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Accurate Lindblad-Form Master Equation for Weakly Damped Quantum Systems Across All Regimes
- Source :
- npj Quantum Information, Vol 6, Iss 1, Pp 1-14 (2020)
- Publication Year :
- 2019
- Publisher :
- arXiv, 2019.
-
Abstract
- Realistic models of quantum systems must include dissipative interactions with an environment. For weakly-damped systems the Lindblad-form Markovian master equation is invaluable for this task due to its tractability and efficiency. This equation only applies, however, when the frequencies of any subset of the system's transitions are either equal (degenerate), or their differences are much greater than the transitions' linewidths (far-detuned). Outside of these two regimes the only available efficient description has been the Bloch-Redfield (B-R) master equation, the efficacy of which has long been controversial due to its failure to guarantee the positivity of the density matrix. The ability to efficiently simulate weakly-damped systems across all regimes is becoming increasingly important, especially in the area of quantum technologies. Here we solve this long-standing problem. We discover that a condition on the slope of the spectral density is sufficient to derive a Lindblad form master equation that is accurate for all regimes. We further show that this condition is necessary for weakly-damped systems to be described by the B-R equation or indeed any Markovian master equation. We thus obtain a replacement for the B-R equation over its entire domain of applicability that is no less accurate, simpler in structure, completely positive, allows simulation by efficient quantum trajectory methods, and unifies the previous Lindblad master equations. We also show via exact simulations that the new master equation can describe systems in which slowly-varying transition frequencies cross each other during the evolution. System identification tools, developed in systems engineering, play an important role in our analysis. We expect these tools to prove useful in other areas of physics involving complex systems.<br />Comment: Revtex4-1, 16 pages, 7 png figures. v2: contains significant new material
- Subjects :
- Density matrix
Quantum Physics
Computer Networks and Communications
Degenerate energy levels
Complex system
System identification
FOS: Physical sciences
Statistical and Nonlinear Physics
01 natural sciences
lcsh:QC1-999
lcsh:QA75.5-76.95
010305 fluids & plasmas
Quantum technology
Computational Theory and Mathematics
0103 physical sciences
Master equation
Computer Science (miscellaneous)
Dissipative system
lcsh:Electronic computers. Computer science
Statistical physics
010306 general physics
Quantum Physics (quant-ph)
Quantum
lcsh:Physics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- npj Quantum Information, Vol 6, Iss 1, Pp 1-14 (2020)
- Accession number :
- edsair.doi.dedup.....3fcedddae44c33a6092fbe562851e0a3
- Full Text :
- https://doi.org/10.48550/arxiv.1906.08279