Clarifying nonstatic-quantum-wave behavior through extending its analysis to the p-quadrature space: Interrelation between the q- and p-space wave-nonstaticities

TL;DR

This paper investigates nonstatic quantum light waves in static environments by analyzing their behavior in both q- and p-spaces, revealing a reciprocal intensity exchange phenomenon due to wave nonstaticity.

Contribution

It extends the analysis of nonstatic quantum waves to the p-quadrature space, uncovering their interrelation and reciprocal intensity exchange in static environments.

Findings

Periodic evolution of probability densities in p- and q-spaces

Opposite phase relationship between q- and p-space wave phases

Identification of a reciprocal optical phenomenon due to wave nonstaticity

Abstract

If electromagnetic parameters of a medium vary in time, quantum light waves traveling in it become nonstatic. A recent report shows that such nonstatic waves can also appear even when the environment is static where the parameters of the medium do not vary. In this work, the properties of nonstatic waves in a static environment are investigated from their $p$-space analysis, focusing on the interrelation between the $q$- and $p$-space nonstatic waves. The probability densities in $p$-space (as well as in $q$-space) for both the nostatic Fock and Gaussian states evolve in a periodic manner, i.e., they constitute belly and node in turn successively as time goes by. If we neglect the displacement of waves, the $q$- and $p$-space wave phases are opposite each other. Since the intensity of the wave in each space is relatively large whenever the wave forms a belly, such a phase difference indicates that periodical intensity exchange between the $q$- and $p$-component waves takes place through their nonstatic evolutions. This is the novel reciprocal optical phenomenon arisen on account of the wave nonstaticity.