Quantum-tunneling rates and stationary solutions in dispersive optical bistability
Abstract
For the model of Drummond and Walls describing dispersive optical bistability, stationary solutions as well as quantum-tunneling rates are calculated by solving a pseudo-Fokker-Planck equation (PFPE), i.e., a Fokker-Planck-like equation with a non-positive-definite diffusion matrix, in terms of matrix continued fractions. Due to the quantum nature of the model, an interesting oscillating variation of the decay rates of the PFPE as a function of the scaling factor for the photon number is found for small cavity damping.
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The approximation of truncating higher-order noise terms underlying Eq. (45) typically loses accuracy when strong interactions and/or very non-perturbative processes in quantum fluctuations are considered, such as quantum tunneling in bistable systems.
“it is important to note that the approximation of truncating higher-order noise terms [85] that underlies (45) typically loses accuracy when strong interactions and/or very non-perturbative processes in the quantum fluctuations are considered, such as quantum tunneling in bistable systems [86,87].”
From How to exploit driving and dissipation to stabilize and manipulate quantum many-body states (2025) · cites this paper as [87]
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How to exploit driving and dissipation to stabilize and manipulate quantum many-body states
Carusotto, I. (2025) · Comptes Rendus. Physique · doi:10.5802/crphys.258 · Cited by 5 · see citing works
“…it is important to note that the approximation of truncating higher-order noise terms [64] that underlies (45) typically loses accuracy when strong interactions and/or very non-perturbative processes in the quantum fluctuations are considered, such as quantum tunneling in bistable systems [65, 66].”
- Authors
- Vogel, K., & Risken, H.
- Affiliations
- Universität Ulm (DE)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1988-09-01
- Volume
- 38
- Issue
- 5
- Pages
- 2409-2422
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2032011486
- Cited by
- 55
- References
- 0
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2021: 4 · 2020: 5 · 2019: 4 · 2017: 2 · 2016: 1 · 2015: 2 · 2014: 3 · 2013: 2 · 2012: 1
- FWCI
- 1.35
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- dispersive optical bistability, stationary solutions, matrix continued fractions, cavity damping, decay rate
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