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arXiv:2304.00236 · Physical Review A

Reconstructing the multiphoton spatial wave function with coincidence wave-front sensing

Yi Zheng, Mu Yang, Yu-Wei Liao, Jin‐Shi Xu, Chuan‐Feng Li, Guang‐Can Guo

Published Apr 13, 2023• 5 citations
arXivHTMLPDF

Abstract

The quantum wave function of multiple particles provides additional information which is inaccessible to detectors working alone. Here, we introduce the coincidence wave-front sensing (CWS) method to reconstruct the phase of the multiphoton transverse spatial wave function. The spatially resolved coincidence photon counting is involved. Numerical simulations of two-photon cases using the weak measurement wave-front sensor are performed to test its correctness, and the phase information hidden in the correlation is revealed. Our work provides a direct spatial way to characterize multipartite quantum systems and leads to fundamental studies like experimental Bohmian mechanics and applications in quantum optical technologies.

DOI
10.1103/physreva.107.042608

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The quantum wave function of multiple particles provides additional information which is inaccessible to detectors working alone. Here, we introduce the coincidence wave-front sensing (CWS) method to reconstruct the phase of the multiphoton transverse spatial wave function. The spatially resolved coincidence photon counting is involved. Numerical simulations of two-photon cases using the weak measurement wave-front sensor are performed to test its correctness, and the phase information hidden in the correlation is revealed. Our work provides a direct spatial way to characterize multipartite quantum systems and leads to fundamental studies like experimental Bohmian mechanics and applications in quantum optical technologies.
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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.
The measurement of a wave function plays a pivotal role in quantum physics and presents a distinctive challenge in experiment. Recent works have shown that both the real and imaginary components of the wave function can be extracted by employing weak or strong measurements, thereby enabling the determination of its amplitude and phase. Here, we propose a simple approach for reconstructing the wave function utilizing the spin-orbit interaction of light at the air-glass interface. By directly measuring the amplitude and employing spatial differentiation to capture the phase gradient, it becomes possible to successfully reconstruct an unknown wave function. To demonstrate its feasibility, we experimentally measure the pure wave function of photons with a Gaussian state. Furthermore, we conduct measurements on a custom state featuring a targeted phase jump to examine the accuracy of our methodology. The measured results show a distribution with high contrast and considerable accuracy, with a fidelity that can exceed 85%. We believe that this work contributes valuable insights into the practical applications of spin-orbit interaction, including optical image processing, wave-front sensing, and quantitative phase imaging.
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The wave function is the cornerstone of quantum mechanics, although it is still open to different interpretations. It has been shown that the amplitude and the phase of a wave function are manifested in the imaginary and real parts of the momentum weak value, respectively. Based on this, we develop a weak measurement scheme to reconstruct the wave function through measuring the momentum weak value. A proof-of-principle experiment is made to confirm the feasibility of our measurement scheme, in which the polarization states and the momentum of light are coupled. We believe the experimental protocol has the potential to be applied in diverse fields such as wave-front sensing, edge detection, and optical communication, and measurement of the momentum weak value may offer valuable insight to better understand quantum mechanics.
Summary form only given. The spatial structure of a photon has proved to be indispensable resource allowing the experimental realization of free-space quantum cryptography or high dimensional entanglement. Although efficient methods for manipulating spatial characteristic of individual photons can be easily transferred from the field of classical optics, their spatial structure cannot be measured using the standard interferometric reference-based methods such as optical holography due to their completely undefined-global phase. Hence, the full recovery of a transverse photon wavefunction still remains a challenging task tackled so far exclusively using indirect methods such as the quantum tomography [1] and weak values measurements [2].Here we present and experimentally demonstrate a different approach based on spatially resolved detection of two-photon interference [3,4]. Although such measurements are usually perceived to be insensitive to the relative phase between two interfering photons we show that rarely considered local phase dependence can be still observed and utilized for direct recovery of a single photon quantum wavefunction. In particular we experimentally show that the complex transversal wavefunction of the unknown photon can be fully recovered from the 2D spatial coincidence pattern resulting from its two-photon interference with the reference photon [5].