Dynamical quantum noise in trapped Bose-Einstein condensates
Open accessAbstract
We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-$P$ and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-$P$ approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial state for the condensate and compare results to those for single-mode models.
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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 [85]
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Gerace, D., & Carusotto, I. (2012) · Physical Review B · doi:10.1103/physrevb.86.144505 · Cited by 88 · see citing works
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
“…predictions for the field correlation functions [58], 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…”
- Authors
- Steel, M. J., Olsen, M. K., Plimak, L. I., Drummond, P. D., Tan, S. M., Collett, M. J., Walls, D. F., & Graham, R.
- Affiliations
- University of Auckland (NZ)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1998-12-01
- Volume
- 58
- Issue
- 6
- Pages
- 4824-4835
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1758308251
- Cited by
- 434
- References
- 1
- Citations by year
- 2026: 5 · 2025: 18 · 2024: 9 · 2023: 28 · 2022: 15 · 2021: 26 · 2020: 9 · 2019: 20 · 2018: 14 · 2017: 15 · 2016: 27 · 2015: 16 · 2014: 14 · 2013: 15 · 2012: 19
- FWCI
- 5.63
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- 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 Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Keywords
- Bose-Einstein condensate, trapped condensates, stochastic partial differential equations, positive-P representation, Wigner function, phase-space representation, numerical stability, weak damping
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