RECONSTRUCTION OF THE QUANTUM STATE OF MULTIMODE LIGHT

Phase-controlled homodyne 2(N+R)-port detection with R local oscillators is analyzed with the aim of reconstructing the quantum state of a correlated N-mode signal field. It is shown that both the (N+R)-fold joint count distributions and the N-fold joint difference-count distributions contain all knowable information on the state of the field. In any case, the minimum number of local oscillators is given by the number of different signal-field frequencies. Two Fourier integrals per mode are found to be required to reconstruct the density matrix of the signal field from the joint difference-count distributions measured in balanced homodyning. To illustrate the theory, it is applied to balanced homodyne 4N-port detection (R=N). In this scheme, the joint difference-count distributions directly yield the joint field-strength distributions of a correlated N-mode signal field. © 1995 The American Physical Society.