We derive the explicit analytical form of the time-dependent coupling parameter to an external field for perfect absorption of traveling single photon fields with arbitrary temporal profiles by a tunable single input-output open quantum system, which can be realized as either a single qubit or single resonator system. However, the time-dependent coupling parameter for perfect absorption has a singularity at $t=0$ and constraints on real systems prohibit a faithful physical realization of the perfect absorber. A numerical example is included to illustrate the absorbers performance under practical limitations on the coupling strength.
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