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arXiv:2304.04936

Digital Holographic Imaging via Direct Quantum Wavefunction Reconstruction

Mengjun Hu, Yong-Sheng ZHang

Published Apr 11, 2023• 0 citations
arXivHTMLPDF

Abstract

Wavefunction is a fundamental concept of quantum theory. Recent studies have shown surprisingly that wavefunction can be directly reconstructed via the measurement of weak value. The weak value based direct wavefunction reconstruction not only gives the operational meaning of wavefunction, but also provides the possibility of realizing holographic imaging with a totally new quantum approach. Here, we review the basic background knowledge of weak value based direct wavefunction reconstruction combined with recent experimental demonstrations. The main purpose of this work focuses on the idea of holographic imaging via direct wavefunction reconstruction. Since research on this topic is still in its early stage, we hope that this work can attract interest in the field of traditional holographic imaging. In addition, the wavefunction holographic imaging may find important applications in quantum information science.

DOI
10.48550/arxiv.2304.04936

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Wavefunction is a fundamental concept of quantum theory. Recent studies have shown surprisingly that wavefunction can be directly reconstructed via the measurement of weak value. The weak value based direct wavefunction reconstruction not only gives the operational meaning of wavefunction, but also provides the possibility of realizing holographic imaging with a totally new quantum approach. Here, we review the basic background knowledge of weak value based direct wavefunction reconstruction combined with recent experimental demonstrations. The main purpose of this work focuses on the idea of holographic imaging via direct wavefunction reconstruction. Since research on this topic is still in its early stage, we hope that this work can attract interest in the field of traditional holographic imaging. In addition, the wavefunction holographic imaging may find important applications in quantum information science.
Wavefunction is a fundamental concept of quantum theory. Recent studies have shown surprisingly that wavefunction can be directly reconstructed via the measurement of weak value. The weak value based direct wavefunction reconstruction not only gives the operational meaning of wavefunction, but also provides the possibility of realizing holographic imaging with a totally new quantum approach. Here, we review the basic background knowledge of weak value based direct wavefunction reconstruction combined with recent experimental demonstrations. The main purpose of this work focuses on the idea of holographic imaging via direct wavefunction reconstruction. Since research on this topic is still in its early stage, we hope that this work can attract interest in the field of traditional holographic imaging. In addition, the wavefunction holographic imaging may find important applications in quantum information science.
The wave function is at the foundation of quantum theory, which is assumed to give a complete description of a quantum system. From early inception, the wave function was introduced as an abstract element of the theory and lacked any way to measure it directly. The situation, however, has somewhat changed with the reporting of the direct measurement of the quantum wave function via weak measurements, giving the wave function a clearly operational definition. The weak measurement method requires sequential measurements of conjugate observables position and momentum with the position measurement sufficiently weak. Surprisingly, recent research showed that performing sequential strong measurements realized the same object, in which case no approximation in weak measurements has to be made. Here, we report on experiments of direct measurements of the two-dimensional transverse wave function of photons via strong measurement, implying that an accurate and clear operational definition may be given to the wave function. We have measured the Gaussian and Laguerre--Gaussian of l=1l=1l=1 spatial wave functions of photons with fidelity of 0.93. As a potential important application, we show that this direct measurement of the wave function provides an alternative way to realize digital holography of three-dimensional objects. This realization of direct measurement of the wave function has significant consequences in quantum information processing and quantum imaging.
Efficient acquiring information from a quantum state is important for research in fundamental quantum physics and quantum information applications. Instead of using standard quantum state tomography method with reconstruction algorithm, weak values were proposed to directly measure density matrix elements of quantum state. Recently, similar to the concept of weak value, modular values were introduced to extend the direct measurement scheme to nonlocal quantum wavefunction. However, this method still involves approximations, which leads to inherent low precision. Here, we propose a new scheme which enables direct measurement for ideal value of the nonlocal density matrix element without taking approximations. Our scheme allows more accurate characterization of nonlocal quantum states, and therefore has greater advantages in practical measurement scenarios.
The wave function is important for understanding and predicting the behavior of photons. Recent studies have shown that wave function can be reconstructed through weak measurement. But currently, the relationships of wave function, weak value, and probe are single and not complete. Here, we propose a wave function reconstruction method based on complex weak values and complex shift probes. Four relationships of them are built and the wave function can be reconstructed by position and momentum shift probes. The complex weak values can be obtained by adjusting the pre- and post-selection in weak measurement, while the complex shift probes originate from the complex nature of the Fresnel coefficient in total internal reflection. To demonstrate the feasibility of the proposed scheme, an experiment of phase distribution reconstruction is achieved by a real weak value and a momentum shift probe; the experimental results agree well with the theory and show a high contrast. Therefore, the wave function can be conveniently reconstructed by our scheme and the relationships between the wave function, weak values, and probes become more complete. This work provides a valuable reference for the application of weak measurement in image processing, quantitative phase imaging, and label-free biological imaging.
The ability to manipulate light has allowed scientists to verify fundamental theories of physics and to develop a new generation of technologies that use photons as a primary resource. Recent developments in quantum measurement theory have offered new alternatives to approach some of the most remarkable problems in quantum physics. Consequently, the principles of quantum mechanics have been exploited in the development of quantum technologies such as optical metrology, quantum communication, and quantum information. In recent years, weak measurements and two of its most remarkable variants: weak value amplification and direct measurement, have been developed and are considered important resources for quantum applications. In this paper, we discuss weak measurements and some significant applications of weak values. We elaborate on how distinct forms of weak values are used to observe and amplify small effects or to directly measure the quantum wave function of photons, a crucial task for schemes for quantum communication and quantum information. We also review some of the most recent methods for weak value amplification and direct measurement that our group has developed.