Loss of coherence and dressing in QED

The dynamics of a free charged particle, initially described by a coherent wave packet, interacting with an environment, i.e., the electromagnetic field characterized by a temperature $T$, is studied. Using the dipole approximation, the exact expressions for the evolution of the reduced density matrix both in momentum and configuration space and the vacuum and the thermal contribution to decoherence are obtained. The time behavior of the coherence lengths in the two representations are given. Through the analysis of the dynamic of the field structure associated with the particle the vacuum contribution is shown to be linked to the birth of correlations between the single momentum components of the particle wave packet and the virtual photons of the dressing cloud.

Figure 1

(Color online) ${\Gamma }_{\mathrm{vac}}^{p,p^{\prime }}\left(t\right)$ and ${\Gamma }_{\mathrm{th}}^{p,p^{\prime }}\left(t\right)$ as a function of $\zeta =2\alpha (\mathit{p}-{\mathit{p}}^{\prime }{)}^2∕3\pi m_0^2{c}^2$, in the case $T=300\mathrm{K}$.

Figure 2

(Color online) Time development of $\exp [-{\Gamma }_{\mathrm{vac}}^{p,p^{\prime }}(t\left)\right]$ (20) as a function of the coupling constant $\alpha =e^2∕\hslash c$ in the case $\mid \mathit{p}-{\mathit{p}}^{\prime }\mid ∕m_{0}c=0.1$. The time is taken in units of $t\Omega$ and the range of $\alpha$ is chosen to visualize the vacuum effect on the decoherence.

Figure 3

(Color online) Absolute value of the normalized density matrix $Z=\mid {\rho }_S^{p_x,p_x^{\prime }}\left(t\right)\mid ∕N_x$ in one dimension, $N_x=1∕\sqrt{2\pi }\mathrm{\Delta }{p}_x$, with $p_0=0$ and $\mathrm{\Delta }{p}_x∕m_{0}c\approx 0.1$. On the top it is $t=0$ while on the bottom it is $t=3{\tau }_{\mathrm{vac}}$, where ${\tau }_{\mathrm{vac}}$ is taken for $p_x-p_x^{\prime }=\mathrm{\Delta }{p}_x$.

Figure 4

(Color online) Behavior of $S_{\mathrm{lin}}$ in time as a function of $\alpha$.