Mach-Zehnder interferometer in the Fractional Quantum Hall regime

Abstract

We consider tunneling between two edges of Quantum Hall liquids (QHL) of filling factors $ν_{0,1}=1/(2 m_{0,1}+1)$, with $m_0 \geq m_1\geq 0$, through two point contacts forming Mach-Zehnder interferometer. Quasi-particle description of the interferometer is derived explicitly through the instanton duality transformation of the initial electron model. For $m_{0}+m_{1}+1\equiv m>1$, tunneling of quasiparticles of charge $e/m$ leads to non-trivial $m$-state dynamics of effective flux through the interferometer, which restores the regular ``electron'' periodicity of the current in flux. The exact solution available for equal propagation times between the contacts along the two edges demonstrates that the interference pattern in the tunneling current depends on voltage and temperature only through a common amplitude.