Detecting non-Abelian statistics with an electronic Mach-Zehnder interferometer

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Mesoscopic Physics

Background:

• The quantum Hall state at filling factor nu=5/2 is a prime candidate for hosting exotic particles.
• These particles, known as fractionally charged quasiparticles, are theorized to exhibit non-Abelian statistics, crucial for topological quantum computing.
• Understanding and verifying these statistics experimentally is a significant challenge in condensed matter physics.

Purpose of the Study:

• To propose and theoretically demonstrate a method for probing the non-Abelian statistics of fractionally charged quasiparticles.
• To investigate the feasibility of using transport measurements in an electronic Mach-Zehnder interferometer for this purpose.
• To identify measurable signatures of non-Abelian statistics in the interferometer's response.

Main Methods:

• Utilizing an electronic Mach-Zehnder interferometer setup to guide and interfere fractionally charged quasiparticles.
• Performing transport measurements, specifically analyzing the tunneling current through the interferometer.
• Investigating the dependence of the tunneling current on external magnetic flux and controllable tunneling amplitudes via gate voltages.

Main Results:

• The theoretical model predicts a characteristic dependence of the tunneling current on the applied magnetic flux.
• A key finding is the prediction of a nonanalytic dependence of the tunneling current on the tunneling amplitudes.
• These dependencies are shown to be sensitive to the underlying non-Abelian statistics of the quasiparticles.

Conclusions:

• Transport measurements in an electronic Mach-Zehnder interferometer offer a viable experimental pathway to probe non-Abelian statistics.
• The predicted flux and tunneling amplitude dependencies provide experimental signatures to verify the exotic nature of these quasiparticles.
• This work paves the way for experimental verification of non-Abelian statistics, a critical step towards realizing topological quantum computing.