Model for lightcone fluctuations due to stress tensor fluctuations

We study a model for quantum lightcone fluctuations in which vacuum fluctuations of the electric field and of the squared electric field in a nonlinear dielectric material produce variations in the flight times of probe pulses. When this material has a nonzero third order polarizability, the flight time variations arise from squared electric field fluctuations, and are analogous to effects expected when the stress tensor of a quantized field drives passive spacetime geometry fluctuations. We also discuss the dependence of the squared electric field fluctuations upon the geometry of the material, which in turn determines a sampling function for averaging the squared electric field along the path of the pulse. This allows us to estimate the probability of especially large fluctuations, which is a measure of the probability distribution for quantum stress tensor fluctuations.

Figure 1

The switching function $F_{b,d}(x)$.

Figure 2

Modulus of the Fourier transform of $F_{b,d}(x)$ is illustrated. Specifically, the function $g(z)=\sqrt{\pi /2}|{\widehat{F}}_{b,d}(k)|/d$ is plotted as a function of $z=kd$ for the case $b=0.01$.