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arXiv:2010.05790 · Physica A Statistical Mechanics and its Applications

Quantum distributions for the electromagnetic field

M. Grigorescu

Published Jul 29, 2021• 1 citation
arXivHTMLPDF
DOI
10.1016/j.physa.2021.126278

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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.
The gauge invariance of the evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field is illustrated. Explicit expressions for the transformations of ordinary tomograms of states under a gauge transformation of electromagnetic field potentials are obtained. Gauge-independent optical and symplectic tomographic quasi-distributions and tomographic probability distributions of states of quantum system are introduced, and their evolution equations having the Liouville equation in corresponding representations as the classical limit are found.