Standard and Null Weak Values

Weak value (WV) is a quantum mechanical measurement protocol, proposed by Aharonov, Albert, and Vaidman. It consists of a weak measurement, which is weighed in, conditional on the outcome of a later, strong measurement. Here we define another two-step measurement protocol, null weak value (NVW), and point out its advantages as compared to WV. We present two alternative derivations of NWVs and compare them to the corresponding derivations of WVs.Comment: 11 pages, 2 figures. To appear in Quantum Theory: A Two-Time Success Story: Yakir Aharonov Festschrif

Quantum Pump for Fractional Charge

We propose a theoretical scenario for pumping of fractionally charged quasi-particle in the context of $\nu=1/3$ fractional quantum Hall liquid. We consider quasi-particle pumping across an anti-dot level tuned close to the resonance. Fractional charge pumping is achieved by slow and periodic modulation of coupling of the anti-dot level to left and right moving edges of a Hall bar set-up. This is attained by periodically modulating the gate voltages controlling the couplings. In order to obtain quantization of pumped charge in the unit of the electronic charge fraction ($\nu e$) per pumping cycle in the adiabatic limit, we argue that the only possibility is to tune the quasi-particle operator to be irrelevant from being relevant in the renormalization group sense, which can be accomplished by invoking quantum Hall line junctions into the Hall bar geometry. We also comment on possibility for experimental realization of the above scenario.Comment: Version to appear in Europhys. Lett. (2008