Noise and decoherence induced by gravitons

We study quantum noise and decoherence induced by gravitons. We derive a Langevin equation of geodesic deviation in the presence of gravitons. The amplitude of noise correlations tells us that large squeezing is necessary to detect the noise. We also consider the decoherence of spatial superpositions of two massive particles caused by gravitons in the vacuum state and find that gravitons could give a relevant contribution to the decoherence. The decoherence induced by gravitons would offer new vistas to test quantum gravity in tabletop experiments.

Figure 1

Two neighboring timelike geodesics (${\gamma }_{\tau },{\gamma }_{{\tau }^{\prime }}$) separated by ${\xi }^i$ are depicted in the blue lines and the green lines show two neighboring spacelike geodesics (${\gamma }_s,{\gamma }_{s^{\prime }}$) orthogonal to the geodesic ${\gamma }_{\tau }$ in the spacelike hypersurface ${\mathrm{\Sigma }}_s$. We introduce the Fermi normal coordinate system using the orthogonal geodesics at the point $P(0,t)$.

Figure 2

Timelike curves of two massive particles ${\gamma }_{\tau }$ and ${\gamma }_{{\tau }^{\prime }}$, and the ${\gamma }_{{\tau }^{\prime }}$ is in a superposition state of two spatially separated locations ${\xi }_1(t)$ and ${\xi }_2(t)$. The superposition state survives ${\xi }_1(t)\ne {\xi }_2(t)$ for the duration $0<t<t_{\mathrm{f}}$.

Figure 3

The schematic diagram of the configuration of the superposition state given in Eq. (4.5). The trajectory at $x^i={\xi }^i$ is spatially superposed across the distance $\mathrm{\Delta }\xi (t)$ for the duration $0<t<t_{\mathrm{f}}$. The superposition state consists of the dotted red and green lines. The averaged trajectory of the two dotted lines $\xi$ is time independent.

Figure 4

A plot of $G(x)$. $G(x)$ grows polynomially for $x\ll 1$ and then oscillatory behavior converges to order unity for $x\gtrsim 10$.

Figure 5

The separation of the configuration of the superposition state as a function of time. The blue solid line indicates the configuration given in Eq. (4.12). The configuration of Eq. (4.5) repeats $N$ times as time evolves. The duration of the superposition state is $T_{\mathrm{s}}$ and each configuration repeats in particular time interval $T_{\mathrm{c}}$.

Figure 6

The schematic diagram of each trajectory of a charged particle. The superposition state survives for $0<t<t_{\mathrm{f}}$.

Figure 7

The diagram which contributes to $\mathrm{\Gamma }$. Two blobs are the external sources which are given by the difference of external current densities. External sources are connected by the wavy internal line which is the symmetric propagator of photons.