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Einstein, Podolsky and Rosen's prediction on incompleteness of quantummechanics was overturned by experimental tests on Bell's inequality thatconfirmed the existence of quantum entanglement. In X-ray optics, entangledphoton pairs can be generated by X-ray parametric down conversion (XPDC), whichhas certain wavelength window. Meanwhile, free electron laser (FEL) hassuccessfully lased at X-ray frequencies recently. However, FEL is usually seenas a classical light source, and its quantum effects are considered minorcorrections to the classical theory. Here we investigate entangled X-ray photonpair emissions in FEL. We establish a theory for coherently amplified entangledphoton pair emission from microbunched electron pulses in the undulator. Wenumerically demonstrate the properties of entangled emission, and provide ascheme to generate highly entangled X-ray photon pairs, which is of greatimportance in X-ray quantum optics. Our work shows a unique advantage of FELsover synchrotrons in entangled X-ray photon pair generation.

Entangled X-ray Photon Pair Generation by Free Electron Lasers