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

Law, K. T.; Feldman, D. E.; Gefen, Yuval

doi:10.1103/physrevb.74.045319

Cited by 106 publications

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“…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].…”

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confidence: 99%

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confidence: 99%

“…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.…”

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confidence: 99%

“…Ref. [10]), and the operatorsX 1 andX 2 correspond to the e=4 charge transfer from the outer to the inner edge at QPC1 and QPC2, respectively. The forward and backward tunneling rates w and w ÿ can be calculated in the second order of perturbation theory.…”

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confidence: 99%

“…Ref. [10]), and the topological charge changes according to the fusion rules [19]. Specifically, the initial value of the topological charge fuses with : If the initial charge is 1 or , then the final charge is ; if the initial charge is , then the final charge is 1 or .…”

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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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