Temporal and spectral properties of quantum light

TL;DR

This paper reviews the transition from classical to quantum optics, focusing on electromagnetic modes, their quantization, and quantum properties such as correlations and Gaussian states, providing a comprehensive overview of the field.

Contribution

It offers a unified approach to classical and quantum optics, emphasizing mode quantization, quantum correlations, and Gaussian states, with insights into multi-mode interactions and phase conjugation.

Findings

Classical spectral densities are measured and interpreted.

Quantum properties of single modes, especially Gaussian states, are characterized.

A unifying framework for multi-mode quadratic Hamiltonians is presented.

Abstract

The modes of the electromagnetic field are solutions of Maxwell's equations taking into account the material boundary conditions. The field modes of classical optics - properly normalized - are also the mode functions of quantum optics. Quantum physics adds that the excitation within each mode is quantized in close analogy to the harmonic oscillator. A complete set of mode functions forms a basis with which any new modes can be reconstructed. In full generality each electromagnetic mode function in the four dimensional space-time is mathematically equivalent to a harmonic oscillator. The quantization of the electromagnetic field defines the excitation per mode and the correlation between modes. In classical optics there can be oscillations and stochastic fluctuations of amplitude, phase, polarization et cetera. In quantum optics there are in addition uncertain quantum field components, quantum correlations and quantized energies. Here, we present selected topics from classical to quantum optics. We start in the second chapter with the classical optics description of a light field and its spectral densities, their measurement and their interpretation. In the third chapter the quantum properties of a single light mode are reviewed as well as ways to measure these quantum properties. Gaussian states of a light mode are emphasized, i. e. states for which the Wigner function has a two dimensional Gaussian shape. The fourth chapter will be concerned with more than one mode presenting a unifying approach to quadratic Hamiltonians including phase conjugation which is related to time reversal.