Post-selected von Neumann measurement with Hermite–Gaussian and Laguerre–Gaussian pointer states
Through the von Neumann interaction followed by post-selection, we can extract not only the eigenvalue of an observable of the measured system but also the weak value. In this post-selected von Neumann measurement, the initial pointer state of the measuring device is assumed to be a fundamental Gaus...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2015-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/17/8/083029 |
| _version_ | 1797751193030623232 |
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| author | Yusuf Turek Hirokazu Kobayashi Tomotada Akutsu Chang-Pu Sun Yutaka Shikano |
| author_facet | Yusuf Turek Hirokazu Kobayashi Tomotada Akutsu Chang-Pu Sun Yutaka Shikano |
| author_sort | Yusuf Turek |
| collection | DOAJ |
| description | Through the von Neumann interaction followed by post-selection, we can extract not only the eigenvalue of an observable of the measured system but also the weak value. In this post-selected von Neumann measurement, the initial pointer state of the measuring device is assumed to be a fundamental Gaussian wave function. By considering the optical implementation of the post-selected von Neumann measurement, higher-order Gaussian modes can be used. In this paper, we consider the Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) modes as pointer states and calculate the average shift of the pointer states of the post-selected von Neumann measurement by assuming the system observable $\hat{A}$ with ${\hat{A}}^{2}=\hat{I}$ and ${\hat{A}}^{2}=\hat{A}$ for an arbitrary interaction strength, where $\hat{I}$ represents the identity operator. Our results show that the HG and LG pointer states for a given coupling direction have advantages and disadvantages over the fundamental Gaussian mode in improving the signal-to-noise ratio. We expect that our general treatment of the weak values will be helpful for understanding the connection between weak- and strong-measurement regimes and may be used to propose new experimental setups with higher-order Gaussian beams to investigate further the applications of weak measurement in optical systems such as the optical vortex. |
| first_indexed | 2024-03-12T16:43:58Z |
| format | Article |
| id | doaj.art-d6553fb3b3444fcf832807a4e7e498b6 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:43:58Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-d6553fb3b3444fcf832807a4e7e498b62023-08-08T14:19:47ZengIOP PublishingNew Journal of Physics1367-26302015-01-0117808302910.1088/1367-2630/17/8/083029Post-selected von Neumann measurement with Hermite–Gaussian and Laguerre–Gaussian pointer statesYusuf Turek0Hirokazu Kobayashi1Tomotada Akutsu2Chang-Pu Sun3Yutaka Shikano4Research Center of Integrative Molecular Systems (CIMoS), Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, Aichi 444-8585, Japan; State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, and University of the Chinese Academy of Sciences , Beijing 100190, People’s Republic of ChinaDepartment of Electronic and Photonic System Engineering, Kochi University of Technology , Tosayamada-cho, Kochi 782–0003, JapanNational Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan; Department of Astronomical Science, The Graduate University for Advanced Studies (SOKENDAI) , Mitaka, Tokyo 181-8588, JapanBeijing Computational Science Research Center, Beijing 100084, People’s Republic of ChinaResearch Center of Integrative Molecular Systems (CIMoS), Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, Aichi 444-8585, Japan; Institute for Quantum Studies, Chapman University , Orange, CA 92866, USA; Materials and Structures Laboratory, Tokyo Institute of Technology , Yokohama 226-8503, JapanThrough the von Neumann interaction followed by post-selection, we can extract not only the eigenvalue of an observable of the measured system but also the weak value. In this post-selected von Neumann measurement, the initial pointer state of the measuring device is assumed to be a fundamental Gaussian wave function. By considering the optical implementation of the post-selected von Neumann measurement, higher-order Gaussian modes can be used. In this paper, we consider the Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) modes as pointer states and calculate the average shift of the pointer states of the post-selected von Neumann measurement by assuming the system observable $\hat{A}$ with ${\hat{A}}^{2}=\hat{I}$ and ${\hat{A}}^{2}=\hat{A}$ for an arbitrary interaction strength, where $\hat{I}$ represents the identity operator. Our results show that the HG and LG pointer states for a given coupling direction have advantages and disadvantages over the fundamental Gaussian mode in improving the signal-to-noise ratio. We expect that our general treatment of the weak values will be helpful for understanding the connection between weak- and strong-measurement regimes and may be used to propose new experimental setups with higher-order Gaussian beams to investigate further the applications of weak measurement in optical systems such as the optical vortex.https://doi.org/10.1088/1367-2630/17/8/083029von Neumann interactionquantum measurementweak measurementhigher-order Gaussian modesignal-to-noise ratioweak-value amplification |
| spellingShingle | Yusuf Turek Hirokazu Kobayashi Tomotada Akutsu Chang-Pu Sun Yutaka Shikano Post-selected von Neumann measurement with Hermite–Gaussian and Laguerre–Gaussian pointer states New Journal of Physics von Neumann interaction quantum measurement weak measurement higher-order Gaussian mode signal-to-noise ratio weak-value amplification |
| title | Post-selected von Neumann measurement with Hermite–Gaussian and Laguerre–Gaussian pointer states |
| title_full | Post-selected von Neumann measurement with Hermite–Gaussian and Laguerre–Gaussian pointer states |
| title_fullStr | Post-selected von Neumann measurement with Hermite–Gaussian and Laguerre–Gaussian pointer states |
| title_full_unstemmed | Post-selected von Neumann measurement with Hermite–Gaussian and Laguerre–Gaussian pointer states |
| title_short | Post-selected von Neumann measurement with Hermite–Gaussian and Laguerre–Gaussian pointer states |
| title_sort | post selected von neumann measurement with hermite gaussian and laguerre gaussian pointer states |
| topic | von Neumann interaction quantum measurement weak measurement higher-order Gaussian mode signal-to-noise ratio weak-value amplification |
| url | https://doi.org/10.1088/1367-2630/17/8/083029 |
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