The Synthetic Hilbert Space of Laser-Driven Free-Electrons

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.

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).

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