Speaker
Description
Due to recent experimental developments in integrated photonics, the question of the Photon Induced Near-field Electron Microscopy (PINEM) in the low occupation regime – i.e. when the cavity is populated by a weak number of photons - has drawn an increasing theoretical and experimental interest [1-3]. Indeed, in this situation, the classical model of the electromagnetic field falls short to describe the electron-cavity interaction, and a full quantum description becomes required. Several works have already pioneered this problem and predicted strong quantum mechanical effects in PINEM [1-3].
The goal of our work is to pursue this effort in order to understand which properties of the electromagnetic field are imprinted on the electron wavefunction during the interaction. In the classical regime, the intensity and the phase of the field are encoded in the electron wavefunction [4,5], which can be used to reconstruct the near-field of an optical cavity, and its dynamic [6,7]. However, in quantum optics, other parameters are needed to describe light, such as number-phase uncertainty, field fluctuations, and quantum coherence [1,8]. In this presentation, we will show how these additional parameters influence the final electron wavefunction.
Our approach is based on the use of the Wigner function – roughly speaking, a probability distribution of the quantum state in the phase space (momentum-space) – which is a powerful visualization tool which was introduced for PINEM in [4]. This function gives visually access to information on the final electron state and its interaction with light, such as the energy exchange, density modulation and quantum coherence.
In order to further explain these observations, we will make use of different quantum mechanical pictures, which are unitary transformation the photonic phase space. More precisely, we used the vacuum picture [9] – i.e. a translation of the phase space – in order to split quantum and classical contribution of the field in the interaction, and the squeezed picture – i.e. a hyperbolic rotation of the phase space – to identify the modulation of the electron due to field fluctuation. In other words, these pictures allow us to go from a complex interaction in a simple space, to a simpler interaction in a more complex space.
In the spirit of [10], by combining these technics, we will identify different types of scattering processes, e.g., spontaneous and stimulated decays, quantum and classical electron density modulations. More generally, for a wide range of initial photonic states, we will quantify the contribution of each of these processes to the total scattering, and connect them to different properties of the electromagnetic field (number of photons, mean field, and fluctuation). For instance, using the vacuum picture, we will show that the interaction with a coherent state is a combination of classical density modulation (due to the mean field) and spontaneous decay (due to the fluctuation of the state, identical to the vacuum). In other words, the PINEM in the quantum regime can be seen as combination of classical PINEM and EELS.
References:
[1] V. Di Giulio, M. Kociak, et F. J. G. De Abajo, « Probing quantum optical excitations with fast electrons », Optica, vol. 6, no 12, p. 1524, déc. 2019, doi: 10.1364/OPTICA.6.001524.
[2] O. Kfir, « Entanglements of Electrons and Cavity Photons in the Strong-Coupling Regime », Phys. Rev. Lett., vol. 123, no 10, p. 103602, sept. 2019, doi: 10.1103/PhysRevLett.123.103602.
[3] G. Arend et al., « Electrons herald non-classical light », 17 septembre 2024, arXiv: arXiv:2409.11300. doi: 10.48550/arXiv.2409.11300.
[4] A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, et C. Ropers, « Quantum coherent optical phase modulation in an ultrafast transmission electron microscope », Nature, vol. 521, no 7551, p. 200‑203, mai 2015, doi: 10.1038/nature14463.
[5] F. J. García De Abajo, A. Asenjo-Garcia, et M. Kociak, « Multiphoton Absorption and Emission by Interaction of Swift Electrons with Evanescent Light Fields », Nano Lett., vol. 10, no 5, p. 1859‑1863, mai 2010, doi: 10.1021/nl100613s.
[6] K. E. Echternkamp, A. Feist, S. Schäfer, et C. Ropers, « Ramsey-type phase control of free-electron beams », Nature Phys, vol. 12, no 11, p. 1000‑1004, nov. 2016, doi: 10.1038/nphys3844.
[7] J. H. Gaida et al., « Attosecond electron microscopy by free-electron homodyne detection », Nat. Photon., févr. 2024, doi: 10.1038/s41566-024-01380-8.
[8] V. Di Giulio et F. J. García De Abajo, « Free-electron shaping using quantum light », Optica, vol. 7, no 12, p. 1820, déc. 2020, doi: 10.1364/OPTICA.404598.
[9] S. M. Barnett, « On single-photon and classical interference », Phys. Scr., vol. 97, no 11, p. 114004, nov. 2022, doi: 10.1088/1402-4896/ac971a.
[10] J. Dalibard, J. Dupont-Roc, et C. Cohen-Tannoudji, « Vacuum fluctuations and radiation reaction : identification of their respective contributions », J. Phys. France, vol. 43, no 11, p. 1617‑1638, 1982, doi: 10.1051/jphys:0198200430110161700.