Full counting statistics of quantum point contacts with time-dependent transparency

We analyze the zero-temperature full counting statistics (FCS) for the charge transfer across a biased tunnel junction. We find the FCS from the eigenvalues of the density matrix of outgoing states of one lead. In the general case of a general time-dependent bias and time-dependent transparency we solve for these eigenvalues numerically. We report the FCS for the case of a step pulse applied between the leads and a constant barrier transparency (this case is equivalent to Fermi-edge singularity problem). We have also studied combinations of a time-dependent barrier transparency and biases between the leads. In particular, we look at protocols which excite the minimal number of excitations for a given charge transfer (low-noise electron source) and protocols which maximize entanglement of charge states