Noise and counting statistics of insulating phases in one-dimensional optical lattices

We discuss the correlation properties of current-carrying states of one-dimensional insulators, which could be realized by applying an impulse to atoms loaded onto an optical lattice. While the equilibrium noise has a gapped spectrum, the quantum uncertainty encoded in the amplitudes for the Zener process gives a zero-frequency contribution out of equilibrium. We derive a general expression for the generating function of the full counting statistics and find that the particle transport obeys binomial statistics with doubled charge, resulting in super-Poissonian noise that originates from the coherent creation of particle-hole pairs.

Figure 1

(Color online) (a) Schematic view of particle-hole pair production in a one-dimensional insulator subject to a force. (b) The discretization used to evaluate the counting statistics.