We show how the input-output formalism for cascaded quantum systems combined with the quantum trajectory approach yields a compact and physically intuitive description of single photons propagating through a coupled cavity array. As a new application, we obtain the time-dependent spectrum of such a single photon, which directly reflects the fact that only certain frequency components of single-photon wavepackets are trapped inside the cavities and hence are delayed in time. We include in our description the actual generation of the single photon, by assuming we have a single emitter in one of the resonators.
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