Abstract

One of the important achievements in modern quantum optics is the development of the technique of optical homodyne tomography and its application to the reconstruction of quantum states of light.¹ Recently it was shown that by using optical homodyne detectors, one can directly sample the density matrix, and a simple procedure was outlined to obtain the photon-number distribution of light (diagonal elements of the density matrix).² This approach has allowed one to measure the photon statistics of very weak light signals, which otherwise would not be possible by use of direct detection.³ However, for quantum state reconstruction of non-classical light with a large average photon number, the requirement on the quantum efficiency of detection is extremely severe. Interesting, quantum features wash out very rapidly with degradation of the quantum efficiency from unity. The requirement applies not only to the photodetector efficiency, but also to homodyne efficiency, which is given by the overlap integral of the signal and local oscillator (LO) modes. To achieve an acceptable level of homodyne efficiency, one has to carefully match the LO and the signal modes. In the case of a nondegenerate optical parametric amplifier (NOPA), such a matched LO can be obtained from the same parametric process as the signal.⁴ With type-II phase matching, for example, a light beam injected with polarization at +45°, to excite the e- and 0- waves equally, can be utilized as a matched LO for the detection of squeezed vacuum in the −45° polarization direction.⁴

© 1997 Optical Society of America