Toward Atomic-Resolution Quantum Measurements with Coherently Shaped Free Electrons

Abstract

Free electrons provide a powerful tool to probe material properties at atomic-scale spatial resolution. Recent advances in ultrafast electron microscopy enable the manipulation of free electron wavefunctions using laser pulses. It would be of great importance if one could combine the spatial resolution of electron probes with the ability of laser pulses to probe coherent phenomena in quantum systems. To this end, we propose a novel technique that leverages free electrons that are coherently-shaped by laser pulses to measure quantum coherence in materials. Developing a quantum theory of electronqubit interactions in materials, we show how the energy spectrum of laser-shaped electrons enables measuring the qubit Block-sphere state and decoherence time (𝑻 𝟐 ).Finally, we present how such shaped electrons can detect and quantify superradiance from multiple qubits. Our scheme could be implemented in an ultrafast transmission electron microscope (UTEM), opening the way towards the full characterization of the state of quantum systems at atomic-scale resolution.

Optical Excitations with Electron Beams: Challenges and Opportunities

“…The PINEM spectrum responds to the overall coupling strength |β ref + β sample | 2 (see the discussion on the addition property of after eq 11 ), which contains an interference term 2Re{β ref * β sample } that can again amplify a weak PINEM signal from an illuminated sample by mixing it with a strong reference. This effect has also been studied in connection with the interaction between a free electron and a two-level atom, 178 , 181 , 211 where the inelastic electron signal is found to contain a component that scales linearly with the electron-atom coupling coefficient if the electron wave function is modulated and the atom is prepared in a coherent superposition of ground and excited states that is phase-locked with respect to the electron modulation (in contrast to a quadratic dependence on the coupling coefficient if the atom is prepared in the ground state). We remark the necessity of precise timing (i.e., small uncertainty compared with the optical period of the excitation) between the electron modulation and the amplitudes of ground and excited states in the two-level system.…”

Ultrafast non-destructive measurement of the quantum state of light with free electrons

“…We derive an analytical expression for the electron's spectrum, which captures the regimes of high photon flux as well as small photon flux with arbitrary statistics and can be achieved experimentally by increasing the coupling between light and free electrons. Our analytical derivation simplifies the analysis of the PINEM interaction and is further applicable in the fast-developing field of free-electron-boundelectron interaction [70][71][72][73][74] . From a practical point of view, we analyzed the potential capabilities and applications of the FEQOD concept.…”

The Synthetic Hilbert Space of Laser-Driven Free-Electrons

“…In this synthetic Hilbert space, we supply a proof of the ability for full control of a qudit of size 2 or 4 and develop methods toward the full control of qudits of arbitrary dimensions on the same single electron. Our work promotes new capabilities based on transaction of quantum information at the interface between electron microscopy and quantum information, toward free-electron-based quantum communication and quantum electron microscopy [25][26][27][28] . Looking forward, the ability to encode high-dimensional quantum states on a single electron suggests the possibility to implement new schemes of fault-tolerant quantum information on such platforms.…”