Counting statistics for arbitrary cycles in quantum pumps.

We study noise-related properties of current in adiabatic pumps. A symmetry of the problem allows us to relate the statistics of charge transport in the case of one-channel leads to the geometry of loops on a sphere (for many channels on a higher-dimensional manifold). This provides a unifying framework, which simplifies analysis of transport in various realizations of pumps. For each pumping cycle, the average current and its minimal variance are given by the areas enclosed by the corresponding loop on the sphere and on a minimal surface (soap film) spanned by this loop. We formulate conditions for quantization of the pumped charge.

Statistics and noise in a quantum measurement process

We study the quantum measurement process by a single-electron transistor or a quantum point contact coupled to a quantum bit. We find a unified description of the statistics of the monitored quantity, the current, in the regime of strong measurement and derive the probability distributions for the current and charge in different stages of the process. In the parameter regime of the strong measurement the current develops a telegraph-noise behavior which can be detected in the noise spectrum. This description applies for a wide class of quantum measurements.