Time-optimal quantum control of nonlinear two-level systems
Abstract
Nonlinear two-level Landau-Zener type equations for systems with relevance for Bose-Einstein condensates and nonlinear optics are considered and the minimal time ${T}_{\mathrm{min}}$ to drive an initial state to a given target state is investigated. Surprisingly, the nonlinearity may be canceled by a time-optimal unconstrained driving and ${T}_{\mathrm{min}}$ becomes independent of the nonlinearity. For constrained and unconstrained driving explicit expressions are derived for ${T}_{\mathrm{min}}$, the optimal driving, and the protocol.
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Chen et al showed that for nonlinear systems with unconstrained controls, the maximal quantum speed is independent of the strength of the nonlinearity, and nonlinear systems at maximal speed evolve as fast as equivalent linear systems.
“This claim was refuted by Chen et al [267], and they showed explicitly that the maximal quantum speed of nonlinear systems for unconstrained controls is independent of the strength of the non-linearity, and that non-linear systems at maximal speed evolve as fast as equivalent linear systems.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [267]
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- Authors
- Chen, X., Ban, Y., & Hegerfeldt, G. C.
- Affiliations
- Shanghai University (CN)
- University of Göttingen (DE)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2016-08-19
- Volume
- 94
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2507785970
- Cited by
- 28
- References
- 46
- Citations by year
- 2026: 2 · 2025: 2 · 2024: 3 · 2023: 3 · 2022: 3 · 2021: 3 · 2020: 2 · 2019: 1 · 2018: 3 · 2017: 5 · 2016: 1
- FWCI
- 1.58
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- TECNALIA Publications (Fundación TECNALIA Research & Innovation) (submittedVersion, public-domain)
- Funders
- National Natural Science Foundation of China (11474193, 61404079)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- time-optimal control, quantum control, minimal time, Bose-Einstein condensate, nonlinear optics
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