We experimentally demonstrate that a nonclassical state prepared in an atomic memory can be efficiently transferred to a single mode of free-propagating light. By retrieving on demand a single excitation from a cold atomic gas, we realize an efficient source of single photons prepared in a pure, fully controlled quantum state. We characterize this source using two detection methods, one based on photon-counting analysis and the second using homodyne tomography to reconstruct the density matrix and Wigner function of the state. The latter technique allows us to completely determine the mode of the retrieved photon in its fine phase and amplitude details and demonstrate its nonclassical field statistics by observing a negative Wigner function. We measure a photon retrieval efficiency up to 82% and an atomic memory coherence time of 900 ns. This setup is very well suited to study interactions between atomic excitations and use them in order to create and manipulate more sophisticated quantum states of light with a high degree of experimental control. Precisely controlling quantum states of light is crucial for many quantum information processing (QIP) tasks. In this respect, cold atomic ensembles are a very versatile tool. In the past decade, they have been extensively used to store and retrieve quantum states of light [1] and, more recently, to manipulate them using atomic interactions [2][3][4]. Quite often, however, the resulting quantum states were characterized only partially, typically by photon correlation measurements insensitive to the exact frequency or temporal envelope of the emitted photons. Although independent atomic ensembles have been shown to emit photons with a good degree of indistinguishability [5][6][7][8], their exact wave functions remained to be characterized. Demonstrating that strongly nonclassical states stored in an atomic ensemble can be retrieved on demand as single-mode, Fouriertransform limited light pulses is an important requirement to use such systems in QIP and to connect them to other QIP devices.A very convenient way to fully characterize the retrieved quantum state is to use homodyne tomography [9], by reconstructing the photons' density matrix and Wigner function from the quadrature distributions of the light field measured by interference with a bright local oscillator. Since this technique characterizes the light's field rather than its intensity, it is intrinsically single mode and very sensitive to optical losses. Therefore, observing nonclassical features in the reconstructed quantum state proves that it can truly be emitted on demand, detected with a high efficiency, and controlled in all of its degrees of freedom which must exactly match those of the local oscillator. For a nonclassical state, the field's quadrature statistics are described by a non-Gaussian Wigner function taking negative values: losses or imperfections in the spatial mode, the polarization, the temporal envelope, or the frequency of the state will degrade the signal and eventually make its Wigner fu...