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arXiv:1907.10281

Free-Electron Qubits

Ori Reinhardt, Chen Mechel, Morgan H. Lynch, Ido E. Kaminer

Published Jul 24, 2019• 0 citations
arXivHTMLPDF

Abstract

Free-electron interactions with laser-driven nanophotonic nearfields can quantize the electrons' energy spectrum and provide control over this quantized degree of freedom. We propose to use such interactions to promote free electrons as carriers of quantum information and find how to create a qubit on a free electron. We find how to implement the qubit's non-commutative spin-algebra, then control and measure the qubit state with a universal set of 1-qubit gates. These gates are within the current capabilities of femtosecond-pulsed laser-driven transmission electron microscopy. Pulsed laser driving promise configurability by the laser intensity, polarizability, pulse duration, and arrival times.

DOI
10.48550/arxiv.1907.10281

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Free-electron interactions with laser-driven nanophotonic nearfields can quantize the electrons' energy spectrum and provide control over this quantized degree of freedom. We propose to use such interactions to promote free electrons as carriers of quantum information and find how to create a qubit on a free electron. We find how to implement the qubit's non-commutative spin-algebra, then control and measure the qubit state with a universal set of 1-qubit gates. These gates are within the current capabilities of femtosecond-pulsed laser-driven transmission electron microscopy. Pulsed laser driving promise configurability by the laser intensity, polarizability, pulse duration, and arrival times.
Abstract Free‐electron interactions with laser‐driven nearfields can quantize the electrons’ energy spectrum and provide control over this quantized degree of freedom. The study proposes to use such interactions to promote free electrons as carriers of quantum information and show how to create a qubit on a free electron, which holds promise for applications in electron microscopy and spectroscopy. A method to implement the qubit's noncommutative spin algebra, and to control and measure the qubit state with a universal set of 1‐qubit gates is shown. These gates are within the current capabilities of ultrafast transmission electron microscopes. Laser‐driven free‐electron qubits promise configurability by the laser intensity, frequency, and polarizability, simultaneously with high‐resolution temporal control on femtosecond timescales.
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.
Free electrons provide a powerful tool for probing material properties at atomic resolution. Recent advances in ultrafast electron microscopy enable the manipulation of free-electron wave functions using laser pulses. It would be of great importance if one could combine the spatial resolution of electron microscopes with the ability of laser pulses to probe coherent phenomena in quantum systems. To this end, we propose a novel concept that leverages free electrons that are coherently shaped by laser pulses to measure quantum coherence in materials. We develop the quantum theory of interactions between shaped electrons and arbitrary qubit states in materials, and show how the postinteraction electron energy spectrum enables measuring the qubit state (on the Bloch sphere) and the decoherence or relaxation times (T_{2}/T_{1}). Finally, we describe how such electrons can detect and quantify superradiance from multiple qubits. Our scheme can be implemented in ultrafast transmission electron microscopes (UTEM), opening the way toward the full characterization of the state of quantum systems at atomic resolution.
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Controlled interaction of laser light with electron beams is fundamental for ultrafast electron microscopy and electron-based quantum optics, yet their direct coupling is forbidden in free space. Here we use longitudinally polarized light at a thin membrane and show that the emerging focal fields can modulate the electron beam in a direct, coherent and linear way, without the need for nanostructured materials or slanted interaction geometries. Also, we use vectorial polarizations to excite and probe three-dimensional nanophotonic near-fields in metallic mesocrystals by coherent electron energy gain and loss. We find that longitudinal electric fields excite axial near-fields in a direct way while longitudinal magnetic fields excite oscillating ring currents via azimuthal electric fields. These possibilities enable tilt-free, collinear generation of attosecond electron pulses or free-electron qubits and provide novel imaging modes in ultrafast electron microscopy and metamaterial tomography.