Photon number conservation in time dependent systems

TL;DR

This paper demonstrates that photon number conservation can occur in time-dependent systems with parity-time symmetry, even when energy conservation is broken, revealing new insights into photon amplification mechanisms.

Contribution

It shows that photon number conservation is more broadly applicable than energy conservation in certain time-dependent systems with parity-time symmetry.

Findings

Photon number conservation can hold despite energy non-conservation.

Photon amplification involves photons climbing a frequency ladder.

Parity-time symmetry enables photon conservation in non-static systems.

Abstract

Time dependent systems in general do not conserve photons nor do they conserve energy. However when parity time symmetry holds Maxwells equations can sometimes both conserve photon number and energy. Here we show that photon conservation is the more widely applicable law which can hold in circumstances where energy conservation is violated shedding further light on an amplification mechanism identified in previous papers as a process of conserved photons climbing a frequency ladder.