Quantum delay in the time of arrival of free-falling atoms
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914648504139776 |
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| author | Beau, Mathieu Martellini, Lionel |
| author_facet | Beau, Mathieu Martellini, Lionel |
| contents | Using standard results from statistics, we show that for Gaussian quantum systems the distribution of a time measurement at a fixed position can be directly inferred from the distribution of a position measurement at a fixed time as given by the Born rule. In an application to a quantum particle of mass $m$ falling in a uniform gravitational field $g$, we use this approach to obtain an exact explicit expression for the probability density of the time-of-arrival (TOA). In the long time-of-flight approximation, we predict that the average positive relative shift with respect to the classical TOA in case of a zero initial mean velocity is asymptotically given by $δ= \frac{q^2}{2} $ when the factor $q\equiv \frac{\hbar}{2mσ\sqrt{2gx}} \ll 1$ (semi-classical regime), and by $δ= \sqrt{\frac{2}π}q $ when $q\gg 1$ (quantum regime), where $σ$ is the width of the initial Gaussian wavepacket and $x$ is the mean distance to the detector. We also discuss experimental conditions under which these predictions can be tested. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02141 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum delay in the time of arrival of free-falling atoms Beau, Mathieu Martellini, Lionel Quantum Physics General Relativity and Quantum Cosmology Atomic Physics Using standard results from statistics, we show that for Gaussian quantum systems the distribution of a time measurement at a fixed position can be directly inferred from the distribution of a position measurement at a fixed time as given by the Born rule. In an application to a quantum particle of mass $m$ falling in a uniform gravitational field $g$, we use this approach to obtain an exact explicit expression for the probability density of the time-of-arrival (TOA). In the long time-of-flight approximation, we predict that the average positive relative shift with respect to the classical TOA in case of a zero initial mean velocity is asymptotically given by $δ= \frac{q^2}{2} $ when the factor $q\equiv \frac{\hbar}{2mσ\sqrt{2gx}} \ll 1$ (semi-classical regime), and by $δ= \sqrt{\frac{2}π}q $ when $q\gg 1$ (quantum regime), where $σ$ is the width of the initial Gaussian wavepacket and $x$ is the mean distance to the detector. We also discuss experimental conditions under which these predictions can be tested. |
| title | Quantum delay in the time of arrival of free-falling atoms |
| topic | Quantum Physics General Relativity and Quantum Cosmology Atomic Physics |
| url | https://arxiv.org/abs/2306.02141 |