Readout and retrieval processes are proposed for efficient, high-fidelity quantum state transfer between a matter qubit, encoded in the level structure of a single atom or ion, and a photonic qubit, encoded in a time-reversal-symmetric single-photon wave packet. They are based on controlling spontaneous photon emission and absorption of a matter qubit on demand in free space by stimulated Raman adiabatic passage. As these processes do not involve mode selection by high-finesse cavities or photon transport through optical fibers, they offer interesting perspectives as basic building blocks for free-space quantum-communication protocols.PACS numbers: 42.50. Pq,03.67.Bg,42.50.Ct,42.50.Ex High-fidelity quantum state transfer between single photons acting as "flying qubits" and matter qubits, such as atoms or ions, acting as "stationary" memory "qubits" is a crucial process for quantum technological applications. It is an important elementary readout and retrieval process in quantum-communication protocols [1] in which quantum information exchange between distant stationary matter qubits is achieved by photon transport through optical fibers or through free-space channels. Whereas fiber based quantum communication offers advantages for local networks [2] free-space implementations are of special interest for the realization of a future worldwide satellite-based quantum-communication network [3].Motivated by its significance for quantum communication the realization of efficient light matter coupling in free space has been subject of recent experimental [4][5][6] and theoretical [7] investigations. Although efficient, high-fidelity quantum state transfer from a matter qubit to a photonic qubit can be achieved by spontaneous photon emission, realizing the reverse process in free space is a formidable experimental challenge. Exploiting timereversal symmetry it has been shown that almost perfect absorption of a single photon in free space is possible provided the single-photon wave packet has an exponentially growing temporal envelope [7]. An interesting probabilistic method for generating and shaping a single-photon wave packet with an exponentially rising envelope has been developed recently [8,9]. The inherent probabilistic nature of the procedure stems from the usage of a photon source based on spontaneous four-wave mixing [10] and the shaping of the wave packet by using electro-optical amplitude modulation. However, the probabilistic nature of these processes is a disadvantage for applications concerning readout and retrieval processes of quantum information and procedures capable of performing such tasks on demand in a deterministic way are favorable.In fiber and cavity based quantum-communication schemes a proposal to overcome the obstacles of probabilistic photon generation and probabilistic wave packet shaping has been developed by Cirac. et al. [11] and has been implemented experimentally by Ritter et al. [12], recently. In this experiment a laser pulse controls the interaction of a single trapped atom wi...