The narrowband coupling of free electrons with ultrahigh-Q photonic cavity modes


  Ofer Kfir  ,  Jan-Wilke Henke [2,3]  ,  Arslan Sajid Raja [4,5]  ,  Armin Feist [2,3]  ,  Guanhao Huang [4,5]  ,  Germaine Arend [2,3]  ,  Yujia Yang [4,5]  ,  F. Jasmin Kappert [2,3]  ,  Rui Ning Wang [4,5]  ,  Marcel Möller [2,3]  ,  Jiahe Pan [4,5]  ,  Junqiu Liu [4,5]  ,  Claus Ropers [2,3]  ,  Tobias J. Kippenberg [4,5]  
[1] Tel Aviv University, Tel Aviv, Israel
[2] University of Goettingen, Goettingen, Germany
[3] Max Planck Institute of Multidisciplinary Sciences, Goettingen, Germany
[4] Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
[5] Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland

Free electrons emerge as a novel type of experimentally accessible quantum system, in which continuous degrees of freedom such as the electron momentum and spatial structure can be photonically manipulated with extreme nonlinearity and at room temperature.

Motivated by the seminal experimental contribution of photonic cavities with ultrahigh quality factor (ultrahigh-Q) to optical cavity quantum electrodynamics [1], this work [2] introduces integrated silicon photonics into the realm of electron-photon coupling. The integrated photonics system lowered the required photon flux for free-electron manipulation nine orders of magnitude compared with previous experiments and increased the accuracy of electron spectroscopy a thousand-fold.

In this experiment, the electrons were delivered and manipulated within a transmission electron microscope (TEM) operated in a low magnification mode to enable a parallel electron beam. The beam grazed the top surface of a silicon-photonic chip, comprising ultrahigh-Q of silicon nitride critically coupled to a fiber-coupled bus waveguide. Single electrons within a continuous beam accelerated to 115 keV (58% the speed of light, separated by ~3 nanoseconds) matched the phase velocity of the cavity mode, thus exchanging a few photons with a cavity pumped by four microwatts, and reached hundreds of energy-exchange orders under milliwatt pumping. Furthermore, the relativistic electron velocity interacts selectively with the co-propagating cavity mode, thus probing it independently of its degenerate counter-propagating mode.

The demonstrated capability for electron-photon interactions within electron microscopes with continuous beam [2,3] offer two paradigm shifts: first, the manipulated wavefunction of the electron may be combined with the atomic resolution imaging of electron microscope for targeting individual quantum systems, and second, the low-light required for such manipulation paves the way toward entanglement between electrons and photons, or mediate the entanglement of two free electrons [4].

[1]         T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Observation of Strong Coupling between One Atom and a Monolithic Microresonator, Nature 443, 671 (2006).

[2]          J.-W. Henke, A. S. Raja, A. Feist, G. Huang, G. Arend, Y. Yang, F. J. Kappert, R. N. Wang, M. Möller, J. Pan, J. Liu, O. Kfir, C. Ropers, and T. J. Kippenberg, Integrated Photonics Enables Continuous-Beam Electron Phase Modulation, Nature 600, 653 (2021).

[3]          R. Dahan, A. Gorlach, U. Haeusler, A. Karnieli, O. Eyal, P. Yousefi, M. Segev, A. Arie, G. Eisenstein, P. Hommelhoff, and I. Kaminer, Imprinting the Quantum Statistics of Photons on Free Electrons, Science 373, (2021).

[4]          O. Kfir, Entanglements of Electrons and Cavity Photons in the Strong-Coupling Regime, Phys. Rev. Lett. 123, 103602 (2019).