationally symmetric. We show that eigenvalues of the canonical angular momentum of the atom can take fractional values when the atom is cooled down to its lowest kinetic energy level. The fractional part of canonical angular momentum is dual to that of the fractional angular momenta realized by using a charged particle. Another approach of getting the fractional angular momentum is also presented. The differences between these two approaches are investigated.In 1984, Aharonov and Casher predicted that there would exist a topology phase when a neutral particle possessing a non-vanishing magnetic dipole moment moved around a uniformly charged infinitely long filament with its direction paralleling to the filament [1]. It is named Aharonov-Casher (AC) effect.In three-dimensional space, the Hamiltonian which governs the dynamics of a neutral particle possessing a permanent magnetic dipole moment in the background of an electric field is given bywhere m is the mass of the neutral particle, p = −i ∇ is the canonical momentum, µ is the magnitude of the magnetic dipole moment, c is the speed of light in vacuum, n is the unit vector along the magnetic dipole moment and E is the electric field. In AC effect setting, the electric field is produced by a uniformly charged infinitely long filament [1]. The explicit form of the electric field in AC effect isin which λ is charges per unit length on the long filament, ǫ 0 is the permittivity of vacuum, r is the distance between the atom and the long filament and e r is the unit vector along the radial direction on the plane where the atom moves. For AC setting, the last term in Hamiltonian (1) disappears since ∇ · E AC = 0 for r = 0. Hamiltonian (1) is the non-relativistic limit of a relativistic spin-half particle which possesses a permanent magnetic dipole moment in the background of an * Electronic address: jingjian@mail. buct. edu. cn † Electronic address: dongsh2@yahoo. com electromagnetic field. When the neutral atom moves around the uniformly charged infinitely long filament, it will receive a topology phase. The acquired topology phase is given bywhich has been observed in the experiment [2]. Possible classical explanations about AC effect have been presented [3,4]. Inspired by the work of Aharonov and Casher, refs.[5-11] studied topological phases neutral particles would receive in various backgrounds. AC effect is dual to the Aharonov-Bohm (AB) effect. Over half century ago, Aharonov and Bohm predicted that a charged particle would generate a topology phase when it circled around a long-thin flux-carried solenoid. It is known as AB effect [12].The Hamiltonian which describes a charged particle in the background of magnetic potentials in three-dimensional s...

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“…A function of the above form corresponds to inserting Laughlin quasi-holes [8,9] with locations at the zeros of the polynomial f . Each of those carries a fraction 1/ℓ of an electron's charge, and is expected to behave as an anyon [1,17] with statistics parameter −1/ℓ.…”

Section: Introductionmentioning

confidence: 99%

The Laughlin liquid in an external potential

Rougerie

Yngvason

2017

Lett Math Phys

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Abstract. We study natural perturbations of the Laughlin state arising from the effects of trapping and disorder. These are N -particle wave functions that have the form of a product of Laughlin states and analytic functions of the N variables. We derive an upper bound to the ground state energy in a confining external potential, matching exactly a recently derived lower bound in the large N limit. Irrespective of the shape of the confining potential, this sharp upper bound can be achieved through a modification of the Laughlin function by suitably arranged quasi-holes.

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Emergence of Fractional Statistics for Tracer Particles in a Laughlin Liquid

Cited by 49 publications

References 45 publications

Anyonic statistics of quantum impurities in two dimensions

Anyonic statistics of quantum impurities in two dimensions

The fractional angular momentum realized by a neutral cold atom

The Laughlin liquid in an external potential

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