Imprinting the quantum statistics of photons on free electrons

Raphael Dahan^a, Alexey Gorlach^a, Urs Haeusler^b^,^c, Aviv Karnieli^a^,^d, Ori Eyal^a, Peyman Yousefi^b, Mordechai Segev^a^,^e, Ady Arie^f, Gadi Eisenstein^a, Peter Hommelhoff^b, Ido Kaminer^a

^aDepartment of Electrical Engineering, Russell Berrie Nanotechnology Institute, and Solid-State Institute, Technion– Israel Institute of Technology, Haifa, Israel

^bDepartment of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 1, Erlangen, Germany

^cCavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, United Kingdom

^dRaymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel-Aviv, Israel

^eDepartment of Physics, Technion – Israel Institute of Technology, Haifa, Israel

^fSchool of Electrical Engineering, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv , Israel, Tel-Aviv, Israel

Proceedings of Electron Beam Spectroscopy for Nanooptics 2021 (EBSN2021)

Online, Spain, 2021 June 14th - 15th

Organizers: Mathieu Kociak and Nahid Talebi

Oral, Raphael Dahan, presentation 032
Publication date: 8th June 2021

Recent theoretical works on the interaction of free electrons with light[1],[2] predicted how the interaction is altered by the quantum properties of light, leading to new exciting application such as electron-electron entanglement[2], new types of quantum light source[3], novel ideas for electron shaping[4], and quantum state tomography of light[5]. Yet, to this day – in all experiments involving the interaction between free electrons and light – the light acted as a classical wave, disregarding its quantum nature.

We observe the effect of the quantum statistics of photons on free-electron interactions with light. Our study shows interactions for different statistics passing continuously from Poissonian up to thermal statistics, unveiling a surprising manifestation of Bohr's Correspondence Principle: the continuous transition from quantum walk[6],[7] to classical random walk of a free electron on the energy ladder. The electron walker serves as the probe in non-destructive quantum detection experiments, measuring the photon statistics as well as degrees of coherence g2(0) and higher-orders gn(0). Unlike conventional quantum-optical detectors, the electron can perform both quantum weak measurements[8] and projective measurements of light by evolving into an entangled joint-state with the photons.

We achieve this free-electron–quantum-light interaction using the inverse design of silicon-photonic nanostructures recently used for miniaturizing particle accelerators[10]. We use these nanostructures in a transmission electron microscope (TEM) to facilitate a strong free-electron–light interaction, i.e., each electron exchanges multiple photons with the light field. Such strong interactions were previously only realized with intense laser pulses in photon-induced nearfield electron microscopy (PINEM). In contrast with such intense pulses that can be considered as coherent states, all other states of light are usually not so intense – necessitating an optimized interaction in specialized nanostructures.

The interaction efficiency is high enough to enable the use of continuous-wave (CW) light, while still maintaining the strong interaction. Recent experimental works have shown that even weak CW electron–light interactions (up to one photon absorbed/emitted by the electron) have intriguing applications[10],[11] Our experiment offers an avenue for taking these ideas forward to regimes of stronger interactions with CW light. Our findings suggest hitherto inaccessible concepts in quantum optics: free-electron-based non-destructive quantum tomography of light, even with ultrafast modulation of the photon statistics or the field quadratures[5]. The study of high-efficiency electron–light coupling constitutes an important step towards combined attosecond-temporal and sub-Å-spatial resolution microscopy.

References:

[1] Kfir, O. Entanglements of Electrons and Cavity Photons in the Strong-Coupling Regime. Physical Review Letters 123, 103602 (2019).

[2] Di Giulio, V., Kociak, M. & de Abajo, F. J. G. Probing quantum optical excitations with fast electrons. Optica 6, 1524–1534 (2019).

[3] Ben Hayun, A. et al. Shaping quantum photonic states using free electrons. Science Advances 7, 4270–4280 (2021).

[4] Giulio, V. di & de Abajo, F. J. G. Free-Electron Shaping Using Quantum Light. Optica 7, 1820–1830 (2020).

[5] Gorlach, A. et al. Ultrafast non-destructive measurement of the quantum state of light using free electrons. arXiv:2012.12069 (2020).

[6] Perets, H. B. et al. Realization of quantum walks with negligible decoherence in waveguide lattices. Physical Review Letters 100, 170506 (2008).

[7] Karski, M. et al. Quantum walk in position space with single optically trapped atoms. Science 325, 174–177 (2009).

[8] Aharonov, Y., Albert, D. Z. & Vaidman, L. How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351–1354 (1988).

[9] Sapra, N. V. et al. On-chip integrated laser-driven particle accelerator. Science 367, 79 (2020).

[10] Schwartz, O. et al. Laser phase plate for transmission electron microscopy. Nature Methods 16, 1016–1020 (2019).

[11] Ryabov, A., Thurner, J. W., Nabben, D., Tsarev, M. v. & Baum, P. Attosecond metrology in a continuous-beam transmission electron microscope. Science Advances 6, eabb1393 (2020).

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