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Physica A Statistical Mechanics and its Applications

Interference effects on the quasi-probability distributions of the electromagnetic field

Arthur M. Moraes, Marta João Francisco Silva Souza, CELIA M. A. DANTAS

Published Mar 1, 2001• 2 citations
Publisher
DOI
10.1016/s0378-4371(00)00530-6

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Based on the first principles of quantum mechanic the density of probability distribution function W(x,p) is created for quantum electromagnetic field (QEF) - Figs. 1, 2. Unlike a well-known distributions of density of quasi-probability (as Wigner function et.c.) W(x,p) can be measured directly in 8-port homodyne experiment or in the experiment we propose. Using W(x,p) one can calculate the probability to have the field quadratures x and p in a chosen area of a phase space, find the minimum in amplitude or phase fluctuations of QEF. W(x,p) predicts the lemniscate-of-ellipse shape of the dispersion of squeezed QEF (Loudon, 1989; Kimble, 1986). Using a methods of quantum optic in experimental study of W(x,p) one can reconstruct the wave function of QEF and, in principle, the wave function of an emitting substance.
We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the observables of interest and their time-evolution. Nevertheless, positive probability distributions for measurement outcomes can be obtained from the KQPD by taking into account the effect of measurement back-action and imprecision. Negativity in the KQPD can be linked to an interference effect and acts as an indicator for non-classical behavior. Notable examples of the KQPD are the Wigner function and the full counting statistics, both of which have been used extensively to describe systems in the absence as well as in the presence of a measurement apparatus. Here we discuss the KQPD and its moments in detail and connect it to various time-dependent problems including weak values, fluctuating work, and Leggett-Garg inequalities. Our results are illustrated using the simple example of two subsequent, non-commuting spin measurements.