Third order nonlinear correlation of the electromagnetic vacuum at near-infrared frequencies

TL;DR

This paper investigates how third-order nonlinear effects, specifically four-wave mixing, influence electro-optic sampling measurements of quantum electromagnetic states at near-infrared frequencies, revealing new nonlinear correlation phenomena.

Contribution

It demonstrates experimentally and theoretically that third-order nonlinear mixing affects electro-optic sampling and quantum correlation measurements at near-infrared frequencies.

Findings

Identification of third-order nonlinear effects in electro-optic sampling.

Experimental evidence of four-wave mixing with the electromagnetic vacuum.

Conditions where nonlinear correlation dominates over traditional electro-optic correlation.

Abstract

In recent years, electro-optic sampling, which is based on Pockel's effect between an electromagnetic mode and a copropagating, phase-matched ultrashort probe, has been largely used for the investigation of broadband quantum states of light, especially in the mid-infrared and terahertz frequency range. The use of two mutually delayed femtosecond pulses at near-infrared frequencies allows the measurement of quantum electromagnetic radiation in different space-time points. Their correlation allows therefore direct access to the spectral content of a broadband quantum state at terahertz frequencies after Fourier transformation. In this work, we will prove experimentally and theoretically that when using strongly focused coherent ultrashort probes, the electro-optic sampling technique can be affected by the presence of a third-order nonlinear mixing of the probes' electric field at near-infrared frequencies. Moreover, we will show that these third-order nonlinear phenomena can also influence correlation measurements of the quantum electromagnetic radiation. We will prove that the four-wave mixing of the coherent probes' electric field with their own electromagnetic vacuum at near-infrared frequencies results in the generation of a higher-order nonlinear correlation term. The latter will be characterized experimentally, proving its local nature requiring the physical overlap of the two probes. The parameters regime where higher order nonlinear correlation results predominant with respect to electro-optic correlation of terahertz radiation is provided.