Quantum arrival times in free fall
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913963266015232 |
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| author | Beau, Mathieu Szczepanski, Timothey Martellini, Rafael Martellini, Lionel |
| author_facet | Beau, Mathieu Szczepanski, Timothey Martellini, Rafael Martellini, Lionel |
| contents | The probability distribution of a time measurement $T_x$ at position $x$ can be inferred from the probability distribution of a position measurement $X_t$ at time $t$ as given by the Born rule [Time-of-arrival distributions for continuous quantum systems and application to quantum backflow, Phys. Rev. A 110, 052217 (2024)]. In an application to free-fall, this finding has been used to predict the existence of a mass-dependent positive relative shift with respect to the classical time-of-arrival in the long time-of-flight regime for dropped quantum particles [M. Beau and L. Martellini, Quantum delay in the time of arrival of free-falling atoms, Phys. Rev. A 109, 012216 (2024).]. The present paper extends these results in two important directions. We first show that for a Gaussian quantum particle of mass $m$ dropped in a uniform gravitational field $g$, the uncertainties about time and position measurements are related by the relation $ ΔT_x ΔX_t \geq \frac{\hbar}{2mg} . $ This novel form of uncertainty relation suggests that choosing the initial state so as to obtain a lower uncertainty in the measured position leads to a higher uncertainty in the measured arrival time. Secondly, we examine the case of a free-falling particle starting from a non-Gaussian initial superposed state, for which we predict the presence of gravitationally induced interferences and oscillations in the mean time-of-arrival as a function of the detector's position that can be interpreted as the signature of a Zitterbewegung-like effect. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_21295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum arrival times in free fall Beau, Mathieu Szczepanski, Timothey Martellini, Rafael Martellini, Lionel Quantum Physics General Relativity and Quantum Cosmology Mathematical Physics The probability distribution of a time measurement $T_x$ at position $x$ can be inferred from the probability distribution of a position measurement $X_t$ at time $t$ as given by the Born rule [Time-of-arrival distributions for continuous quantum systems and application to quantum backflow, Phys. Rev. A 110, 052217 (2024)]. In an application to free-fall, this finding has been used to predict the existence of a mass-dependent positive relative shift with respect to the classical time-of-arrival in the long time-of-flight regime for dropped quantum particles [M. Beau and L. Martellini, Quantum delay in the time of arrival of free-falling atoms, Phys. Rev. A 109, 012216 (2024).]. The present paper extends these results in two important directions. We first show that for a Gaussian quantum particle of mass $m$ dropped in a uniform gravitational field $g$, the uncertainties about time and position measurements are related by the relation $ ΔT_x ΔX_t \geq \frac{\hbar}{2mg} . $ This novel form of uncertainty relation suggests that choosing the initial state so as to obtain a lower uncertainty in the measured position leads to a higher uncertainty in the measured arrival time. Secondly, we examine the case of a free-falling particle starting from a non-Gaussian initial superposed state, for which we predict the presence of gravitationally induced interferences and oscillations in the mean time-of-arrival as a function of the detector's position that can be interpreted as the signature of a Zitterbewegung-like effect. |
| title | Quantum arrival times in free fall |
| topic | Quantum Physics General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2502.21295 |