Abstract
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.
- Received 14 November 1994
DOI:https://doi.org/10.1103/PhysRevA.51.4240
©1995 American Physical Society