Perfect excitation of a matter qubit by a single photon in free space

We propose a scheme for perfect excitation of a single two-level atom by a single photon in free space. The photon state has to match the time reversed photon state originating from spontaneous decay of a two-level system. We discuss its experimental preparation. The state is characterized by a particular asymmetric exponentially-shaped temporal profile. Any deviations from this ideal state limit the maximum absorption. Although perfect excitation requires an infinite amount of time we demonstrate that there is a class of initial one-photon quantum states which can achieve almost perfect absorption even for a finite interaction time. Our results pave the way for realizing perfect coupling between flying and stationary qubits in free space thus opening a possibility for building scalable quantum networks.