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arXiv:1910.11685

Demonstration of weak measurements, projective measurements, and quantum-to-classical transitions in ultrafast free electron-photon interactions

Yiming Pan, Eliahu Cohen, Ebrahim Karimi, Avraham Gover, Norbert Schönenberger, Tomáš Chlouba, Kangpeng Wang, Saar Nehemia, Peter Hommelhoff, Ido E. Kaminer, Yakir Aharonov

Published Oct 24, 2019• 2 citations
arXivHTMLPDF

Abstract

Abstract How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. Here, we develop a new measurement-based framework for characterizing the classical and quantum free electron-photon interactions and then experimentally test it. We first analyze the transition from projective to weak measurement in generic light-matter interactions and show that any classical electron-laser-beam interaction can be represented as an outcome of a weak measurement. In particular, the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement. A universal factor, exp(Γ2 /2) , quantifies the measurement regimes and their transition from quantum to classical, where Γ corresponds to the ratio between the electron wavepacket size and the optical wavelength. This measurement-based formulation is experimentally verified in both limits of photon-induced near-field electron microscopy and the classical acceleration regime using a dielectric laser accelerator. Our results shed new light on the transition from quantum to classical electrodynamics, enabling to employ the essence of wave-particle duality of both light and electrons in quantum measurement for exploring and applying many quantum and classical light-matter interactions.

DOI
10.48550/arxiv.1910.11685

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Abstract How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. Here, we develop a new measurement-based framework for characterizing the classical and quantum free electron-photon interactions and then experimentally test it. We first analyze the transition from projective to weak measurement in generic light-matter interactions and show that any classical electron-laser-beam interaction can be represented as an outcome of a weak measurement. In particular, the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement. A universal factor, exp(Γ2 /2) , quantifies the measurement regimes and their transition from quantum to classical, where Γ corresponds to the ratio between the electron wavepacket size and the optical wavelength. This measurement-based formulation is experimentally verified in both limits of photon-induced near-field electron microscopy and the classical acceleration regime using a dielectric laser accelerator. Our results shed new light on the transition from quantum to classical electrodynamics, enabling to employ the essence of wave-particle duality of both light and electrons in quantum measurement for exploring and applying many quantum and classical light-matter interactions.
How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. Here, we develop a new measurement-based framework for characterizing the classical and quantum free electron-photon interactions and then experimentally test it. We first analyze the transition from projective to weak measurement in generic light-matter interactions and show that any classical electron-laser-beam interaction can be represented as an outcome of weak measurement. In particular, the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement. A universal factor, [Formula: see text], quantifies the measurement regimes and their transition from quantum to classical, where [Formula: see text] corresponds to the ratio between the electron wavepacket size and the optical wavelength. This measurement-based formulation is experimentally verified in both limits of photon-induced near-field electron microscopy and the classical acceleration regime using a DLA. Our results shed new light on the transition from quantum to classical electrodynamics, enabling us to employ the essence of the wave-particle duality of both light and electrons in quantum measurement for exploring and applying many quantum and classical light-matter interactions.
We provide a theoretical framework to describe the dynamics of a free-electron beam interacting with quantized bound systems in arbitrary electromagnetic environments. This expands the quantum optics toolbox to incorporate free-electron beams for applications in highly tunable quantum control, imaging, and spectroscopy at the nanoscale. The framework recovers previously studied results and shows that electromagnetic environments can amplify the intrinsically weak coupling between a free-electron and a bound electron to reach previously inaccessible interaction regimes. We leverage this enhanced coupling for experimentally feasible protocols in coherent qubit control and towards the nondestructive readout and projective control of the electron beam's quantum-number statistics. Our framework is broadly applicable to microwave-frequency qubits, optical nanophotonics, cavity quantum electrodynamics, and emerging platforms at the interface of electron microscopy and quantum information.
How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. We developed a new measurement-based framework for characterizing the classical and quantum free electron-photon interactions. We first analyze the transition from projective measurement to weak measurement in generic light-matter interactions, and show that any classical electron-laser-beam interaction can be represented as an outcome of a weak measurement. In particular, the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement. A universal decay factor exp⁡(−Γ2/2)\exp(-\Gamma^2/2)exp(−Γ2/2), quantifies the measurement regimes and their transition from quantum to classical, where Γ\GammaΓ corresponds to the ratio between the electron wavepacket size and the optical wavelength. This presentation of the measurement transition from projective to weak sheds new light on the transition from quantum-to-classical electrodynamics, enabling to employ the very essence of wave-particle duality in quantum measurement for exploring and applying a variety of quantum and classical types of electron-photon interactions.
Quantum measurement remains puzzling through the mist of their stormy history from the early birth of quantum mechanics to state-of-the-art quantum technologies. Here, we report the observation of measurement transition from weak to strong in a single trapped 40Ca+40Ca^+40Ca+ ion system. By realizing a cat state of the ion's vibrational motion by pre- and post-selecting its internal electronic state, we observed the transition from weak value asymptotics to expectation value asymptotics. More precisely, the weak-to-strong measurement transition is characterized by a universal transition factor exp⁡(−Γ2/2)\exp(-\Gamma^2/2)exp(−Γ2/2), where Γ\GammaΓ is a dimensionless coupling parameter related to the system-apparatus interaction. This transition, which continuously connects Aharonov's weak measurement and von Neumann' strong projective measurement, is capable of opening new experimental possibilities for testing quantum foundations, as well as novel applications for computation in trapped ions and other physical systems.
There are two opposing points of view on the nature of light: the first one manifests the wave-particle duality as a fundamental property of the nature; the second one claims that photons do not exist and the light is a continuous classical wave, while the so-called “quantum” properties of this field appear only as a result of its interaction with matter. In this paper we show that many quantum phenomena which are traditionally described by quantum electrodynamics can be described if light is considered within the limits of classical electrodynamics without quantization of radiation. These phenomena include the double-slit experiment, the photoelectric effect, the Compton effect, the Hanbury Brown and Twiss effect, the so-called multiphoton ionisation of atoms, etc. We show that this point of view allows also explaining the “wave-particle duality” of light in Wiener experiments with standing waves. We show that the Born rule for light can easily be derived from Fermi’s golden rule as an approximation for low-intense light or for short exposure time. We show that the Heisenberg uncertainty principle for “photons” has a simple classical sense and cannot be considered as a fundamental limitation of accuracy of simultaneous measurements of position and momentum or time and energy. We conclude that the concept of a “photon” is superfluous in explanation of light-matter interactions.
Abstract One of the common conceptions of nature, typically derived from the experiences with classical systems, is that attributes of the matter coexist with the substance. In the quantum regime, however, the quantum particle itself and its physical property may be in spatial separation, known as the quantum Cheshire cat effect. While there have been several reports to date on the observation of the quantum Cheshire cat effect, all such experiments are based on first-order interferometry and destructive projection measurement, thus allowing simple interpretation due to measurement-induced disturbance and also subject to trivial interpretation based on classical waves. In this work, we report an experimental observation of the quantum Cheshire cat effect with noninvasive weak quantum measurement as originally proposed. The use of the weak-measurement probe has allowed us to identify the location of the single photon and that of the disembodied polarization state in a quantum interferometer. The weak-measurement probe based on two-photon interference makes our observation unable to be explained by classical physics. We furthermore elucidate the quantum Cheshire cat effect as quantum interference of the transition amplitudes for the photon and the polarization state which are directly obtained from the measurement outcomes or the weak values. Our work not only reveals the true quantum nature of Cheshire cat effect but also sheds light on a comprehensive understanding for the counter-intuitive quantum phenomena.