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arXiv:0705.4385 · Physical Review Letters

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

Ralf Schützhold, Gernot Schaller, Dietrich Habs

Published Mar 3, 2008• 61 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.100.091301

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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.
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An accessible tabletop source for the production of entangled x rays is crucial for the field of high-energy quantum optics. Here, we present a detailed analysis of the entanglement and polarization of the two photons emitted by an electron in an intense laser wave (nonlinear double-Compton scattering), by working within the framework of strong-field QED. By identifying contributions to the emission probability stemming from the electron being either on-shell or off-shell between the two-photon emissions, we show that the entangled photons are generated via the off-shell contribution for moderate beam energies, which are realizable on a tabletop setup. We propose an experiment to produce and isolate pairs of entangled x rays, through spectral filtering.
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Entanglement plays crucial roles in quantum optics, providing a prerequisite for these recent unprecedented leaps. Nevertheless, the study of quantum entanglement under the influence of relativity, an important ingredient of quantum optics, still needs to be explored. In parallel, integrated photonic chips, particularly those with the aid of transformation optics, have simulated various relativity phenomena including gravitational lensing and Unruh radiation. However, thus far, studying relativistic quantum optics on this type of platform has not yet occurred. Here, we propose and experimentally realize quantum walks of entangled photons near an emulated Rindler horizon. Remarkably, we find that quantum interference near the synthetic horizon leads to a counterintuitive phenomenon of optical escape. Our study paves the way to a tabletop platform for studying quantum phenomena in various relativistic space-time metrics, and may bring an implication for the test of quantum theory in relativity. Published by the American Physical Society 2024
Spontaneous parametric down-conversion (SPDC) is a widely used method of creating correlated and entangled photon pairs, but its extension to the X-ray regime is very limited by the weak nonlinear response of conventional birefringent crystals, and by absorption and scattering of the high energy photons. This work investigates an alternative approach based on free-electron lasers (FELs), where a relativistic electron beam in an undulator acts as an effective nonlinear medium. A semiclassical model for FEL sub-harmonic generation is developed by introducing pump, signal, and idler radiation fields and deriving their coupled propagation equations directly from the electron equations of motion and Maxwell’s equations. The nonlinear interaction is shown to arise from collective phase matching of the ponderomotive phases, leading to three effective susceptibilities, one for each modal interaction to the electron beam, that replace the second-order nonlinear susceptibility of ordinary SPDC. Analytical expressions for the nonlinear beam currents and coupling coefficients are derived using the slowly varying envelope approximation (SVEA). The resulting coupled wave equations show the same modal relations as optical SPDC and predict exponential growth of vacuum-seeded signal and idler fields under near phase-matched conditions. Simplified scaling laws of the effective susceptibilities show that the interaction strength increases with undulator strength and decreases strongly with electron-beam energy, while efficient generation requires near resonant conditions for the signal and idler. By introducing stochastic vacuum fluctuations as initial conditions, the model can be derived semi-classically, connecting the FEL gain dynamics and spontaneous photon-pair generation. The results indicate that x-ray free-electron lasers may support spontaneous parametric down-conversion and could become an alternate more efficient source of correlated photons in the x-ray regime, with an exponential dependence on the pump amplitude, and without the limitations of the ineffective conventional nonlinear optical materials. The semi-classical model forms an understanding of the SPDC process and its dependence on the FEL dynamics, and a foundation for future fully quantum optical derivations in order to investigate photon statistics, coherence, and entanglement generation rigorously in FEL-based systems.