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Full Counting Statistics of Quantum Point Contact with Time-dependent Transparency

We analyse 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 maximise entanglement of charge states.