Visualizing quantum entanglement in Bose-Einstein condensates without state vectors
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917884901457920 |
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| author | Thompson, Russell B. |
| author_facet | Thompson, Russell B. |
| contents | Ring polymer self-consistent field theory is used to calculate the critical temperatures and heat capacities of an ideal Bose gas for an order of magnitude more particles than previously reported. A lambda-transition indicative of Bose-Einstein condensation is observed as expected. Using a known proof of spatial mode entanglement in Bose-Einstein condensates, a relationship between boson exchange and quantum entanglement is established. This is done without the use of state vectors, since ring polymer quantum theory uses instead a thermal degree of freedom, sometimes called the "imaginary time", to map classical statistical mechanics onto non-relativistic quantum mechanics through the theorems of density functional theory. It is shown that quantum phenomena, such as Bose-Einstein condensation, boson exchange, entanglement and contextuality, can be visualized in terms of merging and separating ring polymer threads in thermal-space. A possible extension to fermions is mentioned. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Visualizing quantum entanglement in Bose-Einstein condensates without state vectors Thompson, Russell B. Quantum Physics Quantum Gases Statistical Mechanics Ring polymer self-consistent field theory is used to calculate the critical temperatures and heat capacities of an ideal Bose gas for an order of magnitude more particles than previously reported. A lambda-transition indicative of Bose-Einstein condensation is observed as expected. Using a known proof of spatial mode entanglement in Bose-Einstein condensates, a relationship between boson exchange and quantum entanglement is established. This is done without the use of state vectors, since ring polymer quantum theory uses instead a thermal degree of freedom, sometimes called the "imaginary time", to map classical statistical mechanics onto non-relativistic quantum mechanics through the theorems of density functional theory. It is shown that quantum phenomena, such as Bose-Einstein condensation, boson exchange, entanglement and contextuality, can be visualized in terms of merging and separating ring polymer threads in thermal-space. A possible extension to fermions is mentioned. |
| title | Visualizing quantum entanglement in Bose-Einstein condensates without state vectors |
| topic | Quantum Physics Quantum Gases Statistical Mechanics |
| url | https://arxiv.org/abs/2501.03199 |