Homodyne statistics

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Abstract
It is usually assumed that a balanced homodyne detector measures a variable called the quadrature phase amplitude of a signal field. We examine this assumption by obtaining analytic expressions for the probability statistics for the output of such a detector for a single-mode signal with both signal and local oscillator treated quantum mechanically. We investigate the conditions under which the statistics of the quadrature phase are reproduced in the actual output of the detector. We show that the most obvious condition—that the number of quanta in the local oscillator be much larger than the number in the signal—is not sufficient to ensure that a balanced homodyne detector acts like an ideal detector of quadrature phases. Furthermore, we obtain the explicit conditions that are necessary and sufficient to reproduce the interference features in the homodyne statistics of a superposition of coherent states. DOI: http://dx.doi.org/10.1103/PhysRevA.42.474 © 1990 The American Physical Society