Tabletop Creation of Entangled Multi-keV Photon Pairs and the Unruh Effect

Electrons moving in a strong periodic electromagnetic field (e.g., laser or undulator) may convert quantum vacuum fluctuations into pairs of entangled photons, which can be understood in terms of the Unruh effect. Apart from verifying this striking phenomenon, the considered effect may allow the construction of a tabletop source for entangled photons (“photon pair laser”) and the associated quantum-optics applications in the multi-keV regime with near-future facilities.

Figure 1

$E\mathrm{\text{−}}\vartheta$ plot of the one-photon probability of classical (Larmor, left half of image) and quantum (Unruh, right) radiation in the laboratory frame (averaged over rotations around beam axis). An electron with a boost factor of $\gamma =300$ hits a counterpropagating optical Gaussian laser pulse with an intensity of ${10}^{18}\mathrm{W}/{\mathrm{cm}}^2$ and a width of 100 cycles. The photon energy $E$ ranges from zero (bottom) to 2 MeV (top) and $\vartheta$ varies from zero (middle) to $1/100$ (left and right boundary). In the chosen color coding (not the same in the two images), red indicates a large and dark blue a vanishing probability. The black isolines denote the same values in both pictures and show that the quantum radiation dominates in certain phase-space regions (which could be extracted with apertures and energy filters). As one may infer from the visibility of the second harmonic, relativistic effects already start to play a role for this set of parameters (${\dot{\mathit{r}}}_{\mathrm{cl}}^2\approx 1/9$). Therefore, we numerically calculated the full electron trajectory (including the impact of the magnetic field) and inserted it into Eqs. (6, 7, 10), respectively.