Photon State Evolution in Arbitrary Time-Varying Media

TL;DR

This paper presents an instantaneous eigenstate method to analyze quantum photon state evolution in media with arbitrary time-dependent properties, simplifying calculations and enabling precise control of photon states.

Contribution

The paper introduces a novel instantaneous eigenstate approach that simplifies quantum state evolution analysis in time-varying media, bypassing complex Schrödinger equations.

Findings

Maximum single photon pair generation probability is 25%.

Bell states can be generated with up to 84% probability.

Spectral profiles of emitted photons can be precisely controlled.

Abstract

We introduce the instantaneous eigenstate method to study the evolution of quantum states in media with arbitrary time-varying permittivity and permeability. This method leverages the Heisenberg equation to bypass the Schr\"odinger equation, which leads to a complicated infinite set of coupled differential equations. Instead, the method allows the computation of the state evolution by solving only two coupled differential equations. Using this approach, we draw general conclusions about photon statistics in time-varying media. Our findings reveal that the maximum probability of generating a single photon pair from vacuum in such media is 25%, while Bell states can be created with a maximum probability of 84%. Additionally, we demonstrate that the spectral profile of emitted photons can be precisely controlled through the temporal profiles of permittivity and permeability. These results provide deeper insights into photon state manipulation in time-varying media. Furthermore, the instantaneous eigenstate method opens new opportunities to study state evolution in other systems where the Heisenberg equation offers a more tractable solution than the Schr\"odinger equation.