Observation of quantum entanglement between free electrons and photons (2504.13047v1)

Abstract: Quantum entanglement is central to both the foundations of quantum mechanics and the development of new technologies in information processing, communication, and sensing. Entanglement has been realised in a variety of physical systems, spanning atoms, ions, photons, collective excitations, and hybrid combinations of particles. Remarkably, however, photons and free electrons -- the quanta of light and their most elementary sources -- have never been observed in an entangled state. Here, we demonstrate quantum entanglement between free electrons and photons. We show that entanglement is produced when an electron, prepared in a superposition of two beams, passes a nanostructure and generates transition radiation in a polarisation state tied to the electron path. By implementing quantum state tomography, we reconstruct the full density matrix of the electron-photon pair, and show that the Peres-Horodecki separability criterion is violated by more than 7 standard deviations. Based on this foundational element of emerging free-electron quantum optics, we anticipate manifold developments in enhanced electron imaging and spectroscopy beyond the standard quantum limit. More broadly, the ability to generate and measure entanglement opens electron microscopy to previously inaccessible quantum observables and correlations in solids and nanostructures.

Observation of Quantum Entanglement Between Free Electrons and Photons

The paper "Observation of quantum entanglement between free electrons and photons" presents a significant advancement in the paper of quantum mechanics by demonstrating, for the first time, quantum entanglement between free electrons and photons. This novel achievement represents an intersection of quantum optics and electron microscopy, offering new avenues for understanding electron-photon interactions in nanostructures.

Experimental Approach and Findings

The research utilizes a transmission electron microscope (TEM) to achieve coherent splitting of an electron beam through the use of an amplitude grating. By configuring the TEM setup to prepare electrons in a superposition of two beams and directing these beams at nanostructures, the paper successfully generates transition radiation. The radiation exhibits polarization states that are contingent upon the electron's path. Photon polarizations from distinct electron paths are collected, allowing the researchers to reconstruct the joint electron-photon density matrix through quantum state tomography.

The violation of the Peres-Horodecki separability criterion by over 7 standard deviations unequivocally confirms the presence of entanglement between the free electrons and photons. Crucially, the reported fidelity with respect to Bell states exceeds 0.5 by 5 standard deviations, evidencing robust quantum entanglement.

Theoretical Implications

The paper's findings expand the palette of entangled systems to include freely moving electrons, traditionally considered in correlation with bound states such as those in atoms and solid-state structures. This serves as a foundational step in the burgeoning field of free-electron quantum optics, wherein the manipulation of electron beams based on quantum principles can lead to enhanced imaging techniques surpassing standard quantum limits.

Practical Implications

From a practical standpoint, the ability to entangle free electrons with photons enables the exploration of quantum-enhanced electron imaging and spectroscopy techniques, which promise reductions in radiation damage and enhanced sensitivity. The realization of entanglement in electron microscopy is poised to bridge the gap between quantum technologies and traditional imaging applications, thereby facilitating a new class of quantum-mechanical electron probes.

Future Directions

The demonstrated technique opens numerous potential research pathways, including the generation of multipartite entangled states and the exploration of various quantum states by extending measurements to different photonic degrees of freedom such as momentum and angular momentum. Moreover, it sets the stage for developing quantum-enhanced microscopy methods, possibly paving the way toward quantum electron microscopes capable of accessing previously elusive quantum observables in solid-state physics.

Conclusion

By achieving quantum entanglement between free electrons and photons, this paper not only marks a milestone in fundamental quantum physics but also lays the groundwork for integrating quantum computing techniques into electron microscopy. The results present compelling opportunities for further research into the quantum behavior of electron-photon pairs and the development of innovative imaging methodologies that leverage quantum principles.