COMPLETE EXPERIMENTAL CHARACTERIZATION OF THE QUANTUM STATE OF A LIGHT MODE VIA THE WIGNER FUNCTION AND THE DENSITY-MATRIX - APPLICATION TOQUANTUM PHASE DISTRIBUTIONS OF VACUUM AND SQUEEZED-VACUUM STATES

We have used the recently demonstrated method of optical homodyne tomo graphy (OHT) to measure the Wigner quasiprobability distribution (Wign er function) and the density matrix for both a squeezed-vacuum and a v acuum state of a single spatial-temporal mode of the electromagnetic f ield. This method consists of measuring a set of probability distribut ions for many different Hilbert-space representations of the field-qua drature amplitude, using balanced homodyne detection, and then using t omography to obtain the Wigner function. Once the Wigner function is o btained, one can acquire the density matrix, including its complex pha se. In the case of a pure state, this technique yields an experimental ly determined complex wavefunction, as demonstrated here for the vacuu m. The density matrix represents a complete quantum mechanical charact erization of the state. From the measured density matrix we have obtai ned the Pegg-Barnett optical phase distribution, and from the Wigner f unction, the Wigner optical phase distribution.