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arXiv:2210.16312 · Science Advances

Quantum wave function reconstruction by free-electron spectral shearing interferometry

Zhaopin Chen, Bin Zhang, Yiming Pan, Michael B. Kruger

Published Jul 7, 2023• 3 citations
arXivHTMLPDF

Abstract

The quantum wave function measurement of a free electron remains challenging in quantum mechanics and is subject to disputes about ψ-ontic/epistemic interpretations of the wave function. Here, we theoretically propose a realistic spectral method for reconstructing quantum wave function of an electron pulse, free-electron spectral shearing interferometry (FESSI). We use a Wien filter to generate two time-delayed replicas of the electron wave packet and then shift one replica in energy using a light-electron modulator driven by a mid-infrared laser. As a direct demonstration, we numerically reconstruct a pulsed electron wave function with a kinetic energy of 10 keV. FESSI is experimentally feasible and enables us to fully determine distinct orders of spectral phases and their physical implications in quantum foundations and quantum technologies, providing a universal approach to characterize ultrashort electron pulses.

DOI
10.1126/sciadv.adg8516

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The quantum wave function measurement of a free electron remains challenging in quantum mechanics and is subject to disputes about ψ-ontic/epistemic interpretations of the wave function. Here, we theoretically propose a realistic spectral method for reconstructing quantum wave function of an electron pulse, free-electron spectral shearing interferometry (FESSI). We use a Wien filter to generate two time-delayed replicas of the electron wave packet and then shift one replica in energy using a light-electron modulator driven by a mid-infrared laser. As a direct demonstration, we numerically reconstruct a pulsed electron wave function with a kinetic energy of 10 keV. FESSI is experimentally feasible and enables us to fully determine distinct orders of spectral phases and their physical implications in quantum foundations and quantum technologies, providing a universal approach to characterize ultrashort electron pulses.
We present a method for performing quantum state holography, with which we completely characterize the amplitude and phase of an attosecond electron wave packet. Our approach is an extension of a recent publication [J. Mauritsson et al., Phys. Rev. Lett. 105, 053001 (2010)] in which we demonstrated experimentally that the energies and amplitudes of an attosecond electron wave packet can be characterized using attosecond electron interferometry. Here we show theoretically that attosecond electron interferometry can be extended to retrieve the phases of all the states that make up the wave packet. We demonstrate the feasibility of our method by analyzing a wave packet created by a shake-up process. We show that our method can successfully retrieve arbitrary phases and/or lifetimes added to the component eigenstates.
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The ability to characterize the complete quantum state of light is essential for both fundamental and applied science. For single photons the quantum state is provided by the mode that it occupies. The spectral temporal mode structure of light has recently emerged as an essential means for quantum information science. Here we experimentally demonstrate a self-referencing technique to completely determine the pulse-mode structure of single photons by means of spectral shearing interferometry. We detail the calibration and resolution of the measurement and discuss challenges and critical requirements for future advances of this method.
Frequency conversion of nonclassical light enables robust encoding of quantum information based upon spectral multiplexing that is particularly well-suited to integrated-optics platforms. Here we present an intrinsically deterministic linear-optics approach to spectral shearing of quantum light pulses and show it preserves the wave-packet coherence and quantum nature of light. The technique is based upon an electro-optic Doppler shift to implement frequency shear of heralded single-photon wave packets by ±200 GHz, which can be scaled to an arbitrary shift. These results demonstrate a reconfigurable method to controlling the spectral-temporal mode structure of quantum light that could achieve unitary operation.