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Physical Review A

Phase and homodyne statistics of generalized squeezed states

Samuel L. Braunstein, Carlton M. Caves

Published Oct 1, 1990• 47 citations
Publisher

Abstract

We study the statistics of direct, heterodyne, and homodyne detection for some generalized squeezed states. The heterodyne statistics yield ``classical'' phase statistics, which give a clear picture of the phase-sensitive noise of these generalized squeezed states. The homodyne statistics display quantum-mechanical interference effects that are not present for ordinary squeezed states.

DOI
10.1103/physreva.42.4115

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We study the statistics of direct, heterodyne, and homodyne detection for some generalized squeezed states. The heterodyne statistics yield ``classical'' phase statistics, which give a clear picture of the phase-sensitive noise of these generalized squeezed states. The homodyne statistics display quantum-mechanical interference effects that are not present for ordinary squeezed states.
We study the statistics of direct, heterodyne, and homodyne detection for generalized squeezed states generated by three-model interaction Hamiltonians. One model interaction generates correlated triplets of photons, and the other two generate correlated quadruplets. The heterodyne statistics are described by an essentially classical phase-space distribution, the quantum Q function. From the Q functions we derive classical probability distributions for phase, which display phase-sensitive noise with three or four peaks for the three- and four-photon interactions, respectively. The homodyne statistics display quantum-mechanical interference fringes, which are not present for ordinary squeezed states. We provide a simple qualitative picture that relates the shape of the Q function to the interference features seen in the homodyne statistics. This picture allows us to explain all the gross features of the homodyne statistics for these models.
We use our interpretation of homodyne and heterodyne detection of squeezed states, viz., quantum correlation between photons as expressed in second-order correlation functions, to study various cases. In particular, we introduce the coherence time of the local oscillator and show its influence on the possible noise reduction. We also study the case in which the local oscillator is not much stronger than the squeezed state and analyze the influence of phase jitter. This approach could explain some experimental results and suggest improvements in detection schemes.
The double-homodyne and the heterodyne detection schemes for phase shifts between two synchronous modes of the electromagnetic field are analyzed in the framework of quantum estimation theory. The probability operator-valued measures (POM's) of the detectors are evaluated and compared with the ideal one in the limit of strong local reference oscillator. The present operational approach leads to a reasonable definition of phase measurement, whose sensitivity is actually related to the output r.m.s. noise of the photodetector. We emphasize that the simple-homodyne scheme does not correspond to a proper phase-shift measurements as it is just a zero-point detector. The sensitivity of all detection schemes are optimized at fixed energy with respect to the input state of radiation. It is shown that the optimal sensitivity can be actually achieved using suited squeezed states.