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arXiv:2111.13130

Quantum states interrogation using a pre-shaped free electron wavefunction

Zhang, Bin, Du Ran, Reuven Ianconescu, A. Friedman, Jacob Scheuer, Amnon Yariv, Avraham Gover

Published Nov 25, 2021• 1 citation
arXivHTMLPDF

Abstract

We present a comprehensive theory for interrogation of the quantum state of a two-level system (TLS) based on a free-electron - bound-electron resonant interaction scheme. The scheme is based on free electrons, whose quantum electron wavefunction is pre-shaped or optically modulated by lasers in an electron microscope setup and then inelastically scattered by a quantum TLS target (e.g., atom, quantum dot, crystal defect center, etc.) upon traversing in proximity to the target. Measurement of the post-interaction energy spectrum of the electrons, probes and quantifies the full Bloch sphere parameters of a pre-excited TLS and enables coherent control of the qubit states. The exceptional advantage of this scheme over laser-based ones is the atomic-scale spatial resolution of addressing individual TLS targets. Thus, this scheme opens new horizons for electron microscopy in material interrogation and quantum information technology.

DOI
10.48550/arxiv.2111.13130

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We present a comprehensive theory for interrogation of the quantum state of a two-level system (TLS) based on a free-electron - bound-electron resonant interaction scheme. The scheme is based on free electrons, whose quantum electron wavefunction is pre-shaped or optically modulated by lasers in an electron microscope setup and then inelastically scattered by a quantum TLS target (e.g., atom, quantum dot, crystal defect center, etc.) upon traversing in proximity to the target. Measurement of the post-interaction energy spectrum of the electrons, probes and quantifies the full Bloch sphere parameters of a pre-excited TLS and enables coherent control of the qubit states. The exceptional advantage of this scheme over laser-based ones is the atomic-scale spatial resolution of addressing individual TLS targets. Thus, this scheme opens new horizons for electron microscopy in material interrogation and quantum information technology.
We present a comprehensive theory for interrogation of the quantum state of a two-level system (TLS) based on a free-electron--bound-electron resonant interaction scheme. The scheme is based on free electrons, whose quantum electron wavefunction is preshaped or optically modulated by lasers in an electron microscope setup and then inelastically scattered by a quantum TLS target (e.g., atom, quantum dot, and crystal defect center) upon traversing in proximity to the target. Measurement of the postinteraction energy spectrum of the electrons probes and quantifies the full Bloch sphere parameters of a pre-excited TLS and enables coherent control of the qubit states. The exceptional advantage of this scheme over laser-based ones is atomic-scale spatial resolution of addressing individual TLS targets. Thus, this scheme opens horizons for electron microscopy in material interrogation and quantum information technology.
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.
We present a fully quantum model for the excitation of a bound electron based on the “free-electron bound-electron resonant interaction” (FEBERI) scheme. The bound electron is modeled as a quantum two-level system (TLS) at any initial quantum (qubit) state, and the free electron is presented as a pre-shaped quantum electron wavepacket (QEW). In the case that the QEW is short or modulated at optical frequency, the TLS quantum state may be coherently controlled with multiple modulation-correlated QEWs. For this case, we derive the transition probability of the TLS due to interaction with a multi-particle beam based on an analytical approximate solution of the Schrodinger equation that amounts to using Born’s probabilistic interpretation of the quantum electron wavefunction. We verify the credibility of the analytical model at its validity ranges using a fully quantum density matrix computation procedure. It is shown that the transition probability can grow quadratically with the number of correlated QEWs and exhibit Rabi oscillation. The study indicates a possibility of engineering the quantum state of a TLS by utilizing a beam of shaped QEWs.
We present a comprehensive relativistic quantum-mechanical theory for interaction of a free electron with a bound electron in a model, where the free electron is represented as a finite-size quantum electron wave packet (QEW) and the bound electron is modeled by a quantum two-level system (TLS). The analysis reveals the wave-particle duality nature of the QEW, delineating the point-particle-like and wavelike interaction regimes and manifesting the physical reality of the wave function dimensions when interacting with matter. This QEW size dependence may be used for interrogation and coherent control of superposition states in a TLS and for enhancement of cathodoluminescence and electron energy-loss spectroscopy in electron microscopy.
One of the astounding consequences of quantum mechanics is that it allows the detection of a target using an incident probe, with only a low probability of interaction of the probe and the target. This 'quantum weirdness' could be applied in the field of electron microscopy to generate images of beam-sensitive specimens with substantially reduced damage to the specimen. A reduction of beam-induced damage to specimens is especially of great importance if it can enable imaging of biological specimens with atomic resolution. Following a recent suggestion that interaction-free measurements are possible with electrons, we now analyze the difficulties of actually building an atomic resolution interaction-free electron microscope, or "quantum electron microscope". A quantum electron microscope would require a number of unique components not found in conventional transmission electron microscopes. These components include a coherent electron beam-splitter or two-state-coupler, and a resonator structure to allow each electron to interrogate the specimen multiple times, thus supporting high success probabilities for interaction-free detection of the specimen. Different system designs are presented here, which are based on four different choices of two-state-couplers: a thin crystal, a grating mirror, a standing light wave and an electro-dynamical pseudopotential. Challenges for the detailed electron optical design are identified as future directions for development. While it is concluded that it should be possible to build an atomic resolution quantum electron microscope, we have also identified a number of hurdles to the development of such a microscope and further theoretical investigations that will be required to enable a complete interpretation of the images produced by such a microscope.
The modulation and engineering of the free-electron wave function bring new ingredients to the electron-matter interaction. We consider the dynamics of a free-electron passing by a two-level system fully quantum mechanically and study the enhancement of interaction from the modulation of the free-electron wave function. In the presence of resonant modulation of the free-electron wave function, we show that the electron energy loss and gain spectrum is greatly enhanced for a coherent initial state of the two-level system. Thus, a modulated electron can function as a probe of the atomic coherence. We further find that distantly separated two-level atoms can be entangled through interacting with the same free electron. Effects of modulation-induced enhancement can also be observed using a dilute beam of modulated electrons.