Imaging Quantum Coherence using Electron Wavepackets

Until recently, work in quantum optics focused on light interacting with <i>bound-electron</i> systems such as atoms, quantum dots, and nonlinear optical crystals. In contrast, <i>free-electron</i> systems enable fundamentally different physical phenomena, as their energy distribution is continuous and not discrete, allowing for tunable transitions and selection rules. Free electrons also enable unique capabilities in microscopy and spectroscopy that are otherwise inaccessible.<br/><br/>Recent theoretical and experimental breakthroughs involving quantum interactions of free electrons spawned an exciting new field: <i>free-electron quantum optics</i>. We developed a platform for exploring coherent free-electron interactions at the nanoscale, and used it to demonstrate the first coherent interaction of a free electron with quantum statistics of photons.<br/><br/>These capabilities open new paths toward using free electrons as carriers of quantum information. Concepts of quantum optics with free electrons also promote new modalities in electron microscopy. We recently demonstrated the first instance of coherent amplification in electron microscopy. Specifically, we present an algorithm-based microscopy approach that uses light-induced electron modulation to demonstrate the coherent amplification effect in electron imaging of optical near-fields. We provide a simultaneous time-, space-, and phase-resolved measurement in a microdrum made from a hexagonal boron nitride membrane, visualizing the sub-cycle dynamics of 2D polariton wavepackets therein. Our experiments show a 20-fold coherent amplification of the near-field signal compared to conventional electron near-field imaging, resolving peak field amplitudes of few kV/m.<br/><br/>Our vision is to develop a microscope that can image coherence, going beyond conventional imaging of matter to also <i>image the quantum state of matter</i> and probe quantum correlations between individual quantum systems.<br/><br/>-N. Rivera and I. Kaminer, Light–matter interactions with photonic quasiparticles, Nature Reviews Physics 2, 538–561 (2020) (Review)<br/>-K. Wang, R. Dahan, M. Shentcis, Y. Kauffmann, A. Ben-Hayun, O. Reinhardt, S. Tsesses, I. Kaminer, Coherent Interaction between Free Electrons and Cavity Photons, Nature 582, 50 (2020)<br/>-R. Ruimy†, A. Gorlach†, C. Mechel, N. Rivera, and I. Kaminer, Towards atomic-resolution quantum measurements with coherently-shaped free electrons, Phys. Rev. Lett. 126, 233403 (2021)<br/>-O. Reinhardt†, C. Mechel†, M. H. Lynch, and I. Kaminer, Free-Electron Qubits, Annalen der Physik 533, 2000254 (2021)<br/>-Y. Kurman†, R. Dahan†, H. Herzig Shenfux, K. Wang, M. Yannai, Y. Adiv, O. Reinhardt, L. H. G. Tizei, S. Y. Woo, J. Li, J. H. Edgar, M. Kociak, F. H. L. Koppens, and I. Kaminer, Spatiotemporal imaging of 2D polariton wavepacket dynamics using free electrons, Science 372, 1181 (2021)<br/>-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, 6561 (2021)<br/>-A. Karnieli†, S. Tsesses†, R. Yu†, N. Rivera, Z. Zhao, A. Arie, S. Fan, and I. Kaminer, Quantum sensing of strongly coupled light-matter systems using free electrons, Science Advances 9, add2349 (2023)<br/>-R. Dahan†, G. Baranes†, A. Gorlach, R. Ruimy, N. Rivera, and I. Kaminer, Creation of Optical Cat and GKP States Using Shaped Free Electrons, to appear in PRX (2022); arXiv:2206.08828<br/>-T. Bucher et al., Coherently amplified ultrafast imaging in a free-electron interferometer, arXiv:2305.04877