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On the Interplay of Control Fields and Spontaneous Emission in Laser Cooling
Abstract
Optimal control theory (OCT) is applied to the problem of cooling molecular rotations. The optimal field gives rise to a striking behavior, in which there is no noticeable increase in the lowest rotational state population until the last percent or so of the control interval, at which point the population jumps to 1. Further analysis of the intermediate time interval reveals that cooling is taking place all along, in the sense that the purity of the system, as measured by Tr(ρ 2 ), is increasing monotonically in time. Once the system becomes almost completely pure, the external control field can transfer the amplitude to the lowest rotational state by a completely Hamiltonian manipulation. This mechanism is interesting because it suggests a possible way of accelerating cooling, by exploiting the cooling induced by spontaneous emission to all the ground electronic state levels, not just the lowest rotational level. However, it also raises a major paradox: it may be shown that external control fields, no matter how complicated, cannot change the value of Tr(ρ 2 ); changing this quantity requires spontaneous emission which is inherently uncontrollable. What place is there then for control, let alone optimal control, using external fields? We discuss the resolution to this paradox with a detailed analysis of cooling in a two-level system.
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“Indeed, quantum mechanics in separable Hilbert spaces turns out to be essentially matrix analysis [30, 31].”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [30]
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Metadata
- Authors
- Tannor, D. J., & Bartana, A.
- Affiliations
- Weizmann Institute of Science (IL)
- ORCID
- Tannor, David J.
- Venue
- The Journal of Physical Chemistry A
- Publisher
- American Chemical Society (ACS)
- Published
- 1999-12-01
- Volume
- 103
- Issue
- 49
- Pages
- 10359-10363
- ISSN
- 1089-5639 (ISSN-L)
- 1520-5215
- OpenAlex
- W1965086377
- Cited by
- 83
- References
- 5
- Citations by year
- 2024: 1 · 2023: 1 · 2022: 1 · 2021: 3 · 2020: 3 · 2019: 1 · 2018: 2 · 2017: 3 · 2016: 4 · 2015: 6 · 2014: 2 · 2013: 3 · 2012: 5
- FWCI
- 2.02
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Journal of Physical Chemistry A (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Laser-Matter Interactions and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Keywords
- laser cooling, molecular rotation, optimal control, spontaneous emission, control field, rotational state populations, two-level system, population transfer
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