Experimentally probing anomalous time evolution of a single photon

Ryo Okamoto, Eliahu Cohen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In quantum mechanics, a quantum system is irreversibly collapsed by a projective measurement. Hence, delicately probing the time evolution of a quantum system holds the key to understanding curious phenomena. Here, we experimentally explore an anomalous time evolution, where, illustratively, a particle disappears from a box and emerges in a different box, with a certain moment in which it can be found in neither of them. In this experiment, we directly probe this curious time evolution of a single photon by measuring up to triple-operator sequential weak values (SWVs) using a novel probeless scheme. The naive interpretation provided by single-operator weak values (WVs) seems to imply the “disappearance” and “re-appearance” of a photon as theoretically predicted. However, double- and triple-operator SWVs, representing temporal correlations between the aforementioned values, show that spatial information about the photon does not entirely vanish in the intermediate time. These results show that local values (in space and time) alone, such as single-operator WVs, cannot fully explain all types of quantum evolution in time-higher order correlations are necessary in general, shedding new light on time evolution in quantum mechanics. The probeless measurement technique proposed here for measuring multiple-operator WVs can be straightforwardly extended to study various other cases of curious quantum evolution in time.

Original languageEnglish
Article numberpgad157
JournalPNAS Nexus
Issue number5
StatePublished - 1 May 2023

Bibliographical note

Publisher Copyright:
© The Author(s) 2023. Published by Oxford University Press on behalf of National Academy of Sciences. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.


This work has been supported by the PRESTO program (JPMJPR15P4) of the Japan Science and Technology Agency (JST), and Grants-in-Aid (Nos. 20H01828, 18K18733, and 17H02936) from the Japan Society for the Promotion of Science (JSPS). E.C. was supported by a grant (No. FQXi-RFP-CPW-2006) from the Foundational Questions Institute and the Fetzer Franklin Fund, a donor advised fund of the Silicon Valley Community Foundation, the Israel Innovation Authority under Project Nos. 70002 and 73795, the Quantum Science and Technology Program of the Israeli Council of Higher Education, the Israeli Ministry of Science and Technology, and the Pazy Foundation.

FundersFunder number
Fetzer Franklin Fund
Quantum Science and Technology Program of the Israeli Council of Higher Education
Silicon Valley Community Foundation
Foundational Questions Institute
Japan Society for the Promotion of ScienceFQXi-RFP-CPW-2006
Japan Science and Technology Agency17H02936, 18K18733, 20H01828
Ministry of science and technology, Israel
PAZY Foundation
Israel Innovation Authority70002, 73795


    • heralded single photon
    • quantum dynamics
    • quantum optics
    • sequential weak value


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