The Synthetic Hilbert Space of Laser-Driven Free-Electrons

TL;DR

This paper explores the use of laser-driven free electrons as a controllable quantum system, constructing a synthetic Hilbert space for quantum information processing with potential applications in microscopy and spectroscopy.

Contribution

It introduces the concept of a synthetic Hilbert space for free electrons, demonstrating how to encode and manipulate qudits, including full control of a 4-dimensional qudit.

Findings

Full control of a 4-dimensional qudit demonstrated

Protocols for arbitrary dimension qudit control outlined

Potential applications in quantum microscopy and spectroscopy

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.