When Does A Particle Arrive?

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Simone Roncallo^1,2, Krzysztof Sacha³, and Lorenzo Maccone^1,2

¹Dipartimento di Fisica, Università degli Studi di Pavia, Via Agostino Bassi 6, I-27100, Pavia, Italy
²INFN Sezione di Pavia, Via Agostino Bassi 6, I-27100, Pavia, Italy
³Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, ulica Profesora Stanisława Łojasiewicza 11, PL-30-348 Kraków, Poland

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Abstract

We compare the proposals that have appeared in the literature to describe a measurement of the time of arrival of a quantum particle at a detector. We show that there are multiple regimes where different proposals give inequivalent, experimentally discriminable, predictions. This analysis paves the way for future experimental tests.

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Featured image: A particle prepared in a superposition of two Gaussian wave packets. When the packets overlap near the detector, time of arrival interference is observed.

Popular summary

Measurements of time are problematic in quantum mechanics since, unlike position and momentum, time is not described by an observable. Simple questions like “When does a particle arrive at a detector?” are difficult to treat. In the literature, this is the time of arrival problem. Several solutions have been considered, mostly grouped into three main approaches: Kijowski’s axiomatic construction, the quantum flux and the quantum clock proposals. However, they all lead to different predictions!

We identify realizable regimes for experimentally discriminating these approaches. Our results show that discrepancies appear in strongly quantum regimes, namely when the particle displays quantum interference in the time of arrival: destructive interference at times when it is less likely to detect the particle, constructive interference when detection is more likely to happen.

► BibTeX data

@article{Roncallo2023whendoesparticle, doi = {10.22331/q-2023-03-30-968}, url = {https://doi.org/10.22331/q-2023-03-30-968}, title = {When does a particle arrive?}, author = {Roncallo, Simone and Sacha, Krzysztof and Maccone, Lorenzo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {968}, month = mar, year = {2023}<br /> }

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Cited by

[1] Ranjan Modak and S. Aravinda, “Non-Hermitian description of sharp quantum resetting”, arXiv:2303.03790, (2023).

[2] Tajron Jurić and Hrvoje Nikolić, “Passive quantum measurement: Arrival time, quantum Zeno effect and gambler’s fallacy”, arXiv:2207.09140, (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2023-03-30 12:56:20). The list may be incomplete as not all publishers provide suitable and complete citation data.

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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2023-03-30-968/

Time Stamp: March 30, 2023

Time Stamp: Jul 11, 2023

When does a particle arrive?

Republished By Plato

Abstract

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