Quantum Interference and Complex Photon Statistics in Waveguide QED. (arXiv:1710.01543v3 [quant-ph] UPDATED)

We obtain photon statistics by using a quantum jump approach tailored to a
system in which one or two qubits are coupled to a one-dimensional waveguide.
Photons confined in the waveguide have strong interference effects, which are
shown to play a vital role in quantum jumps and photon statistics. For a single
qubit, for instance, bunching of transmitted photons is heralded by a jump that
increases the qubit population. We show that the distribution and correlations
of waiting times offer a clearer and more precise characterization of photon
bunching and antibunching. Further, the waiting times can be used to
characterize complex correlations of photons which are hidden in
$g^{(2)}(\tau)$, such as a mixture of bunching and antibunching.

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