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arXiv · 2203.02895

The Synthetic Hilbert Space of Laser-Driven Free-Electrons

Guy Braiman·Ori Reinhardt·Chen Mechel·Omer Levi·Ido Kaminer
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Abstract

Recent advances in laser interactions with coherent free electrons have enabled to shape the electron's quantum state. Each electron becomes a superposition of energy levels on an infinite quantized ladder, shown to contain up to thousands of energy levels. We propose to utilize the quantum nature of such laser-driven free electrons as a "synthetic Hilbert space" in which we construct and control qudits (quantum digits). The question that motivates our work is what qudit states can be accessed using electron-laser interactions, and whether it is possible to implement any arbitrary quantum gate. We find how to encode and manipulate free-electron qudit states, focusing on dimensions which are powers of 2, where the qudit represents multiple qubits implemented on the same single electron - algebraically separated, but physically joined. As an example, we prove the possibility to fully control a 4-dimenisonal qudit, and reveal the steps required for full control over any arbitrary dimension. Our work enriches the range of applications of free electrons in microscopy and spectroscopy, offering a new platform for continuous-variable quantum information.

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Guy Braiman, Ori Reinhardt, Chen Mechel, Omer Levi, Ido Kaminer. 2022-11-04. The Synthetic Hilbert Space of Laser-Driven Free-Electrons. https://doi.org/10.22331/q-2023-01-03-888

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