Analysis of light-wave nonstaticity in the coherent state

TL;DR

This paper investigates the nonstatic properties of light waves in a coherent state, revealing periodic shape variations, energy conservation, and phase space rotation effects, which deepen understanding of quantum light wave dynamics.

Contribution

It provides a detailed analysis of nonstatic quantum light waves in coherent states, highlighting their periodic shape changes and phase space behavior, which were not previously characterized.

Findings

Wave shape varies periodically with belly and node features.

Total energy remains conserved despite shape changes.

Quadrature fluctuations and uncertainty products vary periodically.

Abstract

The characteristics of nonstatic quantum light waves in the coherent state in a static environment is investigated. It is shown that the shape of the wave varies periodically as a manifestation of its peculiar properties of nonstaticity like the case of the Fock-state analysis for a nonstatic wave. A belly occurs in the graphic of wave evolution whenever the wave is maximally displaced in the quadrature space, whereas a node takes place every time the wave passes the equilibrium point during its oscillation. In this way, a belly and a node appear in turn successively. Whereas this change of wave profile is accompanied by the periodic variation of electric and magnetic energies, the total energy is conserved. The fluctuations of quadratures also vary in a regular manner according to the wave transformation in time. While the resultant time-varying uncertainty product is always larger than (or, at least, equal to) its quantum-mechanically allowed minimal value ($\hbar/2$), it is smallest whenever the wave constitutes a belly or a node. The mechanism underlying the abnormal features of nonstatic light waves demonstrated here can be interpreted by the rotation of the squeezed-shape contour of the Wigner distribution function in phase space.