The Synthetic Hilbert Space Of Laser-Driven Free-Electrons

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Guy Braiman, Ori Reinhardt, Chen Mechel, Omer Levi, and Ido Kaminer

Department of Electrical and Computer Engineering and Solid State Institute, Technion – Israel Institute of Technology, 32000 Haifa, Israel

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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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Featured image: Illustration of the synthetic Hilbert space of a laser-driven free electron.

Popular summary

Various platforms for quantum information processing are being studied nowadays. In this work we propose a new platform for continuous-variable quantum information – free electrons. We propose to utilize the energy levels on the quantized ladder of a single laser-driven free electron as a “synthetic Hilbert space” in which we can construct and control qudits (quantum digits).

► BibTeX data

@article{Braiman2023synthetichilbert, doi = {10.22331/q-2023-01-03-888}, url = {https://doi.org/10.22331/q-2023-01-03-888}, title = {The {S}ynthetic {H}ilbert {S}pace of {L}aser-{D}riven {F}ree-{E}lectrons}, author = {Braiman, Guy and Reinhardt, Ori and Mechel, Chen and Levi, Omer and Kaminer, Ido}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {888}, month = jan, year = {2023}<br /> }

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Source: https://quantum-journal.org/papers/q-2023-01-03-888/

Time Stamp: January 3, 2023

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The Synthetic Hilbert Space of Laser-Driven Free-Electrons

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