Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics

Camino, Fernando; Zhou, Wei; Goldman, V. J.

doi:10.1103/physrevb.72.075342

Cited by 242 publications

(359 citation statements)

References 42 publications

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“…As a natural generalization, physicist proposed that there exists anyon interpolating between Bose and Fermi statistics, which satisfies fractional statistics [1]. It has become an important concept in condensed matter physics [2][3][4] and has ever been used for successfully explaining the fractional quantum Hall effect (FQHE) [5]. Fractional statistics also play important roles in the theory for non-fermi liquid, Chern-Simon theory, and other aspects [6,7].…”

Section: Introductionmentioning

confidence: 99%

Dynamical properties of hard-core anyons in one-dimensional optical lattices

Hao

Chen

2012

Phys. Rev. A

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We investigate the dynamical properties of anyons confined in one-dimensional optical lattice combined with a weak harmonic trap using the exact numerical method based on a generalized Jordan-Wigner transformation. The density profiles, momentum distribution, occupation distribution and occupations of the lowest natural orbital are obtained for different statistical parameters. The density profiles of anyons display the same behaviors irrespective of statistical parameter in the full evolving period. While the behaviors dependent on statistical property are shown in the momentum distributions and occupations of natural orbitals.

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Section: Introductionmentioning

confidence: 99%

Dynamical properties of hard-core anyons in one-dimensional optical lattices

Hao

Chen

2012

Phys. Rev. A

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“…A recent experiment on the mutual fractional statistics of two quasiparticles with different charges has been published in Ref. 3. It involved a setup consisting of an island of a fractional quantum Hall liquid embedded in a liquid with a different filling factor.…”

Section: Introductionmentioning

confidence: 99%

Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics

2006

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We study transport through an electronic Mach-Zehnder interferometer recently devised at the Weizmann Institute. We show that this device can be used to probe the statistics of quasiparticles in the fractional quantum Hall regime. We calculate the tunneling current through the interferometer as the function of the AharonovBohm flux, temperature, and voltage bias, and demonstrate that its flux-dependent component is strongly sensitive to the statistics of tunneling quasiparticles. More specifically, the flux-dependent and flux-independent contributions to the current are related by a power law, the exponent being a function of the quasiparticle statistics.

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“…Probing fractional statistics is more difficult. It was argued that the mutual statistics of nonidentical quasiparticles was detected in a recent experiment [4] by Camino et al; however, the interpretation of the experimental results remains controversial [5,6]. There are several theoretical proposals for observing the statistics of identical Abelian quasiparticles [7][8][9][10] but none of them has been realized experimentally.…”

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confidence: 99%

Detecting Non-Abelian Statistics with an Electronic Mach-Zehnder Interferometer

2006

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Fractionally charged quasiparticles in the quantum Hall state with a filling factor 5=2 are expected to obey non-Abelian statistics. We demonstrate that their statistics can be probed by transport measurements in an electronic Mach-Zehnder interferometer. The tunneling current through the interferometer exhibits a characteristic dependence on the magnetic flux and a nonanalytic dependence on the tunneling amplitudes which can be controlled by gate voltages. DOI: 10.1103/PhysRevLett.97.186803 PACS numbers: 73.43.Jn, 73.43.Cd, 73.43.Fj One of the central features of the quantum Hall effect (QHE) is the fractional charge and statistics of quasiparticles. The quantum state of bosons or fermions does not change when one particle makes a full turn around another. On the other hand, Laughlin quasiparticles pick up nontrivial phases when they encircle each other. Non-Abelian statistics predicted in some QHE systems [1,2] is even more interesting: The state vector changes its direction in the Hilbert space after a particle makes a full circle.Shot noise experiments [3] allowed the observation of fractional charges in QHE liquids. Probing fractional statistics is more difficult. It was argued that the mutual statistics of nonidentical quasiparticles was detected in a recent experiment [4] by Camino et al.; however, the interpretation of the experimental results remains controversial [5,6]. There are several theoretical proposals for observing the statistics of identical Abelian quasiparticles [7][8][9][10] but none of them has been realized experimentally.Detecting non-Abelian anyons is of special interest due to their promise for fault-tolerant quantum computation [11]. One approach for their observation and probing their statistics is based on current noise in complex geometries [12,13]. A simpler proposal involves current through an Aharonov-Bohm interferometer with trapped quasiparticles [14,15]. This method should work if the number of trapped quasiparticles does not fluctuate on the measurement time scale [9]. Such a condition might be difficult to satisfy in non-Abelian systems, where the excitation gap is relatively low [16].We suggest another method, which is free from this limitation. It uses the electronic Mach-Zehnder interferometer recently designed at the Weizmann Institute [17]; see Fig. 1(a). We consider the 5=2 QHE state and show that the tunneling current I through the interferometer contains signatures of non-Abelian statistics. The current (8) is a periodic function of the magnetic flux through the interferometer with period 0 hc=e, but, in contrast with the Abelian case [10], it is not a simple sine wave. Note the nonanalytic dependence on the interedge tunneling amplitudes ÿ 1 and ÿ 2 at the quantum point contacts (constrictions) QPC1 and QPC2. In the limit of ÿ 2 ÿ 1 , the formula for the current assumes a sinusoidal form, I I 0 I cos 2 = 0 const , where the fluxdependent and flux-independent terms are related by the scaling law: The Letter is organized as follows. First, we briefly discuss the ...

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Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics

Cited by 242 publications

References 42 publications

Dynamical properties of hard-core anyons in one-dimensional optical lattices

Dynamical properties of hard-core anyons in one-dimensional optical lattices

Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics

Detecting Non-Abelian Statistics with an Electronic Mach-Zehnder Interferometer

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