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arXiv:2205.00669 · Optics Letters

Detecting momentum weak value: Shack–Hartmann versus a weak measurement wavefront sensor

Yi Zheng, Mu Yang, Zhenghao Liu, Jin‐Shi Xu, Chuan‐Feng Li, Guang‐Can Guo

Published Oct 1, 2021• 14 citations
arXivHTMLPDF

Abstract

The task of wavefront sensing is to measure the phase of the optical field. Here, we demonstrate that the widely used Shack-Hartmann wavefront sensor detects the weak value of transverse momentum, usually achieved by the method of quantum weak measurement. We extend its input states to partially coherent states and compare it with the weak measurement wavefront sensor, which has a higher spatial resolution but a smaller dynamic range. Since weak values are commonly used in investigating fundamental quantum physics and quantum metrology, our work would find essential applications in these fields.

DOI
10.1364/ol.439174

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The task of wavefront sensing is to measure the phase of the optical field. Here, we demonstrate that the widely used Shack-Hartmann wavefront sensor detects the weak value of transverse momentum, usually achieved by the method of quantum weak measurement. We extend its input states to partially coherent states and compare it with the weak measurement wavefront sensor, which has a higher spatial resolution but a smaller dynamic range. Since weak values are commonly used in investigating fundamental quantum physics and quantum metrology, our work would find essential applications in these fields.
With an extremely high dimensionality, the spatial degree of freedom of entangled photons is a key tool for quantum foundation and applied quantum techniques. To fully utilize the feature, the essential task is to experimentally characterize the multiphoton spatial wave function including the entangled amplitude and phase information at different evolutionary stages. However, there is no effective method to measure it. Quantum state tomography is costly, and quantum holography requires additional references. Here, we introduce quantum Shack-Hartmann wavefront sensing to perform efficient and reference-free measurement of the biphoton spatial wave function. The joint probability distribution of photon pairs at the back focal plane of a microlens array is measured and used for amplitude extraction and phase reconstruction. In the experiment, we observe that the biphoton amplitude correlation becomes weak while phase correlation shows up during free-space propagation. Our work is a crucial step in quantum physical and adaptive optics and paves the way for characterizing quantum optical fields with high-order correlations or topological patterns.
Abstract Direct measurement of wavefunctions has attracted great interest and many different methods have been developed. However, the precision of current techniques is limited by the use of Fourier transform lenses. These measurements require to shear cut the part of particles with momentum , which greatly restricts the efficiency and application of the approaches. Here, a method to directly measure 2D photonic wavefunctions is proposed and experimentally demonstrated by combining the momentum weak measurement technology and the zonal wavefront restoration algorithm. Both the Gaussian and Laguerre–Gaussian wavefunctions are experimentally well reconstructed. This method avoids using the Fourier lens and post selection on the momentum . This is further applied to measure wavefronts with ultra‐high spatial frequency and achieve a pixel resolution, which is difficult for traditional Shack–Hartmann wavefront sensing technologies. This work extends the ability of quantum measurement techniques and will be useful for high‐resolution wavefront sensing.
We introduce an application of the Hartmann sensor, traditionally designed for wavefront sensing, to measure the coherence properties of optical signals. By drawing an analogy between the coherence matrix and the density matrix of a quantum system, we recast the sensor operation as a quantum estimation problem. We experimentally demonstrate its effectiveness in the regime where signals from different apertures significantly overlap, enabling information extraction beyond the reach of standard wavefront sensing.
We show the coherence properties of a signal can be measured by a Hartmann wavefront sensor in a nonclassical regime. Recasting the detection theory of the classical Hartmann sensor in the sense of quantum tomography enables to measure the coherence function, which is an analogy to the density matrix of mixed quantum states. Two methods were tested for the reconstruction of the coherence matrix from the intensity scan in the nonclassical mode of the Hartmann sensor. The reconstruction was performed in a classic way using the POVM matrix and using data pattern tomography.
The wave function is the cornerstone of quantum theory, and various techniques have been proposed for its direct measurement. The reconstruction of the wave function can be achieved by utilizing the real and imaginary components of momentum weak value, which correspond to amplitude and phase differentiation, respectively. However, these methods are limited in their applicability to wave functions with large phase gradients due to the weak coupling condition, which is a fundamental constraint. In this paper, we propose a method for reconstructing wave functions with large phase gradients based on optical differentiation through weak measurement. We have developed a more generalized theory of phase differentiation and implemented a common optical path and fast measurement for wave functions with large phase gradients. The experimental detection of wave functions with varying phase gradients has validated the reliability of our method. This work expands the range of applications for weak measurement while retaining its high resolution and sensitivity advantages, particularly in the field of wavefront sensing.
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.