Generation and investigation of number states of the radiation field

A wide range of applications in quantum information and quantum cryptography requires radiation sources capable of producing a fixed number of photons. This paper reviews the work performed in our laboratory to produce these fields on demand. Two different methods are discussed. The first is based on the one-atom maser or micromaser operating under the conditions of the so-called trapping states. In this situation, the micromaser field stabilizes to a photon number state. Recently, we also succeeded in determining the Wigner function of a single-photon state. The second device, recently realized in our laboratory, uses a single trapped ion in an optical cavity.