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Description
When two or more quantum particles in a many-body system are entangled, its wavefunction cannot be factorized as a product of the wavefunctions of its constituents. It has been central to the ongoing second quantum revolution, as seen in the rapid development of the quantum information science. Initially, the idea of entanglement was dismissed by Albert Einstein himself as the 'spooky' action-at-a-distance. However, as it turned out, the photoelectric effect itself presents a unique opportunity to study the quantum entanglement between the emitted photoelectron and the residual ion – measurement of the kinetic energy of the former determines the exact quantum state of the later. Here, using intense extreme ultraviolet (XUV) pulses from a seeded free-electron laser, FERMI [1], we generate quantum entanglement between a photoelectron wave-packet rapidly expanding in space and a hybrid light-matter system, namely, a He+ ion dressed with an XUV photon. In the presence of the entanglement between these two massive particles, the measured photoelectron spectra clearly show an avoided crossing reminiscent of the Rabi cycling in the XUV-dressed residual ion [2]. In the absence of entanglement, however, the measured kinetic energies of the photoelectrons increase monotonically with increase in the photon energy, as predicted by Einstein’s photoelectric equation. We show that even if the photoelectron wave-packet expands up to a mesoscopic distance of almost 200 nm [3], it still remains entangled to the residual ion. Our results offer opportunities to explore quantum entanglement across ultrafast timescales over macroscopic distances.
References:
[1] E. Allaria et al., Highly coherent and stable pulses from the FERMI seeded free-electron laser in the extreme ultraviolet. Nature Photonics 6, 699 (2012).
[2] S. Nandi et al., Observation of Rabi dynamics with a short-wavelength free-electron laser. Nature 608, 488 (2022).
[3] S. Nandi et al., Generation of entanglement using a short-wavelength seeded free-electron. Science Advances 10, eado0668 (2024).
